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index 226a59d43..0cfcdcc58 100644
--- "a/2023/07/22/DP\346\200\273\347\273\223/index.html"
+++ "b/2023/07/22/DP\346\200\273\347\273\223/index.html"
@@ -2,6 +2,7 @@
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+    <link rel="stylesheet" href="https://lib.baomitu.com/KaTeX/latest/katex.min.css">
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@@ -222,7 +223,7 @@
         
         
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@@ -248,74 +249,110 @@
                 <div class="post-content keep-markdown-body">
                     
 
-                    <h1 id="DP总结"><a href="#DP总结" class="headerlink" title="DP总结"></a>DP总结</h1><h3 id="线性DP"><a href="#线性DP" class="headerlink" title="$线性DP$"></a>$线性DP$</h3><ul>
-<li><h4 id="定义"><a href="#定义" class="headerlink" title="定义:"></a>定义:</h4><blockquote>
-<p>具有线性”阶段”划分的$DP$被称为线性$DP$。</p>
+                    <h1 id="dp总结"><a class="markdownIt-Anchor" href="#dp总结"></a> DP总结</h1>
+<h3 id="线性dp"><a class="markdownIt-Anchor" href="#线性dp"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>线性</mtext><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">线性DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">线</span><span class="mord cjk_fallback">性</span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span></h3>
+<ul>
+<li>
+<h4 id="定义"><a class="markdownIt-Anchor" href="#定义"></a> 定义:</h4>
+<blockquote>
+<p>具有线性&quot;阶段&quot;划分的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span>被称为线性<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span>。</p>
 </blockquote>
 </li>
-<li><h4 id="经典模型"><a href="#经典模型" class="headerlink" title="经典模型"></a>经典模型</h4><blockquote>
-<p>$LIS$ , $LCS$ , $LCIS$(最长公共上升子序列) , $最长公共子序列$ , $数字三角形$。</p>
+<li>
+<h4 id="经典模型"><a class="markdownIt-Anchor" href="#经典模型"></a> 经典模型</h4>
+<blockquote>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>I</mi><mi>S</mi></mrow><annotation encoding="application/x-tex">LIS</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span></span></span></span> , <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>C</mi><mi>S</mi></mrow><annotation encoding="application/x-tex">LCS</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span></span></span></span> , <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>C</mi><mi>I</mi><mi>S</mi></mrow><annotation encoding="application/x-tex">LCIS</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span></span></span></span>(最长公共上升子序列) , <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>最长公共子序列</mtext></mrow><annotation encoding="application/x-tex">最长公共子序列</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">最</span><span class="mord cjk_fallback">长</span><span class="mord cjk_fallback">公</span><span class="mord cjk_fallback">共</span><span class="mord cjk_fallback">子</span><span class="mord cjk_fallback">序</span><span class="mord cjk_fallback">列</span></span></span></span> , <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>数字三角形</mtext></mrow><annotation encoding="application/x-tex">数字三角形</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">数</span><span class="mord cjk_fallback">字</span><span class="mord cjk_fallback">三</span><span class="mord cjk_fallback">角</span><span class="mord cjk_fallback">形</span></span></span></span>。</p>
 </blockquote>
 </li>
-<li><h4 id="例题："><a href="#例题：" class="headerlink" title="例题："></a>例题：</h4><ol>
-<li><h4 id="LCS"><a href="#LCS" class="headerlink" title="LCS"></a><a class="link"   target="_blank" rel="noopener" href="https://www.luogu.com.cn/problem/AT_dp_f" >LCS<i class="fas fa-external-link-alt"></i></a></h4><h5 id="题意："><a href="#题意：" class="headerlink" title="题意："></a>题意：</h5><blockquote>
-<p>求两个字符串中<strong>字典序最小的</strong>$LCS$。</p>
+<li>
+<h4 id="例题"><a class="markdownIt-Anchor" href="#例题"></a> 例题：</h4>
+<ol>
+<li>
+<h4 id="lcs"><a class="markdownIt-Anchor" href="#lcs"></a> <a class="link"   target="_blank" rel="noopener" href="https://www.luogu.com.cn/problem/AT_dp_f" >LCS<i class="fas fa-external-link-alt"></i></a></h4>
+<h5 id="题意"><a class="markdownIt-Anchor" href="#题意"></a> 题意：</h5>
+<blockquote>
+<p>求两个字符串中<strong>字典序最小的</strong><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>C</mi><mi>S</mi></mrow><annotation encoding="application/x-tex">LCS</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span></span></span></span>。</p>
 </blockquote>
-<h5 id="方法"><a href="#方法" class="headerlink" title="方法:"></a>方法:</h5><blockquote>
-<p>用 $vector$ 记录下每一个状态下的答案。</p>
+<h5 id="方法"><a class="markdownIt-Anchor" href="#方法"></a> 方法:</h5>
+<blockquote>
+<p>用 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</mi></mrow><annotation encoding="application/x-tex">vector</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.61508em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mord mathnormal">e</span><span class="mord mathnormal">c</span><span class="mord mathnormal">t</span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span></span></span></span> 记录下每一个状态下的答案。</p>
 </blockquote>
 </li>
-<li><h4 id="最长上升子序列-LIS"><a href="#最长上升子序列-LIS" class="headerlink" title="最长上升子序列(LIS)"></a><a class="link"   target="_blank" rel="noopener" href="https://www.luogu.com.cn/problem/AT_chokudai_S001_h" >最长上升子序列(LIS)<i class="fas fa-external-link-alt"></i></a></h4><h5 id="题意：-1"><a href="#题意：-1" class="headerlink" title="题意："></a>题意：</h5><blockquote>
+<li>
+<h4 id="最长上升子序列lis"><a class="markdownIt-Anchor" href="#最长上升子序列lis"></a> <a class="link"   target="_blank" rel="noopener" href="https://www.luogu.com.cn/problem/AT_chokudai_S001_h" >最长上升子序列(LIS)<i class="fas fa-external-link-alt"></i></a></h4>
+<h5 id="题意-2"><a class="markdownIt-Anchor" href="#题意-2"></a> 题意：</h5>
+<blockquote>
 <ul>
-<li>给定一个长为 <em>n</em> 的序列 $a_i$，求这个序列的最长单调上升子序列长度。</li>
-<li>要求 $O(n log_n)$ 。</li>
+<li>给定一个长为 <em>n</em> 的序列 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>a</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">a_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>，求这个序列的最长单调上升子序列长度。</li>
+<li>要求 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mi>n</mi><mi>l</mi><mi>o</mi><msub><mi>g</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(n log_n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">o</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span> 。</li>
 </ul>
 </blockquote>
-<h5 id="方法："><a href="#方法：" class="headerlink" title="方法："></a>方法：</h5><blockquote>
+<h5 id="方法-2"><a class="markdownIt-Anchor" href="#方法-2"></a> 方法：</h5>
+<blockquote>
 <p>在长度一定的情况下，若结尾元素更小，那么最终答案也就更优。</p>
-<p>所以我们维护一个数组表示当前的$LIS$，每一次插入当前元素。</p>
+<p>所以我们维护一个数组表示当前的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>I</mi><mi>S</mi></mrow><annotation encoding="application/x-tex">LIS</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span></span></span></span>，每一次插入当前元素。</p>
 </blockquote>
-<h5 id="code"><a href="#code" class="headerlink" title="code :"></a>code :</h5><figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string">&lt;bits/stdc++.h&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">define</span> int long long</span></span><br><span class="line"><span class="meta">#<span class="keyword">define</span> rep(i,a,b) for(int i=(a);i&lt;=(b);++i)</span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N=<span class="number">1e6</span> +<span class="number">3</span>;</span><br><span class="line"><span class="type">int</span> n,m,a[N],f[N];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">signed</span> <span class="title">main</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">	cin&gt;&gt;n; <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n;i++) cin&gt;&gt;a[i];</span><br><span class="line">	<span class="built_in">memset</span>(f,<span class="number">0x3f</span>,<span class="keyword">sizeof</span> f);</span><br><span class="line">	<span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n;i++) *<span class="built_in">upper_bound</span>(f+<span class="number">1</span>,f+n+<span class="number">1</span>,a[i])=a[i];</span><br><span class="line">	<span class="type">int</span> res=<span class="number">1</span>; <span class="keyword">while</span>(f[res]!=f[<span class="number">0</span>]) res++;</span><br><span class="line">	cout&lt;&lt;res<span class="number">-1</span>&lt;&lt;endl;</span><br><span class="line">	<span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure></li>
+<h5 id="code"><a class="markdownIt-Anchor" href="#code"></a> code :</h5>
+<figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string">&lt;bits/stdc++.h&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">define</span> int long long</span></span><br><span class="line"><span class="meta">#<span class="keyword">define</span> rep(i,a,b) for(int i=(a);i&lt;=(b);++i)</span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N=<span class="number">1e6</span> +<span class="number">3</span>;</span><br><span class="line"><span class="type">int</span> n,m,a[N],f[N];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">signed</span> <span class="title">main</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">	cin&gt;&gt;n; <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n;i++) cin&gt;&gt;a[i];</span><br><span class="line">	<span class="built_in">memset</span>(f,<span class="number">0x3f</span>,<span class="keyword">sizeof</span> f);</span><br><span class="line">	<span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n;i++) *<span class="built_in">upper_bound</span>(f+<span class="number">1</span>,f+n+<span class="number">1</span>,a[i])=a[i];</span><br><span class="line">	<span class="type">int</span> res=<span class="number">1</span>; <span class="keyword">while</span>(f[res]!=f[<span class="number">0</span>]) res++;</span><br><span class="line">	cout&lt;&lt;res<span class="number">-1</span>&lt;&lt;endl;</span><br><span class="line">	<span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
+</li>
 </ol>
 </li>
 </ul>
-<h3 id="二维平面上的-DP-与-状态压缩-DP"><a href="#二维平面上的-DP-与-状态压缩-DP" class="headerlink" title="二维平面上的$DP$ 与 状态压缩$DP$"></a>二维平面上的$DP$ 与 状态压缩$DP$</h3><ul>
-<li><h5 id="怎样判断？"><a href="#怎样判断？" class="headerlink" title="怎样判断？"></a>怎样判断？</h5><blockquote>
+<h3 id="二维平面上的dp-与-状态压缩dp"><a class="markdownIt-Anchor" href="#二维平面上的dp-与-状态压缩dp"></a> 二维平面上的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span> 与 状态压缩<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span></h3>
+<ul>
+<li>
+<h5 id="怎样判断"><a class="markdownIt-Anchor" href="#怎样判断"></a> 怎样判断？</h5>
+<blockquote>
 <p>二维平面看题面。</p>
-<p>状态压缩的$n\le 22$。</p>
+<p>状态压缩的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>≤</mo><mn>22</mn></mrow><annotation encoding="application/x-tex">n\le 22</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719400000000001em;vertical-align:-0.13597em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">2</span><span class="mord">2</span></span></span></span>。</p>
 </blockquote>
 </li>
-<li><h4 id="例题：-1"><a href="#例题：-1" class="headerlink" title="例题："></a>例题：</h4><ol>
-<li><h4 id="Grid-2"><a href="#Grid-2" class="headerlink" title="Grid 2"></a><a class="link"   target="_blank" rel="noopener" href="https://www.luogu.com.cn/problem/AT_dp_y" >Grid 2<i class="fas fa-external-link-alt"></i></a></h4><h5 id="题目："><a href="#题目：" class="headerlink" title="题目："></a>题目：</h5><blockquote>
-<p>给一个 <em>H</em>×<em>W</em> 的网格，每一步只能向右或向下走，给出 $n$ 个坐标，这些坐标对应的位置不能经过，求从左上角 (<em>1</em>,<em>1</em>)走到右下角 (<em>H</em>,<em>W</em>) 的方案数，答案对 $10^9+7$ 取模。</p>
+<li>
+<h4 id="例题-2"><a class="markdownIt-Anchor" href="#例题-2"></a> 例题：</h4>
+<ol>
+<li>
+<h4 id="grid-2"><a class="markdownIt-Anchor" href="#grid-2"></a> <a class="link"   target="_blank" rel="noopener" href="https://www.luogu.com.cn/problem/AT_dp_y" >Grid 2<i class="fas fa-external-link-alt"></i></a></h4>
+<h5 id="题目"><a class="markdownIt-Anchor" href="#题目"></a> 题目：</h5>
+<blockquote>
+<p>给一个 <em>H</em>×<em>W</em> 的网格，每一步只能向右或向下走，给出 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span> 个坐标，这些坐标对应的位置不能经过，求从左上角 (<em>1</em>,<em>1</em>)走到右下角 (<em>H</em>,<em>W</em>) 的方案数，答案对 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><msup><mn>0</mn><mn>9</mn></msup><mo>+</mo><mn>7</mn></mrow><annotation encoding="application/x-tex">10^9+7</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.897438em;vertical-align:-0.08333em;"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">9</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">7</span></span></span></span> 取模。</p>
 </blockquote>
-<h5 id="思路："><a href="#思路：" class="headerlink" title="思路："></a>思路：</h5><blockquote>
-<p>首先对于 $f_{i,j}\ (1\le i\le H,1\le j\le W)$ 可行性显然，但空间不够。我们只能对着 $n$ 个坐标开数组。</p>
-<p>我们设方程 $f_i$  表示从 (<em>1,1</em>) 做到第<em>i</em>个坐标，且只经过第$i$个坐标的方案总数。</p>
+<h5 id="思路"><a class="markdownIt-Anchor" href="#思路"></a> 思路：</h5>
+<blockquote>
+<p>首先对于 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi></mrow></msub><mtext> </mtext><mo stretchy="false">(</mo><mn>1</mn><mo>≤</mo><mi>i</mi><mo>≤</mo><mi>H</mi><mo separator="true">,</mo><mn>1</mn><mo>≤</mo><mi>j</mi><mo>≤</mo><mi>W</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">f_{i,j}\ (1\le i\le H,1\le j\le W)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.036108em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace"> </span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.79549em;vertical-align:-0.13597em;"></span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mclose">)</span></span></span></span> 可行性显然，但空间不够。我们只能对着 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span> 个坐标开数组。</p>
+<p>我们设方程 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">f_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>  表示从 (<em>1,1</em>) 做到第<em>i</em>个坐标，且只经过第<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">i</span></span></span></span>个坐标的方案总数。</p>
 <p>那么，我们尝试使用容斥原理进行转移</p>
 <ul>
-<li>从 (<em>1,1</em>) 到 ($x_i,y_i$) 的方案数是 ${C_{x_i-1+y_i-1}^{x_i -1}}$ </li>
+<li>从 (<em>1,1</em>) 到 (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>i</mi></msub><mo separator="true">,</mo><msub><mi>y</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">x_i,y_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>) 的方案数是 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>C</mi><mrow><msub><mi>x</mi><mi>i</mi></msub><mo>−</mo><mn>1</mn><mo>+</mo><msub><mi>y</mi><mi>i</mi></msub><mo>−</mo><mn>1</mn></mrow><mrow><msub><mi>x</mi><mi>i</mi></msub><mo>−</mo><mn>1</mn></mrow></msubsup></mrow><annotation encoding="application/x-tex">{C_{x_i-1+y_i-1}^{x_i -1}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2984239999999998em;vertical-align:-0.402416em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8960079999999999em;"><span style="top:-2.433692em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mbin mtight">−</span><span class="mord mtight">1</span><span class="mbin mtight">+</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:-0.03588em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.1449000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.402416em;"><span></span></span></span></span></span></span></span></span></span></span></li>
 <li>从某一个坐标转移过来的方案数是 $\sum C_{x_i-x_j+y_i-y_j}^{x_i -x_j} $</li>
 </ul>
 </blockquote>
 </li>
-<li><h4 id="Matching"><a href="#Matching" class="headerlink" title="Matching"></a><a class="link"   target="_blank" rel="noopener" href="https://vjudge.csgrandeur.cn/contest/569557#problem/O" >Matching<i class="fas fa-external-link-alt"></i></a></h4><h5 id="题目：-1"><a href="#题目：-1" class="headerlink" title="题目："></a>题目：</h5><blockquote>
-<p>给定 <em>N</em>，表示有 N 个男生和 N 个女生，再给你一个矩阵 a，如果$a_{i,j}$ 等于 1，表示 <em>i</em> 这个男生和 <em>j</em> 这个女生可以匹配成一对，否则不能。 问要匹配 N 对的方案数。答案对 $10^9+7$ 取模。</p>
+<li>
+<h4 id="matching"><a class="markdownIt-Anchor" href="#matching"></a> <a class="link"   target="_blank" rel="noopener" href="https://vjudge.csgrandeur.cn/contest/569557#problem/O" >Matching<i class="fas fa-external-link-alt"></i></a></h4>
+<h5 id="题目-2"><a class="markdownIt-Anchor" href="#题目-2"></a> 题目：</h5>
+<blockquote>
+<p>给定 <em>N</em>，表示有 N 个男生和 N 个女生，再给你一个矩阵 a，如果<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>a</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi></mrow></msub></mrow><annotation encoding="application/x-tex">a_{i,j}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span> 等于 1，表示 <em>i</em> 这个男生和 <em>j</em> 这个女生可以匹配成一对，否则不能。 问要匹配 N 对的方案数。答案对 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><msup><mn>0</mn><mn>9</mn></msup><mo>+</mo><mn>7</mn></mrow><annotation encoding="application/x-tex">10^9+7</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.897438em;vertical-align:-0.08333em;"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">9</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">7</span></span></span></span> 取模。</p>
 </blockquote>
-<h5 id="思路：-1"><a href="#思路：-1" class="headerlink" title="思路："></a>思路：</h5><blockquote>
+<h5 id="思路-2"><a class="markdownIt-Anchor" href="#思路-2"></a> 思路：</h5>
+<blockquote>
 <p>状压男生，枚举女生</p>
 </blockquote>
 </li>
 </ol>
 </li>
 </ul>
-<h3 id="区间-DP"><a href="#区间-DP" class="headerlink" title="区间$DP$"></a>区间$DP$</h3><p>​	<strong>都离不开三重循环: $\sum\limits_{长度} \sum\limits_{左端点} \sum\limits_{转移的断点} f…$</strong></p>
+<h3 id="区间dp"><a class="markdownIt-Anchor" href="#区间dp"></a> 区间<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span></h3>
+<p>​	<strong>都离不开三重循环: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><munder><mo>∑</mo><mtext>长度</mtext></munder><munder><mo>∑</mo><mtext>左端点</mtext></munder><munder><mo>∑</mo><mtext>转移的断点</mtext></munder><mi>f</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">\sum\limits_{长度} \sum\limits_{左端点} \sum\limits_{转移的断点} f...</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.744341em;vertical-align:-0.994336em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.750005em;"><span style="top:-2.105664em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord cjk_fallback mtight">长</span><span class="mord cjk_fallback mtight">度</span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.994336em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.750005em;"><span style="top:-2.105664em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord cjk_fallback mtight">左</span><span class="mord cjk_fallback mtight">端</span><span class="mord cjk_fallback mtight">点</span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.994336em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.750005em;"><span style="top:-2.105664em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord cjk_fallback mtight">转</span><span class="mord cjk_fallback mtight">移</span><span class="mord cjk_fallback mtight">的</span><span class="mord cjk_fallback mtight">断</span><span class="mord cjk_fallback mtight">点</span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.994336em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span></span></span></span></strong></p>
 <ol>
-<li><h4 id="石子合并"><a href="#石子合并" class="headerlink" title="石子合并"></a><a href="luogu.com.cn/problem/P1880">石子合并</a></h4><h5 id="题目：-2"><a href="#题目：-2" class="headerlink" title="题目："></a>题目：</h5><blockquote>
+<li>
+<h4 id="石子合并"><a class="markdownIt-Anchor" href="#石子合并"></a> <a href="luogu.com.cn/problem/P1880">石子合并</a></h4>
+<h5 id="题目-3"><a class="markdownIt-Anchor" href="#题目-3"></a> 题目：</h5>
+<blockquote>
 <p>在一个圆形操场的四周摆放 <em>N</em> 堆石子，现要将石子有次序地合并成一堆，规定每次只能选相邻的 2 堆合并成新的一堆，并将新的一堆的石子数，记为该次合并的得分。</p>
 <p>试设计出一个算法,计算出将 N* 堆石子合并成 1 堆的最小得分和最大得分。</p>
 </blockquote>
-<h5 id="思路：-2"><a href="#思路：-2" class="headerlink" title="思路："></a>思路：</h5><blockquote>
+<h5 id="思路-3"><a class="markdownIt-Anchor" href="#思路-3"></a> 思路：</h5>
+<blockquote>
 <p>令<code>dp[i][j]</code>表示区间<code>[i,j]</code>的最小价值。</p>
 <p>不妨从终点考虑问题，即结果为两个子区间合并的最小值再加上合并需要的代价即可。</p>
 <p>枚举两个子区间，即枚举这个区间的中间点k，使这个区间被分为<code>[i,k]</code>和<code>[k+1,j]</code>两个区间，取一遍最小值加上合并的即为当前区间所求。</p>
@@ -323,34 +360,44 @@ <h5 id="思路：-2"><a href="#思路：-2" class="headerlink" title="思路："
 <p>所以<code>dp[i][j]=min(dp[i][j],dp[i][k]+dp[k+1][j]+sum[j]-sum[i-1])</code></p>
 </blockquote>
 </li>
-<li><h4 id="Deque"><a href="#Deque" class="headerlink" title="Deque"></a><a class="link"   target="_blank" rel="noopener" href="https://vjudge.csgrandeur.cn/contest/569557#problem/L" >Deque<i class="fas fa-external-link-alt"></i></a></h4><h5 id="题目：-3"><a href="#题目：-3" class="headerlink" title="题目："></a>题目：</h5><blockquote>
-<p>给定 N 个数的序列 $A$。</p>
+<li>
+<h4 id="deque"><a class="markdownIt-Anchor" href="#deque"></a> <a class="link"   target="_blank" rel="noopener" href="https://vjudge.csgrandeur.cn/contest/569557#problem/L" >Deque<i class="fas fa-external-link-alt"></i></a></h4>
+<h5 id="题目-4"><a class="markdownIt-Anchor" href="#题目-4"></a> 题目：</h5>
+<blockquote>
+<p>给定 N 个数的序列 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">A</span></span></span></span>。</p>
 <p>A 和 B 轮流取数，每个人每次可以从序列<strong>头部</strong>或者<strong>尾部</strong>取走一个数（直到序列为空）。</p>
 <p>A 和 B 都希望自己取得的数的总和尽可能大。</p>
 <p>假设最优策略下，A 取得的数的总和是 X，B 取得的数的总和是 Y， 请输出 X-Y。</p>
 </blockquote>
-<h5 id="思路：-3"><a href="#思路：-3" class="headerlink" title="思路："></a>思路：</h5><blockquote>
-<p>显然游戏过程中剩下的数必然是连续的一段。设 $f_{i,j}$ 表示剩下下标为 $[i,j]$ 的数时，先手（并非当前的先手而是开始时的先手，下同）能取得的最大分数差。</p>
+<h5 id="思路-4"><a class="markdownIt-Anchor" href="#思路-4"></a> 思路：</h5>
+<blockquote>
+<p>显然游戏过程中剩下的数必然是连续的一段。设 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi></mrow></msub></mrow><annotation encoding="application/x-tex">f_{i,j}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span> 表示剩下下标为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mi>i</mi><mo separator="true">,</mo><mi>j</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[i,j]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">[</span><span class="mord mathnormal">i</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span><span class="mclose">]</span></span></span></span> 的数时，先手（并非当前的先手而是开始时的先手，下同）能取得的最大分数差。</p>
 <p>分两种情况讨论：</p>
 <ul>
-<li>已经取走的数为偶数个，此时先手取，$f_{i,j}$&#x3D;$max⁡$ ($f_{i+1,j}+a_i$,$f_{i,j-1}$,$f_{i,j-1}+a_j$)</li>
-<li>已经取走的数为奇数个，此时后手取，$f_{i,j}$&#x3D;$max$⁡ ($f_{i+1,j}-a_i$,$f_{i,j-1}$,$f_{i,j-1}-a_j$)</li>
+<li>已经取走的数为偶数个，此时先手取，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi></mrow></msub></mrow><annotation encoding="application/x-tex">f_{i,j}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span>=<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi><mi>a</mi><mi>x</mi><mtext>⁡</mtext></mrow><annotation encoding="application/x-tex">max⁡</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">a</span><span class="mord mathnormal">x</span><span class="mord">⁡</span></span></span></span> (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo>+</mo><mn>1</mn><mo separator="true">,</mo><mi>j</mi></mrow></msub><mo>+</mo><msub><mi>a</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">f_{i+1,j}+a_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>,<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">f_{i,j-1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span>,<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>a</mi><mi>j</mi></msub></mrow><annotation encoding="application/x-tex">f_{i,j-1}+a_j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span>)</li>
+<li>已经取走的数为奇数个，此时后手取，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi></mrow></msub></mrow><annotation encoding="application/x-tex">f_{i,j}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span>=<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">max</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">a</span><span class="mord mathnormal">x</span></span></span></span>⁡ (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo>+</mo><mn>1</mn><mo separator="true">,</mo><mi>j</mi></mrow></msub><mo>−</mo><msub><mi>a</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">f_{i+1,j}-a_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>,<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">f_{i,j-1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span>,<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>−</mo><msub><mi>a</mi><mi>j</mi></msub></mrow><annotation encoding="application/x-tex">f_{i,j-1}-a_j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span>)</li>
 </ul>
 </blockquote>
 </li>
 </ol>
-<h3 id="换根-DP"><a href="#换根-DP" class="headerlink" title="换根$DP$"></a>换根$DP$</h3><p>​	<strong>本质上只是把序列变成了树</strong></p>
+<h3 id="换根dp"><a class="markdownIt-Anchor" href="#换根dp"></a> 换根<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span></h3>
+<p>​	<strong>本质上只是把序列变成了树</strong></p>
 <ol>
-<li><h4 id="Subtree"><a href="#Subtree" class="headerlink" title="Subtree"></a><a class="link"   target="_blank" rel="noopener" href="https://vjudge.csgrandeur.cn/contest/569557#problem/V" >Subtree<i class="fas fa-external-link-alt"></i></a></h4><h5 id="题目：-4"><a href="#题目：-4" class="headerlink" title="题目："></a>题目：</h5><blockquote>
-<p>有一个 <em>n</em> 个节点的树，对一些节点染色，使得所有被染色的节点是一个连通块。求对于 $1,2,3,…,n$每个节点，该节点被染色的方案个数。所有答案对 <em>M</em> 取模。</p>
+<li>
+<h4 id="subtree"><a class="markdownIt-Anchor" href="#subtree"></a> <a class="link"   target="_blank" rel="noopener" href="https://vjudge.csgrandeur.cn/contest/569557#problem/V" >Subtree<i class="fas fa-external-link-alt"></i></a></h4>
+<h5 id="题目-5"><a class="markdownIt-Anchor" href="#题目-5"></a> 题目：</h5>
+<blockquote>
+<p>有一个 <em>n</em> 个节点的树，对一些节点染色，使得所有被染色的节点是一个连通块。求对于 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mn>3</mn><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo separator="true">,</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">1,2,3,...,n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">3</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">n</span></span></span></span>每个节点，该节点被染色的方案个数。所有答案对 <em>M</em> 取模。</p>
 </blockquote>
-<h5 id="思路：-4"><a href="#思路：-4" class="headerlink" title="思路："></a>思路：</h5><blockquote>
-<p>我们设$p_i$表示以$i$为跟的子树中的可行方案数,$q_i$表示$i$的父节点中除了$i$的方案数。</p>
-<p>那么，有$ans_i&#x3D;(q_i+1)*p_i$。</p>
+<h5 id="思路-5"><a class="markdownIt-Anchor" href="#思路-5"></a> 思路：</h5>
+<blockquote>
+<p>我们设<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">p_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>表示以<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">i</span></span></span></span>为跟的子树中的可行方案数,<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>q</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">q_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>表示<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">i</span></span></span></span>的父节点中除了<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">i</span></span></span></span>的方案数。</p>
+<p>那么，有<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><mi>n</mi><msub><mi>s</mi><mi>i</mi></msub><mo>=</mo><mo stretchy="false">(</mo><msub><mi>q</mi><mi>i</mi></msub><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mo>∗</mo><msub><mi>p</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">ans_i=(q_i+1)*p_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord mathnormal">a</span><span class="mord mathnormal">n</span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>。</p>
 </blockquote>
 </li>
 </ol>
-<h3 id="DP-优化"><a href="#DP-优化" class="headerlink" title="$DP$优化"></a>$DP$优化</h3><p>​	<strong>根据方程运用相应的数据结构即可</strong>。</p>
+<h3 id="dp优化"><a class="markdownIt-Anchor" href="#dp优化"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span>优化</h3>
+<p>​	<strong>根据方程运用相应的数据结构即可</strong>。</p>
 
                 </div>
 
@@ -466,7 +513,7 @@ <h3 id="DP-优化"><a href="#DP-优化" class="headerlink" title="$DP$优化"></
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+              window.KeepCommentPlugin.walineOptions.serverURL = 'blog-1uv64df2r-liaohengfengs-projects.vercel.app'
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@@ -504,7 +551,7 @@ <h3 id="DP-优化"><a href="#DP-优化" class="headerlink" title="$DP$优化"></
             <div class="pc-post-toc left-toc">
                 <div class="post-toc-wrap border-box">
     <div class="post-toc border-box">
-        <ol class="nav"><li class="nav-item nav-level-1"><a class="nav-link" href="#DP%E6%80%BB%E7%BB%93"><span class="nav-text">DP总结</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#%E7%BA%BF%E6%80%A7DP"><span class="nav-text">$线性DP$</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#%E5%AE%9A%E4%B9%89"><span class="nav-text">定义:</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E7%BB%8F%E5%85%B8%E6%A8%A1%E5%9E%8B"><span class="nav-text">经典模型</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E4%BE%8B%E9%A2%98%EF%BC%9A"><span class="nav-text">例题：</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#LCS"><span class="nav-text">LCS</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E6%84%8F%EF%BC%9A"><span class="nav-text">题意：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%96%B9%E6%B3%95"><span class="nav-text">方法:</span></a></li></ol></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E6%9C%80%E9%95%BF%E4%B8%8A%E5%8D%87%E5%AD%90%E5%BA%8F%E5%88%97-LIS"><span class="nav-text">最长上升子序列(LIS)</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E6%84%8F%EF%BC%9A-1"><span class="nav-text">题意：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%96%B9%E6%B3%95%EF%BC%9A"><span class="nav-text">方法：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#code"><span class="nav-text">code :</span></a></li></ol></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#%E4%BA%8C%E7%BB%B4%E5%B9%B3%E9%9D%A2%E4%B8%8A%E7%9A%84-DP-%E4%B8%8E-%E7%8A%B6%E6%80%81%E5%8E%8B%E7%BC%A9-DP"><span class="nav-text">二维平面上的$DP$ 与 状态压缩$DP$</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%8E%E6%A0%B7%E5%88%A4%E6%96%AD%EF%BC%9F"><span class="nav-text">怎样判断？</span></a></li></ol></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E4%BE%8B%E9%A2%98%EF%BC%9A-1"><span class="nav-text">例题：</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#Grid-2"><span class="nav-text">Grid 2</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E7%9B%AE%EF%BC%9A"><span class="nav-text">题目：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%9D%E8%B7%AF%EF%BC%9A"><span class="nav-text">思路：</span></a></li></ol></li><li class="nav-item nav-level-4"><a class="nav-link" href="#Matching"><span class="nav-text">Matching</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E7%9B%AE%EF%BC%9A-1"><span class="nav-text">题目：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%9D%E8%B7%AF%EF%BC%9A-1"><span class="nav-text">思路：</span></a></li></ol></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#%E5%8C%BA%E9%97%B4-DP"><span class="nav-text">区间$DP$</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#%E7%9F%B3%E5%AD%90%E5%90%88%E5%B9%B6"><span class="nav-text">石子合并</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E7%9B%AE%EF%BC%9A-2"><span class="nav-text">题目：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%9D%E8%B7%AF%EF%BC%9A-2"><span class="nav-text">思路：</span></a></li></ol></li><li class="nav-item nav-level-4"><a class="nav-link" href="#Deque"><span class="nav-text">Deque</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E7%9B%AE%EF%BC%9A-3"><span class="nav-text">题目：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%9D%E8%B7%AF%EF%BC%9A-3"><span class="nav-text">思路：</span></a></li></ol></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#%E6%8D%A2%E6%A0%B9-DP"><span class="nav-text">换根$DP$</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#Subtree"><span class="nav-text">Subtree</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E7%9B%AE%EF%BC%9A-4"><span class="nav-text">题目：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%9D%E8%B7%AF%EF%BC%9A-4"><span class="nav-text">思路：</span></a></li></ol></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#DP-%E4%BC%98%E5%8C%96"><span class="nav-text">$DP$优化</span></a></li></ol></li></ol></li></ol>
+        <ol class="nav"><li class="nav-item nav-level-1"><a class="nav-link" href="#dp%E6%80%BB%E7%BB%93"><span class="nav-text"> DP总结</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#%E7%BA%BF%E6%80%A7dp"><span class="nav-text"> 线性DP线性DP线性DP</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#%E5%AE%9A%E4%B9%89"><span class="nav-text"> 定义:</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E7%BB%8F%E5%85%B8%E6%A8%A1%E5%9E%8B"><span class="nav-text"> 经典模型</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E4%BE%8B%E9%A2%98"><span class="nav-text"> 例题：</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#lcs"><span class="nav-text"> LCS</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E6%84%8F"><span class="nav-text"> 题意：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%96%B9%E6%B3%95"><span class="nav-text"> 方法:</span></a></li></ol></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E6%9C%80%E9%95%BF%E4%B8%8A%E5%8D%87%E5%AD%90%E5%BA%8F%E5%88%97lis"><span class="nav-text"> 最长上升子序列(LIS)</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E6%84%8F-2"><span class="nav-text"> 题意：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%96%B9%E6%B3%95-2"><span class="nav-text"> 方法：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#code"><span class="nav-text"> code :</span></a></li></ol></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#%E4%BA%8C%E7%BB%B4%E5%B9%B3%E9%9D%A2%E4%B8%8A%E7%9A%84dp-%E4%B8%8E-%E7%8A%B6%E6%80%81%E5%8E%8B%E7%BC%A9dp"><span class="nav-text"> 二维平面上的DPDPDP 与 状态压缩DPDPDP</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%8E%E6%A0%B7%E5%88%A4%E6%96%AD"><span class="nav-text"> 怎样判断？</span></a></li></ol></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E4%BE%8B%E9%A2%98-2"><span class="nav-text"> 例题：</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#grid-2"><span class="nav-text"> Grid 2</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E7%9B%AE"><span class="nav-text"> 题目：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%9D%E8%B7%AF"><span class="nav-text"> 思路：</span></a></li></ol></li><li class="nav-item nav-level-4"><a class="nav-link" href="#matching"><span class="nav-text"> Matching</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E7%9B%AE-2"><span class="nav-text"> 题目：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%9D%E8%B7%AF-2"><span class="nav-text"> 思路：</span></a></li></ol></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#%E5%8C%BA%E9%97%B4dp"><span class="nav-text"> 区间DPDPDP</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#%E7%9F%B3%E5%AD%90%E5%90%88%E5%B9%B6"><span class="nav-text"> 石子合并</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E7%9B%AE-3"><span class="nav-text"> 题目：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%9D%E8%B7%AF-3"><span class="nav-text"> 思路：</span></a></li></ol></li><li class="nav-item nav-level-4"><a class="nav-link" href="#deque"><span class="nav-text"> Deque</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E7%9B%AE-4"><span class="nav-text"> 题目：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%9D%E8%B7%AF-4"><span class="nav-text"> 思路：</span></a></li></ol></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#%E6%8D%A2%E6%A0%B9dp"><span class="nav-text"> 换根DPDPDP</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#subtree"><span class="nav-text"> Subtree</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E7%9B%AE-5"><span class="nav-text"> 题目：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%9D%E8%B7%AF-5"><span class="nav-text"> 思路：</span></a></li></ol></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#dp%E4%BC%98%E5%8C%96"><span class="nav-text"> DPDPDP优化</span></a></li></ol></li></ol></li></ol>
     </div>
 </div>
 
@@ -682,7 +729,7 @@ <h3 id="DP-优化"><a href="#DP-优化" class="headerlink" title="$DP$优化"></
             <div class="tablet-post-toc">
                 <div class="post-toc-wrap border-box">
     <div class="post-toc border-box">
-        <ol class="nav"><li class="nav-item nav-level-1"><a class="nav-link" href="#DP%E6%80%BB%E7%BB%93"><span class="nav-text">DP总结</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#%E7%BA%BF%E6%80%A7DP"><span class="nav-text">$线性DP$</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#%E5%AE%9A%E4%B9%89"><span class="nav-text">定义:</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E7%BB%8F%E5%85%B8%E6%A8%A1%E5%9E%8B"><span class="nav-text">经典模型</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E4%BE%8B%E9%A2%98%EF%BC%9A"><span class="nav-text">例题：</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#LCS"><span class="nav-text">LCS</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E6%84%8F%EF%BC%9A"><span class="nav-text">题意：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%96%B9%E6%B3%95"><span class="nav-text">方法:</span></a></li></ol></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E6%9C%80%E9%95%BF%E4%B8%8A%E5%8D%87%E5%AD%90%E5%BA%8F%E5%88%97-LIS"><span class="nav-text">最长上升子序列(LIS)</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E6%84%8F%EF%BC%9A-1"><span class="nav-text">题意：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%96%B9%E6%B3%95%EF%BC%9A"><span class="nav-text">方法：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#code"><span class="nav-text">code :</span></a></li></ol></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#%E4%BA%8C%E7%BB%B4%E5%B9%B3%E9%9D%A2%E4%B8%8A%E7%9A%84-DP-%E4%B8%8E-%E7%8A%B6%E6%80%81%E5%8E%8B%E7%BC%A9-DP"><span class="nav-text">二维平面上的$DP$ 与 状态压缩$DP$</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%8E%E6%A0%B7%E5%88%A4%E6%96%AD%EF%BC%9F"><span class="nav-text">怎样判断？</span></a></li></ol></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E4%BE%8B%E9%A2%98%EF%BC%9A-1"><span class="nav-text">例题：</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#Grid-2"><span class="nav-text">Grid 2</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E7%9B%AE%EF%BC%9A"><span class="nav-text">题目：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%9D%E8%B7%AF%EF%BC%9A"><span class="nav-text">思路：</span></a></li></ol></li><li class="nav-item nav-level-4"><a class="nav-link" href="#Matching"><span class="nav-text">Matching</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E7%9B%AE%EF%BC%9A-1"><span class="nav-text">题目：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%9D%E8%B7%AF%EF%BC%9A-1"><span class="nav-text">思路：</span></a></li></ol></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#%E5%8C%BA%E9%97%B4-DP"><span class="nav-text">区间$DP$</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#%E7%9F%B3%E5%AD%90%E5%90%88%E5%B9%B6"><span class="nav-text">石子合并</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E7%9B%AE%EF%BC%9A-2"><span class="nav-text">题目：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%9D%E8%B7%AF%EF%BC%9A-2"><span class="nav-text">思路：</span></a></li></ol></li><li class="nav-item nav-level-4"><a class="nav-link" href="#Deque"><span class="nav-text">Deque</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E7%9B%AE%EF%BC%9A-3"><span class="nav-text">题目：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%9D%E8%B7%AF%EF%BC%9A-3"><span class="nav-text">思路：</span></a></li></ol></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#%E6%8D%A2%E6%A0%B9-DP"><span class="nav-text">换根$DP$</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#Subtree"><span class="nav-text">Subtree</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E7%9B%AE%EF%BC%9A-4"><span class="nav-text">题目：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%9D%E8%B7%AF%EF%BC%9A-4"><span class="nav-text">思路：</span></a></li></ol></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#DP-%E4%BC%98%E5%8C%96"><span class="nav-text">$DP$优化</span></a></li></ol></li></ol></li></ol>
+        <ol class="nav"><li class="nav-item nav-level-1"><a class="nav-link" href="#dp%E6%80%BB%E7%BB%93"><span class="nav-text"> DP总结</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#%E7%BA%BF%E6%80%A7dp"><span class="nav-text"> 线性DP线性DP线性DP</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#%E5%AE%9A%E4%B9%89"><span class="nav-text"> 定义:</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E7%BB%8F%E5%85%B8%E6%A8%A1%E5%9E%8B"><span class="nav-text"> 经典模型</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E4%BE%8B%E9%A2%98"><span class="nav-text"> 例题：</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#lcs"><span class="nav-text"> LCS</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E6%84%8F"><span class="nav-text"> 题意：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%96%B9%E6%B3%95"><span class="nav-text"> 方法:</span></a></li></ol></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E6%9C%80%E9%95%BF%E4%B8%8A%E5%8D%87%E5%AD%90%E5%BA%8F%E5%88%97lis"><span class="nav-text"> 最长上升子序列(LIS)</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E6%84%8F-2"><span class="nav-text"> 题意：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%96%B9%E6%B3%95-2"><span class="nav-text"> 方法：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#code"><span class="nav-text"> code :</span></a></li></ol></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#%E4%BA%8C%E7%BB%B4%E5%B9%B3%E9%9D%A2%E4%B8%8A%E7%9A%84dp-%E4%B8%8E-%E7%8A%B6%E6%80%81%E5%8E%8B%E7%BC%A9dp"><span class="nav-text"> 二维平面上的DPDPDP 与 状态压缩DPDPDP</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%8E%E6%A0%B7%E5%88%A4%E6%96%AD"><span class="nav-text"> 怎样判断？</span></a></li></ol></li><li class="nav-item nav-level-4"><a class="nav-link" href="#%E4%BE%8B%E9%A2%98-2"><span class="nav-text"> 例题：</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#grid-2"><span class="nav-text"> Grid 2</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E7%9B%AE"><span class="nav-text"> 题目：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%9D%E8%B7%AF"><span class="nav-text"> 思路：</span></a></li></ol></li><li class="nav-item nav-level-4"><a class="nav-link" href="#matching"><span class="nav-text"> Matching</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E7%9B%AE-2"><span class="nav-text"> 题目：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%9D%E8%B7%AF-2"><span class="nav-text"> 思路：</span></a></li></ol></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#%E5%8C%BA%E9%97%B4dp"><span class="nav-text"> 区间DPDPDP</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#%E7%9F%B3%E5%AD%90%E5%90%88%E5%B9%B6"><span class="nav-text"> 石子合并</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E7%9B%AE-3"><span class="nav-text"> 题目：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%9D%E8%B7%AF-3"><span class="nav-text"> 思路：</span></a></li></ol></li><li class="nav-item nav-level-4"><a class="nav-link" href="#deque"><span class="nav-text"> Deque</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E7%9B%AE-4"><span class="nav-text"> 题目：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%9D%E8%B7%AF-4"><span class="nav-text"> 思路：</span></a></li></ol></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#%E6%8D%A2%E6%A0%B9dp"><span class="nav-text"> 换根DPDPDP</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#subtree"><span class="nav-text"> Subtree</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E9%A2%98%E7%9B%AE-5"><span class="nav-text"> 题目：</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%80%9D%E8%B7%AF-5"><span class="nav-text"> 思路：</span></a></li></ol></li></ol></li><li class="nav-item nav-level-3"><a class="nav-link" href="#dp%E4%BC%98%E5%8C%96"><span class="nav-text"> DPDPDP优化</span></a></li></ol></li></ol></li></ol>
     </div>
 </div>
 
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index 0c1743176..407e3298b 100644
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+++ b/2023/10/24/CSP/index.html
@@ -2,6 +2,7 @@
 <html lang="zh-CN">
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     <meta charset="utf-8">
+    <link rel="stylesheet" href="https://lib.baomitu.com/KaTeX/latest/katex.min.css">
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@@ -222,7 +223,7 @@
         
         
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-                <i class="icon fas fa-file-word"></i>&nbsp;<span>588 字</span>
+                <i class="icon fas fa-file-word"></i>&nbsp;<span>668 字</span>
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@@ -248,68 +249,73 @@
                 <div class="post-content keep-markdown-body">
                     
 
-                    <h1 id="CSP-游记"><a href="#CSP-游记" class="headerlink" title="$CSP$ 游记"></a>$CSP$ 游记</h1><h3 id="Day-0"><a href="#Day-0" class="headerlink" title="Day 0"></a>Day 0</h3><blockquote>
-<p>晚上去了酒店，和另外几个人一起复习了 $Tarjan$ ，然后就睡了。</p>
-<p>睡觉前想着 $2.5h$ 写前两个题，后两个题打下暴力，应该能拿  <strong>一等</strong>。</p>
+                    <h1 id="csp-游记"><a class="markdownIt-Anchor" href="#csp-游记"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>S</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">CSP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span> 游记</h1>
+<h3 id="day-0"><a class="markdownIt-Anchor" href="#day-0"></a> Day 0</h3>
+<blockquote>
+<p>晚上去了酒店，和另外几个人一起复习了 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mi>a</mi><mi>r</mi><mi>j</mi><mi>a</mi><mi>n</mi></mrow><annotation encoding="application/x-tex">Tarjan</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span><span class="mord mathnormal">a</span><span class="mord mathnormal">n</span></span></span></span> ，然后就睡了。</p>
+<p>睡觉前想着 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2.5</mn><mi>h</mi></mrow><annotation encoding="application/x-tex">2.5h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord">2</span><span class="mord">.</span><span class="mord">5</span><span class="mord mathnormal">h</span></span></span></span> 写前两个题，后两个题打下暴力，应该能拿  <strong>一等</strong>。</p>
 </blockquote>
-<h3 id="Day-1-上午"><a href="#Day-1-上午" class="headerlink" title="Day 1 + 上午"></a>Day 1 + 上午</h3><blockquote>
-<p>$7\ :\ 40$</p>
-<p>早上起来的最早，但发现自己感冒了。喝了只 $蒲地蓝$ ，还戴上了 $开喉剑$ 。</p>
-<p>心里有种不祥的预感，感觉 $T3$ 会是与式子有关的 大模拟。</p>
+<h3 id="day-1-上午"><a class="markdownIt-Anchor" href="#day-1-上午"></a> Day 1 + 上午</h3>
+<blockquote>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>7</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>40</mn></mrow><annotation encoding="application/x-tex">7\ :\ 40</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">7</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">4</span><span class="mord">0</span></span></span></span></p>
+<p>早上起来的最早，但发现自己感冒了。喝了只 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>蒲地蓝</mtext></mrow><annotation encoding="application/x-tex">蒲地蓝</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">蒲</span><span class="mord cjk_fallback">地</span><span class="mord cjk_fallback">蓝</span></span></span></span> ，还戴上了 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>开喉剑</mtext></mrow><annotation encoding="application/x-tex">开喉剑</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">开</span><span class="mord cjk_fallback">喉</span><span class="mord cjk_fallback">剑</span></span></span></span> 。</p>
+<p>心里有种不祥的预感，感觉 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>3</mn></mrow><annotation encoding="application/x-tex">T3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">3</span></span></span></span> 会是与式子有关的 大模拟。</p>
 <p>$\ $</p>
-<p>$8\ :\ 30$</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>8</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>30</mn></mrow><annotation encoding="application/x-tex">8\ :\ 30</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">8</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">3</span><span class="mord">0</span></span></span></span></p>
 <p>到一中集了合，拍了张照。果老师讲了些关于低级失误的事。</p>
 <p>$\ $</p>
-<p>$8\ :\ 30$</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>8</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>30</mn></mrow><annotation encoding="application/x-tex">8\ :\ 30</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">8</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">3</span><span class="mord">0</span></span></span></span></p>
 <p>进了考场，发现座位设计非常 <code>反人类</code>，腿稍稍往前放一点就会碰到膝盖。</p>
-<p>题面与压缩包出现了分离，<del>监考老师也搞了很久</del>。</p>
+<p>题面与压缩包出现了分离，<s>监考老师也搞了很久</s>。</p>
 <p>$\ $</p>
-<p>$8\ :\ 55$</p>
-<p>$T1$ 感觉像约瑟夫，但 手搓样例 后发现每次会消掉 $\lfloor \frac{n-1} {3} \rfloor$ 个，$while(n)$ 即可。</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>8</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>55</mn></mrow><annotation encoding="application/x-tex">8\ :\ 55</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">8</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">5</span><span class="mord">5</span></span></span></span></p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>1</mn></mrow><annotation encoding="application/x-tex">T1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">1</span></span></span></span> 感觉像约瑟夫，但 手搓样例 后发现每次会消掉 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">⌊</mo><mfrac><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mn>3</mn></mfrac><mo stretchy="false">⌋</mo></mrow><annotation encoding="application/x-tex">\lfloor \frac{n-1} {3} \rfloor</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.190108em;vertical-align:-0.345em;"></span><span class="mopen">⌊</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.845108em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">3</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose">⌋</span></span></span></span> 个，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi><mi>h</mi><mi>i</mi><mi>l</mi><mi>e</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">while(n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mord mathnormal">h</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span></span> 即可。</p>
 <p>对于第二个问，有一个显然的性质:</p>
 <blockquote>
-<p>在 $n$ 消掉前，他一定在末尾。</p>
+<p>在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span> 消掉前，他一定在末尾。</p>
 </blockquote>
-<p>所以$while(n)$时判断一下 $(n-1)%3&#x3D;&#x3D;1$ 即可。</p>
+<p>所以<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi><mi>h</mi><mi>i</mi><mi>l</mi><mi>e</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">while(n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mord mathnormal">h</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span></span>时判断一下 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mi mathvariant="normal">%</mi><mn>3</mn><mo>=</mo><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">(n-1)\%3==1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">)</span><span class="mord">%</span><span class="mord">3</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span></span><span class="base"><span class="strut" style="height:0.36687em;vertical-align:0em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span> 即可。</p>
 <p>$\ $</p>
-<p>$9\ :\ 30$</p>
-<p>把 $T1$ 的对拍打了一下，然后发现 $T2$ 是贪心水题，$15min$ 切了。</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>9</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>30</mn></mrow><annotation encoding="application/x-tex">9\ :\ 30</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">9</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">3</span><span class="mord">0</span></span></span></span></p>
+<p>把 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>1</mn></mrow><annotation encoding="application/x-tex">T1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">1</span></span></span></span> 的对拍打了一下，然后发现 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>2</mn></mrow><annotation encoding="application/x-tex">T2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">2</span></span></span></span> 是贪心水题，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>15</mn><mi>m</mi><mi>i</mi><mi>n</mi></mrow><annotation encoding="application/x-tex">15min</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord">5</span><span class="mord mathnormal">m</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span></span></span></span> 切了。</p>
 <p>$\ $</p>
-<p>$9\ :\ 50$</p>
-<p>发现 $T3$ 是二次函数求值，回想起了去年 $T2$ 用 $sqrt$ 爆精度，就筛了 $1e6$ 内的质数。</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>9</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>50</mn></mrow><annotation encoding="application/x-tex">9\ :\ 50</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">9</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">5</span><span class="mord">0</span></span></span></span></p>
+<p>发现 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>3</mn></mrow><annotation encoding="application/x-tex">T3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">3</span></span></span></span> 是二次函数求值，回想起了去年 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>2</mn></mrow><annotation encoding="application/x-tex">T2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">2</span></span></span></span> 用 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>s</mi><mi>q</mi><mi>r</mi><mi>t</mi></mrow><annotation encoding="application/x-tex">sqrt</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.80952em;vertical-align:-0.19444em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">t</span></span></span></span> 爆精度，就筛了 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mi>e</mi><mn>6</mn></mrow><annotation encoding="application/x-tex">1e6</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord mathnormal">e</span><span class="mord">6</span></span></span></span> 内的质数。</p>
 <p>然后模拟即可。</p>
 <p>$\ $</p>
-<p>$11\ :\ 00$</p>
-<p>把前三个题看了一遍，发现没问题，开冲 $T4$。</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>11</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>00</mn></mrow><annotation encoding="application/x-tex">11\ :\ 00</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord">1</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span><span class="mord">0</span></span></span></span></p>
+<p>把前三个题看了一遍，发现没问题，开冲 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>4</mn></mrow><annotation encoding="application/x-tex">T4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">4</span></span></span></span>。</p>
 <p>$\ $</p>
-<p>$12\ :\ 00$</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>12</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>00</mn></mrow><annotation encoding="application/x-tex">12\ :\ 00</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord">2</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span><span class="mord">0</span></span></span></span></p>
 <p>考试结束，预估</p>
-<p>$100\ +\ 100\ +\ 100\ +\ 10\ &#x3D;\ 310  $ ， 感觉<strong>一等</strong>没问题。</p>
+<p>$100\ +\ 100\ +\ 100\ +\ 10\ =\ 310  $ ， 感觉<strong>一等</strong>没问题。</p>
 </blockquote>
-<h3 id="Day-1-下午"><a href="#Day-1-下午" class="headerlink" title="Day 1 + 下午"></a>Day 1 + 下午</h3><blockquote>
-<p>$2\ :\ 30$ </p>
-<p>进入了考场，$pdf$ 的密码老师没找到，延迟了 $5min$。</p>
+<h3 id="day-1-下午"><a class="markdownIt-Anchor" href="#day-1-下午"></a> Day 1 + 下午</h3>
+<blockquote>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>30</mn></mrow><annotation encoding="application/x-tex">2\ :\ 30</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">2</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">3</span><span class="mord">0</span></span></span></span></p>
+<p>进入了考场，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi>d</mi><mi>f</mi></mrow><annotation encoding="application/x-tex">pdf</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span></span></span></span> 的密码老师没找到，延迟了 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>5</mn><mi>m</mi><mi>i</mi><mi>n</mi></mrow><annotation encoding="application/x-tex">5min</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord">5</span><span class="mord mathnormal">m</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span></span></span></span>。</p>
 <p>$\ $</p>
-<p>$3\ :\ 00$</p>
-<p>发现 $T1$ 是水题，枚举所有状态再反过来判断即可。</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>00</mn></mrow><annotation encoding="application/x-tex">3\ :\ 00</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">3</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span><span class="mord">0</span></span></span></span></p>
+<p>发现 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>1</mn></mrow><annotation encoding="application/x-tex">T1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">1</span></span></span></span> 是水题，枚举所有状态再反过来判断即可。</p>
 <p>$\ $</p>
-<p>$3\ :\ 35$</p>
-<p>$T2$ 先打了一个 $O(n^3)$ 的暴力，然后发现枚举右端点太费时间，优化成了 $O(n^2)$</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>35</mn></mrow><annotation encoding="application/x-tex">3\ :\ 35</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">3</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">3</span><span class="mord">5</span></span></span></span></p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>2</mn></mrow><annotation encoding="application/x-tex">T2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">2</span></span></span></span> 先打了一个 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mn>3</mn></msup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(n^3)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span> 的暴力，然后发现枚举右端点太费时间，优化成了 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mn>2</mn></msup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(n^2)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></p>
 <p>$\ $</p>
-<p>$3\ :\ 55$</p>
-<p>看了一下 $T4$ ，感觉像 <code>树上DP</code> ，但没推出来，转去了 $T3$。</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>55</mn></mrow><annotation encoding="application/x-tex">3\ :\ 55</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">3</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">5</span><span class="mord">5</span></span></span></span></p>
+<p>看了一下 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>4</mn></mrow><annotation encoding="application/x-tex">T4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">4</span></span></span></span> ，感觉像 <code>树上DP</code> ，但没推出来，转去了 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>3</mn></mrow><annotation encoding="application/x-tex">T3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">3</span></span></span></span>。</p>
 <p>$\ $</p>
-<p>$6\ :\ 00$</p>
-<p>一直在调 $T3$ ，感觉灵魂出窍。</p>
-<p>$对其原则$ 很好做，但 $4$ 操作难调得死，最后修修补补的过了大样例。</p>
-<p><del><strong>考完发现没有初始化</strong></del>。</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>6</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>00</mn></mrow><annotation encoding="application/x-tex">6\ :\ 00</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">6</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span><span class="mord">0</span></span></span></span></p>
+<p>一直在调 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>3</mn></mrow><annotation encoding="application/x-tex">T3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">3</span></span></span></span> ，感觉灵魂出窍。</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>对其原则</mtext></mrow><annotation encoding="application/x-tex">对其原则</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">对</span><span class="mord cjk_fallback">其</span><span class="mord cjk_fallback">原</span><span class="mord cjk_fallback">则</span></span></span></span> 很好做，但 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4</mn></mrow><annotation encoding="application/x-tex">4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">4</span></span></span></span> 操作难调得死，最后修修补补的过了大样例。</p>
+<p><s><strong>考完发现没有初始化</strong></s>。</p>
 <p>$\ $</p>
-<p>估分 $100\ +\ 50\ +\ +\ ?\ +\ 0\ &#x3D;\ 150^+$</p>
+<p>估分 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>100</mn><mtext> </mtext><mo>+</mo><mtext> </mtext><mn>50</mn><mtext> </mtext><mo>+</mo><mtext> </mtext><mo>+</mo><mtext> </mtext><mo stretchy="false">?</mo><mtext> </mtext><mo>+</mo><mtext> </mtext><mn>0</mn><mtext> </mtext><mo>=</mo><mtext> </mtext><mn>15</mn><msup><mn>0</mn><mo>+</mo></msup></mrow><annotation encoding="application/x-tex">100\ +\ 50\ +\ +\ ?\ +\ 0\ =\ 150^+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">1</span><span class="mord">0</span><span class="mord">0</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">5</span><span class="mord">0</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em;"></span><span class="mord">+</span><span class="mspace"> </span><span class="mclose">?</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.771331em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord">5</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">+</span></span></span></span></span></span></span></span></span></span></span></p>
 </blockquote>
-<h2 id="反思"><a href="#反思" class="headerlink" title="反思"></a>反思</h2><blockquote>
-<p>比赛节奏感觉可以，$S$ 组 $T4$ 没看出来感觉很可惜。</p>
-<p>听说 $J$ 组的 $T4$ 是分层图最短路，考场上自己没去想。</p>
-<p>$S$ 组 $T3$ 能拿多少是多少，得一等的希望就在他身上了。</p>
+<h2 id="反思"><a class="markdownIt-Anchor" href="#反思"></a> 反思</h2>
+<blockquote>
+<p>比赛节奏感觉可以，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi></mrow><annotation encoding="application/x-tex">S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span></span></span></span> 组 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>4</mn></mrow><annotation encoding="application/x-tex">T4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">4</span></span></span></span> 没看出来感觉很可惜。</p>
+<p>听说 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>J</mi></mrow><annotation encoding="application/x-tex">J</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.09618em;">J</span></span></span></span> 组的 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>4</mn></mrow><annotation encoding="application/x-tex">T4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">4</span></span></span></span> 是分层图最短路，考场上自己没去想。</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi></mrow><annotation encoding="application/x-tex">S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span></span></span></span> 组 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>3</mn></mrow><annotation encoding="application/x-tex">T3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">3</span></span></span></span> 能拿多少是多少，得一等的希望就在他身上了。</p>
 </blockquote>
 
                 </div>
@@ -442,7 +448,7 @@ <h2 id="反思"><a href="#反思" class="headerlink" title="反思"></a>反思</
             if (window?.Waline) {
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               window.KeepCommentPlugin.walineOptions.comment = '.post-comments-count'
-              window.KeepCommentPlugin.walineOptions.serverURL = 'https://chat-720woyuwq-liaohengfengs-projects.vercel.app/'
+              window.KeepCommentPlugin.walineOptions.serverURL = 'blog-1uv64df2r-liaohengfengs-projects.vercel.app'
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@@ -480,7 +486,7 @@ <h2 id="反思"><a href="#反思" class="headerlink" title="反思"></a>反思</
             <div class="pc-post-toc left-toc">
                 <div class="post-toc-wrap border-box">
     <div class="post-toc border-box">
-        <ol class="nav"><li class="nav-item nav-level-1"><a class="nav-link" href="#CSP-%E6%B8%B8%E8%AE%B0"><span class="nav-text">$CSP$ 游记</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#Day-0"><span class="nav-text">Day 0</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Day-1-%E4%B8%8A%E5%8D%88"><span class="nav-text">Day 1 + 上午</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Day-1-%E4%B8%8B%E5%8D%88"><span class="nav-text">Day 1 + 下午</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#%E5%8F%8D%E6%80%9D"><span class="nav-text">反思</span></a></li></ol></li></ol>
+        <ol class="nav"><li class="nav-item nav-level-1"><a class="nav-link" href="#csp-%E6%B8%B8%E8%AE%B0"><span class="nav-text"> CSPCSPCSP 游记</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#day-0"><span class="nav-text"> Day 0</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#day-1-%E4%B8%8A%E5%8D%88"><span class="nav-text"> Day 1 + 上午</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#day-1-%E4%B8%8B%E5%8D%88"><span class="nav-text"> Day 1 + 下午</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#%E5%8F%8D%E6%80%9D"><span class="nav-text"> 反思</span></a></li></ol></li></ol>
     </div>
 </div>
 
@@ -658,7 +664,7 @@ <h2 id="反思"><a href="#反思" class="headerlink" title="反思"></a>反思</
             <div class="tablet-post-toc">
                 <div class="post-toc-wrap border-box">
     <div class="post-toc border-box">
-        <ol class="nav"><li class="nav-item nav-level-1"><a class="nav-link" href="#CSP-%E6%B8%B8%E8%AE%B0"><span class="nav-text">$CSP$ 游记</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#Day-0"><span class="nav-text">Day 0</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Day-1-%E4%B8%8A%E5%8D%88"><span class="nav-text">Day 1 + 上午</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#Day-1-%E4%B8%8B%E5%8D%88"><span class="nav-text">Day 1 + 下午</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#%E5%8F%8D%E6%80%9D"><span class="nav-text">反思</span></a></li></ol></li></ol>
+        <ol class="nav"><li class="nav-item nav-level-1"><a class="nav-link" href="#csp-%E6%B8%B8%E8%AE%B0"><span class="nav-text"> CSPCSPCSP 游记</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#day-0"><span class="nav-text"> Day 0</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#day-1-%E4%B8%8A%E5%8D%88"><span class="nav-text"> Day 1 + 上午</span></a></li><li class="nav-item nav-level-3"><a class="nav-link" href="#day-1-%E4%B8%8B%E5%8D%88"><span class="nav-text"> Day 1 + 下午</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#%E5%8F%8D%E6%80%9D"><span class="nav-text"> 反思</span></a></li></ol></li></ol>
     </div>
 </div>
 
diff --git "a/2023/12/09/23.12.9 \350\200\203\350\257\225\346\200\273\347\273\223/index.html" "b/2023/12/09/23.12.9 \350\200\203\350\257\225\346\200\273\347\273\223/index.html"
index 3609ffc0a..0578acb56 100644
--- "a/2023/12/09/23.12.9 \350\200\203\350\257\225\346\200\273\347\273\223/index.html"	
+++ "b/2023/12/09/23.12.9 \350\200\203\350\257\225\346\200\273\347\273\223/index.html"	
@@ -2,6 +2,7 @@
 <html lang="zh-CN">
 <head>
     <meta charset="utf-8">
+    <link rel="stylesheet" href="https://lib.baomitu.com/KaTeX/latest/katex.min.css">
     <meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=1">
     <meta name="keywords" content="Hexo Theme Keep">
     <meta name="description" content="Hexo Theme Keep">
@@ -27,7 +28,7 @@
     <script class="keep-theme-configurations">
     const KEEP = window.KEEP || {}
     KEEP.hexo_config = {"hostname":"example.com","root":"/","language":"zh-CN","path":"search.xml"}
-    KEEP.theme_config = {"base_info":{"primary_color":"#0066cc","title":"LHF's blog","author":"�����","avatar":"/images/avatar.png","logo":"/images/logo.png","favicon":"/images/logo.png"},"menu":{"Archives":"/archives","Tags":"/tags","Links":"/links","About":"/about"},"first_screen":{"enable":true,"background_img":"/images/bg.svg","background_img_dark":"/images/bg.svg","description":"�����Ͳ�,������ǧ�||����С��,���Գɽ�����","hitokoto":true},"social_contact":{"enable":true,"links":{"github":null,"luogu":"img | /images/luogu.png"}},"scroll":{"progress_bar":true,"percent":true,"hide_header":false},"home":{"category":false,"tag":false,"announcement":null},"post":{"author_badge":{"enable":true,"level_badge":true,"custom_badge":["One","Two","Three"]},"word_count":{"wordcount":true,"min2read":true},"datetime_format":"YYYY-MM-DD HH:mm:ss","copyright_info":false,"share":true,"reward":{"enable":false,"img_link":null,"text":null}},"code_block":{"tools":{"enable":true,"style":"mac"},"highlight_theme":"default"},"toc":{"enable":true,"number":false,"expand_all":false,"init_open":true,"layout":"left"},"website_count":{"busuanzi_count":{"enable":true,"site_uv":true,"site_pv":true,"page_pv":true}},"search":{"path":"search.json","field":"post","content":true,"format":"striptags"},"local_search":{"enable":true,"preload":true},"comment":{"enable":true,"use":"waline","valine":{"appid":null,"appkey":null,"server_urls":null,"placeholder":null},"gitalk":{"github_id":null,"github_admins":null,"repository":null,"client_id":null,"client_secret":null,"proxy":null},"twikoo":{"env_id":null,"region":null,"version":"1.6.21"},"waline":{"server_url":"https://chat-720woyuwq-liaohengfengs-projects.vercel.app/","reaction":false,"version":2},"giscus":{"repo":null,"repo_id":null,"category":"Announcements","category_id":null,"reactions_enabled":false},"artalk":{"server":null},"disqus":{"shortname":null}},"rss":{"enable":false},"lazyload":{"enable":true},"cdn":{"enable":true,"provider":"cdnjs"},"pjax":{"enable":true},"footer":{"since":2024,"word_count":false,"icp":{"enable":false,"record_code":null,"url":"https://beian.miit.gov.cn"},"site_deploy":{"enable":false,"provider":"github","url":null},"shields_style":{"enable":false,"custom":[{"link_url":null,"img_url":null}]}},"inject":{"enable":false,"css":[null],"js":[null]},"root":"","version":"4.0.6"}
+    KEEP.theme_config = {"base_info":{"primary_color":"#0066cc","title":"LHF's blog","author":"�����","avatar":"/images/avatar.png","logo":"/images/logo.png","favicon":"/images/logo.png"},"menu":{"Archives":"/archives","Tags":"/tags","Links":"/links","About":"/about"},"first_screen":{"enable":true,"background_img":"/images/bg.svg","background_img_dark":"/images/bg.svg","description":null,"hitokoto":true},"social_contact":{"enable":true,"links":{"github":null,"luogu":"img | /images/luogu.png"}},"scroll":{"progress_bar":true,"percent":true,"hide_header":false},"home":{"category":false,"tag":false,"announcement":null},"post":{"author_badge":{"enable":true,"level_badge":true,"custom_badge":["One","Two","Three"]},"word_count":{"wordcount":true,"min2read":true},"datetime_format":"YYYY-MM-DD HH:mm:ss","copyright_info":false,"share":true,"reward":{"enable":false,"img_link":null,"text":null}},"code_block":{"tools":{"enable":true,"style":"mac"},"highlight_theme":"default"},"toc":{"enable":true,"number":false,"expand_all":false,"init_open":true,"layout":"left"},"website_count":{"busuanzi_count":{"enable":true,"site_uv":true,"site_pv":true,"page_pv":true}},"search":{"path":"search.json","field":"post","content":true,"format":"striptags"},"local_search":{"enable":true,"preload":true},"comment":{"enable":true,"use":"waline","valine":{"appid":null,"appkey":null,"server_urls":null,"placeholder":null},"gitalk":{"github_id":null,"github_admins":null,"repository":null,"client_id":null,"client_secret":null,"proxy":null},"twikoo":{"env_id":null,"region":null,"version":"1.6.21"},"waline":{"server_url":"blog-1uv64df2r-liaohengfengs-projects.vercel.app","reaction":false,"version":2},"giscus":{"repo":null,"repo_id":null,"category":"Announcements","category_id":null,"reactions_enabled":false},"artalk":{"server":null},"disqus":{"shortname":null}},"rss":{"enable":false},"lazyload":{"enable":true},"cdn":{"enable":true,"provider":"cdnjs"},"pjax":{"enable":true},"footer":{"since":2024,"word_count":false,"icp":{"enable":false,"record_code":null,"url":"https://beian.miit.gov.cn"},"site_deploy":{"enable":false,"provider":"github","url":null},"shields_style":{"enable":false,"custom":[{"link_url":null,"img_url":null}]}},"inject":{"enable":false,"css":[null],"js":[null]},"root":"","version":"4.0.6"}
     KEEP.language_ago = {"second":"%s 秒前","minute":"%s 分钟前","hour":"%s 小时前","day":"%s 天前","week":"%s 周前","month":"%s 个月前","year":"%s 年前"}
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@@ -222,12 +223,12 @@
         
         
             <span class="meta-info-item post-wordcount">
-                <i class="icon fas fa-file-word"></i>&nbsp;<span>418 字</span>
+                <i class="icon fas fa-file-word"></i>&nbsp;<span>675 字</span>
             </span>
         
         
             <span class="meta-info-item post-min2read">
-                <i class="icon fas fa-clock"></i>&nbsp;<span>1 分钟</span>
+                <i class="icon fas fa-clock"></i>&nbsp;<span>3 分钟</span>
             </span>
         
         
@@ -248,63 +249,91 @@
                 <div class="post-content keep-markdown-body">
                     
 
-                    <h1 id="23-12-9-考试总结"><a href="#23-12-9-考试总结" class="headerlink" title="$23.12.9$ 考试总结"></a>$23.12.9$ 考试总结</h1><h3 id="分数-60-（-50-10-0-0"><a href="#分数-60-（-50-10-0-0" class="headerlink" title="分数 : $60$ （$50+10+0+0$)"></a>分数 : $60$ （$50+10+0+0$)</h3><h2 id="A-stick"><a href="#A-stick" class="headerlink" title="A. stick"></a>A. stick</h2><hr>
-<p>先是一个数字，然后一串$0$，最后一串$8$。贪就完了。</p>
-<p>注意模数是 $998244$<font color=red size=26>8</font>$53$。挂分 $50pts$</p>
-<h2 id="B-game"><a href="#B-game" class="headerlink" title="B. game"></a>B. game</h2><hr>
-<p>正解爆搜。少打 <code>break</code>挂 $90pts$。</p>
-<p>答案很多，所以 $yes$ 跑得很快。</p>
-<p>最坏情况$5\times 6$，此时$O(1^4\times2^{14}\times3^{16})$。</p>
+                    <h1 id="23129-考试总结"><a class="markdownIt-Anchor" href="#23129-考试总结"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>23.12.9</mn></mrow><annotation encoding="application/x-tex">23.12.9</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">2</span><span class="mord">3</span><span class="mord">.</span><span class="mord">1</span><span class="mord">2</span><span class="mord">.</span><span class="mord">9</span></span></span></span> 考试总结</h1>
+<h3 id="分数-60-501000"><a class="markdownIt-Anchor" href="#分数-60-501000"></a> 分数 : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>60</mn></mrow><annotation encoding="application/x-tex">60</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">6</span><span class="mord">0</span></span></span></span> （<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50</mn><mo>+</mo><mn>10</mn><mo>+</mo><mn>0</mn><mo>+</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">50+10+0+0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">5</span><span class="mord">0</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">1</span><span class="mord">0</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">0</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span></span></span></span>)</h3>
+<h2 id="a-stick"><a class="markdownIt-Anchor" href="#a-stick"></a> A. stick</h2>
+<hr />
+<p>先是一个数字，然后一串<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span></span></span></span>，最后一串<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>8</mn></mrow><annotation encoding="application/x-tex">8</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">8</span></span></span></span>。贪就完了。</p>
+<p>注意模数是 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>998244</mn></mrow><annotation encoding="application/x-tex">998244</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">9</span><span class="mord">9</span><span class="mord">8</span><span class="mord">2</span><span class="mord">4</span><span class="mord">4</span></span></span></span><font color=red size=26>8</font><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>53</mn></mrow><annotation encoding="application/x-tex">53</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">5</span><span class="mord">3</span></span></span></span>。挂分 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50</mn><mi>p</mi><mi>t</mi><mi>s</mi></mrow><annotation encoding="application/x-tex">50pts</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em;"></span><span class="mord">5</span><span class="mord">0</span><span class="mord mathnormal">p</span><span class="mord mathnormal">t</span><span class="mord mathnormal">s</span></span></span></span></p>
+<h2 id="b-game"><a class="markdownIt-Anchor" href="#b-game"></a> B. game</h2>
+<hr />
+<p>正解爆搜。少打 <code>break</code>挂 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>90</mn><mi>p</mi><mi>t</mi><mi>s</mi></mrow><annotation encoding="application/x-tex">90pts</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em;"></span><span class="mord">9</span><span class="mord">0</span><span class="mord mathnormal">p</span><span class="mord mathnormal">t</span><span class="mord mathnormal">s</span></span></span></span>。</p>
+<p>答案很多，所以 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi><mi>e</mi><mi>s</mi></mrow><annotation encoding="application/x-tex">yes</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mord mathnormal">e</span><span class="mord mathnormal">s</span></span></span></span> 跑得很快。</p>
+<p>最坏情况<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>5</mn><mo>×</mo><mn>6</mn></mrow><annotation encoding="application/x-tex">5\times 6</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">6</span></span></span></span>，此时<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mn>1</mn><mn>4</mn></msup><mo>×</mo><msup><mn>2</mn><mn>14</mn></msup><mo>×</mo><msup><mn>3</mn><mn>16</mn></msup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(1^4\times2^{14}\times3^{16})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord">1</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.897438em;vertical-align:-0.08333em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mord mtight">4</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord">3</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mord mtight">6</span></span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span>。</p>
 <p>注意到数据很小，考虑可行性剪枝即可。</p>
 <p>来自 <a class="link"   target="_blank" rel="noopener" href="http://f7.163.com/" >永远的7日之都<i class="fas fa-external-link-alt"></i></a> :</p>
 <p><img  
                        lazyload
                        alt="image"
                        data-src="https://www.z4a.net/images/2023/12/11/375a1f3119b0cb2173b9acd3a689e50071d0bfe4.jpg1256w_708h_web-article-pic.web"
-                       
+                        alt="" 
                  ></p>
-<h2 id="C-noip"><a href="#C-noip" class="headerlink" title="C.  noip"></a>C.  <strong>noip</strong></h2><hr>
-<p>万恶的 $O2$，$RE\ \ 0$。</p>
-<p>字典序从大到小搜索,$DP$ 预处理 $每个后缀首字母确定的情况下所能得到的最大权值$ ，判断当前是否 $\geq\ x$ $(可行性剪枝)$。</p>
+<h2 id="c-noip"><a class="markdownIt-Anchor" href="#c-noip"></a> C.  <strong>noip</strong></h2>
+<hr />
+<p>万恶的 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mn>2</mn></mrow><annotation encoding="application/x-tex">O2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mord">2</span></span></span></span>，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>R</mi><mi>E</mi><mtext>  </mtext><mn>0</mn></mrow><annotation encoding="application/x-tex">RE\ \ 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mspace"> </span><span class="mspace"> </span><span class="mord">0</span></span></span></span>。</p>
+<p>字典序从大到小搜索,<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span> 预处理 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>每个后缀首字母确定的情况下所能得到的最大权值</mtext></mrow><annotation encoding="application/x-tex">每个后缀首字母确定的情况下所能得到的最大权值</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">每</span><span class="mord cjk_fallback">个</span><span class="mord cjk_fallback">后</span><span class="mord cjk_fallback">缀</span><span class="mord cjk_fallback">首</span><span class="mord cjk_fallback">字</span><span class="mord cjk_fallback">母</span><span class="mord cjk_fallback">确</span><span class="mord cjk_fallback">定</span><span class="mord cjk_fallback">的</span><span class="mord cjk_fallback">情</span><span class="mord cjk_fallback">况</span><span class="mord cjk_fallback">下</span><span class="mord cjk_fallback">所</span><span class="mord cjk_fallback">能</span><span class="mord cjk_fallback">得</span><span class="mord cjk_fallback">到</span><span class="mord cjk_fallback">的</span><span class="mord cjk_fallback">最</span><span class="mord cjk_fallback">大</span><span class="mord cjk_fallback">权</span><span class="mord cjk_fallback">值</span></span></span></span> ，判断当前是否 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≥</mo><mtext> </mtext><mi>x</mi></mrow><annotation encoding="application/x-tex">\geq\ x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719400000000001em;vertical-align:-0.13597em;"></span><span class="mrel">≥</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mtext>可行性剪枝</mtext><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(可行性剪枝)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">可</span><span class="mord cjk_fallback">行</span><span class="mord cjk_fallback">性</span><span class="mord cjk_fallback">剪</span><span class="mord cjk_fallback">枝</span><span class="mclose">)</span></span></span></span>。</p>
 <blockquote>
-<p>学的是 $DP作为部分$ 的思路。</p>
+<p>学的是 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi><mtext>作为部分</mtext></mrow><annotation encoding="application/x-tex">DP作为部分</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mord cjk_fallback">作</span><span class="mord cjk_fallback">为</span><span class="mord cjk_fallback">部</span><span class="mord cjk_fallback">分</span></span></span></span> 的思路。</p>
 </blockquote>
-<h2 id="D-remove"><a href="#D-remove" class="headerlink" title="D. remove"></a>D. remove</h2><hr>
-<p>区间 $DP$。求<br>$$<br>min<br>\left{<br>\begin{aligned}<br>a \times k + b\times\sum\limits_{i&#x3D;1}^{k} \Big (max_i-min_i\Big)<br>\end{aligned}<br>\right}<br>$$</p>
-<p>设方程 $f_{l,r,max,min}$ 表示 消除区间 $[l,r]$ 使其剩下的最大值为 <code>max</code> ，最小值为 <code>min</code> 的最小代价。$g_{l,r}$ 表示 区间$[l,r]$中全消的最小代价。</p>
+<h2 id="d-remove"><a class="markdownIt-Anchor" href="#d-remove"></a> D. remove</h2>
+<hr />
+<p>区间 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span>。求</p>
+<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>m</mi><mi>i</mi><mi>n</mi><mrow><mo fence="true">{</mo><mtable rowspacing="0.24999999999999992em" columnalign="right" columnspacing=""><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>a</mi><mo>×</mo><mi>k</mi><mo>+</mo><mi>b</mi><mo>×</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>k</mi></munderover><mo fence="false">(</mo><mi>m</mi><mi>a</mi><msub><mi>x</mi><mi>i</mi></msub><mo>−</mo><mi>m</mi><mi>i</mi><msub><mi>n</mi><mi>i</mi></msub><mo fence="false">)</mo></mrow></mstyle></mtd></mtr></mtable><mo fence="true">}</mo></mrow></mrow><annotation encoding="application/x-tex">min
+\left\{
+\begin{aligned} 
+a \times k + b\times\sum\limits_{i=1}^{k} \Big (max_i-min_i\Big)
+\end{aligned}
+\right\}
+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.60004em;vertical-align:-1.55002em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.05002em;"><span style="top:-2.49999em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-2.20499em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-3.15001em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.00501em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.30002em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.55002em;"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.9568910000000002em;"><span style="top:-3.9568909999999997em;"><span class="pstrut" style="height:3.836113em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8361130000000003em;"><span style="top:-1.872331em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.277669em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="delimsizing size2">(</span></span><span class="mord mathnormal">m</span><span class="mord mathnormal">a</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">i</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="delimsizing size2">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.4568910000000002em;"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.05002em;"><span style="top:-2.49999em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎭</span></span></span><span style="top:-2.20499em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-3.15001em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎬</span></span></span><span style="top:-4.00501em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.30002em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎫</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.55002em;"><span></span></span></span></span></span></span></span></span></span></span></span></p>
+<p>设方程 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub></mrow><annotation encoding="application/x-tex">f_{l,r,max,min}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span> 表示 消除区间 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[l,r]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">[</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mclose">]</span></span></span></span> 使其剩下的最大值为 <code>max</code> ，最小值为 <code>min</code> 的最小代价。<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>g</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi></mrow></msub></mrow><annotation encoding="application/x-tex">g_{l,r}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span> 表示 区间<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[l,r]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">[</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mclose">]</span></span></span></span>中全消的最小代价。</p>
 <p>所以</p>
 <blockquote>
 <ol>
-<li><h6 id="初始化"><a href="#初始化" class="headerlink" title="初始化 :"></a>初始化 :</h6></li>
+<li>
+<h6 id="初始化"><a class="markdownIt-Anchor" href="#初始化"></a> 初始化 :</h6>
+</li>
 </ol>
-<p>$g_{l,r}&#x3D;min${$f_{l,r,max,min}+a+b\times (r-l)^2$}</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>g</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi></mrow></msub><mo>=</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow><annotation encoding="application/x-tex">g_{l,r}=min</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span></span></span></span>{<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo>+</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>×</mo><mo stretchy="false">(</mo><mi>r</mi><mo>−</mo><mi>l</mi><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">f_{l,r,max,min}+a+b\times (r-l)^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>}</p>
 <ol start="2">
-<li><h6 id="转移"><a href="#转移" class="headerlink" title="转移"></a>转移</h6></li>
+<li>
+<h6 id="转移"><a class="markdownIt-Anchor" href="#转移"></a> 转移</h6>
+</li>
 </ol>
 <p>左边空或右边空 :</p>
 <ul>
-<li>$f_{l,r,max,min}&#x3D;\min{g_{l,k} + f_{k+1,r,max,min}}$</li>
-<li>$f_{l,r,max,min}&#x3D;\min{g_{k+1,r} + f_{l,k,max,min}}$</li>
+<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo>=</mo><mi>min</mi><mo>⁡</mo><mo stretchy="false">{</mo><msub><mi>g</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>k</mi></mrow></msub><mo>+</mo><msub><mi>f</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">f_{l,r,max,min}=\min\{g_{l,k} + f_{k+1,r,max,min}\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.036108em;vertical-align:-0.286108em;"></span><span class="mop">min</span><span class="mopen">{</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.036108em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mclose">}</span></span></span></span></li>
+<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo>=</mo><mi>min</mi><mo>⁡</mo><mo stretchy="false">{</mo><msub><mi>g</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn><mo separator="true">,</mo><mi>r</mi></mrow></msub><mo>+</mo><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>k</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">f_{l,r,max,min}=\min\{g_{k+1,r} + f_{l,k,max,min}\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.036108em;vertical-align:-0.286108em;"></span><span class="mop">min</span><span class="mopen">{</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.036108em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mclose">}</span></span></span></span></li>
 </ul>
 <p>两边都空</p>
 <ul>
-<li>$f_{l,r,max,min}&#x3D;\min{f_{l,r,max,min} + f_{k+1,r,max,min}}$</li>
+<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo>=</mo><mi>min</mi><mo>⁡</mo><mo stretchy="false">{</mo><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo>+</mo><msub><mi>f</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">f_{l,r,max,min}=\min\{f_{l,r,max,min} + f_{k+1,r,max,min}\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.036108em;vertical-align:-0.286108em;"></span><span class="mop">min</span><span class="mopen">{</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.036108em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mclose">}</span></span></span></span></li>
 </ul>
 <p>端点刷表</p>
 <ul>
-<li>$f_{l,r+1,max(max,w_l),min(min,w_r)}&#x3D;f_{l,r,max,min}$</li>
+<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo stretchy="false">(</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><msub><mi>w</mi><mi>l</mi></msub><mo stretchy="false">)</mo><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi><mo stretchy="false">(</mo><mi>m</mi><mi>i</mi><mi>n</mi><mo separator="true">,</mo><msub><mi>w</mi><mi>r</mi></msub><mo stretchy="false">)</mo></mrow></msub><mo>=</mo><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub></mrow><annotation encoding="application/x-tex">f_{l,r+1,max(max,w_l),min(min,w_r)}=f_{l,r,max,min}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.04964em;vertical-align:-0.3551999999999999em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.34480000000000005em;"><span style="top:-2.5198em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3487714285714287em;margin-left:-0.02691em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em;"><span></span></span></span></span></span></span><span class="mclose mtight">)</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span><span class="mpunct mtight">,</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.16454285714285719em;"><span style="top:-2.357em;margin-left:-0.02691em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3551999999999999em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span></li>
 </ul>
 <ol start="3">
-<li><h6 id="g"><a href="#g" class="headerlink" title="g?"></a>g?</h6><p> $g_{l,r}&#x3D;min${$f_{l,r,max,min}+a+b\times(max-min)^2$}</p>
+<li>
+<h6 id="g"><a class="markdownIt-Anchor" href="#g"></a> g?</h6>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>g</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi></mrow></msub><mo>=</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow><annotation encoding="application/x-tex">g_{l,r}=min</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span></span></span></span>{<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo>+</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>×</mo><mo stretchy="false">(</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo>−</mo><mi>m</mi><mi>i</mi><mi>n</mi><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">f_{l,r,max,min}+a+b\times(max-min)^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">m</span><span class="mord mathnormal">a</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>}</p>
+</li>
+<li>
+<h6 id="离散化后-on4"><a class="markdownIt-Anchor" href="#离散化后-on4"></a> 离散化后 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mn>4</mn></msup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(n^4)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></h6>
 </li>
-<li><h6 id="离散化后-O-n-4"><a href="#离散化后-O-n-4" class="headerlink" title="离散化后 $O(n^4)$"></a>离散化后 $O(n^4)$</h6></li>
 </ol>
 </blockquote>
-<hr>
-<h2 id="问题："><a href="#问题：" class="headerlink" title="问题："></a>问题：</h2><ol>
-<li><h5 id="手抄斩手，使用CV大发。"><a href="#手抄斩手，使用CV大发。" class="headerlink" title="手抄斩手，使用CV大发。"></a>手抄斩手，使用CV大发。</h5></li>
-<li><h5 id="O2-要看返回值。"><a href="#O2-要看返回值。" class="headerlink" title="$O2$ 要看返回值。"></a>$O2$ 要看返回值。</h5></li>
-<li><h5 id="对拍数据要把时间卡到满，不能放水。"><a href="#对拍数据要把时间卡到满，不能放水。" class="headerlink" title="对拍数据要把时间卡到满，不能放水。"></a>对拍数据要把时间卡到满，不能放水。</h5></li>
+<hr />
+<h2 id="问题"><a class="markdownIt-Anchor" href="#问题"></a> 问题：</h2>
+<ol>
+<li>
+<h5 id="手抄斩手使用cv大发"><a class="markdownIt-Anchor" href="#手抄斩手使用cv大发"></a> 手抄斩手，使用CV大发。</h5>
+</li>
+<li>
+<h5 id="o2-要看返回值"><a class="markdownIt-Anchor" href="#o2-要看返回值"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mn>2</mn></mrow><annotation encoding="application/x-tex">O2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mord">2</span></span></span></span> 要看返回值。</h5>
+</li>
+<li>
+<h5 id="对拍数据要把时间卡到满不能放水"><a class="markdownIt-Anchor" href="#对拍数据要把时间卡到满不能放水"></a> 对拍数据要把时间卡到满，不能放水。</h5>
+</li>
 </ol>
 
                 </div>
@@ -437,7 +466,7 @@ <h2 id="问题："><a href="#问题：" class="headerlink" title="问题："></a
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+              window.KeepCommentPlugin.walineOptions.serverURL = 'blog-1uv64df2r-liaohengfengs-projects.vercel.app'
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@@ -475,7 +504,7 @@ <h2 id="问题："><a href="#问题：" class="headerlink" title="问题："></a
             <div class="pc-post-toc left-toc">
                 <div class="post-toc-wrap border-box">
     <div class="post-toc border-box">
-        <ol class="nav"><li class="nav-item nav-level-1"><a class="nav-link" href="#23-12-9-%E8%80%83%E8%AF%95%E6%80%BB%E7%BB%93"><span class="nav-text">$23.12.9$ 考试总结</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#%E5%88%86%E6%95%B0-60-%EF%BC%88-50-10-0-0"><span class="nav-text">分数 : $60$ （$50+10+0+0$)</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#A-stick"><span class="nav-text">A. stick</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#B-game"><span class="nav-text">B. game</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#C-noip"><span class="nav-text">C.  noip</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#D-remove"><span class="nav-text">D. remove</span></a><ol class="nav-child"><li class="nav-item nav-level-6"><a class="nav-link" href="#%E5%88%9D%E5%A7%8B%E5%8C%96"><span class="nav-text">初始化 :</span></a></li><li class="nav-item nav-level-6"><a class="nav-link" href="#%E8%BD%AC%E7%A7%BB"><span class="nav-text">转移</span></a></li><li class="nav-item nav-level-6"><a class="nav-link" href="#g"><span class="nav-text">g?</span></a></li><li class="nav-item nav-level-6"><a class="nav-link" href="#%E7%A6%BB%E6%95%A3%E5%8C%96%E5%90%8E-O-n-4"><span class="nav-text">离散化后 $O(n^4)$</span></a></li></ol></li></ol></li></ol></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#%E9%97%AE%E9%A2%98%EF%BC%9A"><span class="nav-text">问题：</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%89%8B%E6%8A%84%E6%96%A9%E6%89%8B%EF%BC%8C%E4%BD%BF%E7%94%A8CV%E5%A4%A7%E5%8F%91%E3%80%82"><span class="nav-text">手抄斩手，使用CV大发。</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#O2-%E8%A6%81%E7%9C%8B%E8%BF%94%E5%9B%9E%E5%80%BC%E3%80%82"><span class="nav-text">$O2$ 要看返回值。</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E5%AF%B9%E6%8B%8D%E6%95%B0%E6%8D%AE%E8%A6%81%E6%8A%8A%E6%97%B6%E9%97%B4%E5%8D%A1%E5%88%B0%E6%BB%A1%EF%BC%8C%E4%B8%8D%E8%83%BD%E6%94%BE%E6%B0%B4%E3%80%82"><span class="nav-text">对拍数据要把时间卡到满，不能放水。</span></a></li></ol></li></ol></li></ol></li></ol></li></ol>
+        <ol class="nav"><li class="nav-item nav-level-1"><a class="nav-link" href="#23129-%E8%80%83%E8%AF%95%E6%80%BB%E7%BB%93"><span class="nav-text"> 23.12.923.12.923.12.9 考试总结</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#%E5%88%86%E6%95%B0-60-501000"><span class="nav-text"> 分数 : 606060 （50+10+0+050+10+0+050+10+0+0)</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#a-stick"><span class="nav-text"> A. stick</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#b-game"><span class="nav-text"> B. game</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#c-noip"><span class="nav-text"> C.  noip</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#d-remove"><span class="nav-text"> D. remove</span></a><ol class="nav-child"><li class="nav-item nav-level-6"><a class="nav-link" href="#%E5%88%9D%E5%A7%8B%E5%8C%96"><span class="nav-text"> 初始化 :</span></a></li><li class="nav-item nav-level-6"><a class="nav-link" href="#%E8%BD%AC%E7%A7%BB"><span class="nav-text"> 转移</span></a></li><li class="nav-item nav-level-6"><a class="nav-link" href="#g"><span class="nav-text"> g?</span></a></li><li class="nav-item nav-level-6"><a class="nav-link" href="#%E7%A6%BB%E6%95%A3%E5%8C%96%E5%90%8E-on4"><span class="nav-text"> 离散化后 O(n4)O(n^4)O(n4)</span></a></li></ol></li></ol></li></ol></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#%E9%97%AE%E9%A2%98"><span class="nav-text"> 问题：</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%89%8B%E6%8A%84%E6%96%A9%E6%89%8B%E4%BD%BF%E7%94%A8cv%E5%A4%A7%E5%8F%91"><span class="nav-text"> 手抄斩手，使用CV大发。</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#o2-%E8%A6%81%E7%9C%8B%E8%BF%94%E5%9B%9E%E5%80%BC"><span class="nav-text"> O2O2O2 要看返回值。</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E5%AF%B9%E6%8B%8D%E6%95%B0%E6%8D%AE%E8%A6%81%E6%8A%8A%E6%97%B6%E9%97%B4%E5%8D%A1%E5%88%B0%E6%BB%A1%E4%B8%8D%E8%83%BD%E6%94%BE%E6%B0%B4"><span class="nav-text"> 对拍数据要把时间卡到满，不能放水。</span></a></li></ol></li></ol></li></ol></li></ol></li></ol>
     </div>
 </div>
 
@@ -653,7 +682,7 @@ <h2 id="问题："><a href="#问题：" class="headerlink" title="问题："></a
             <div class="tablet-post-toc">
                 <div class="post-toc-wrap border-box">
     <div class="post-toc border-box">
-        <ol class="nav"><li class="nav-item nav-level-1"><a class="nav-link" href="#23-12-9-%E8%80%83%E8%AF%95%E6%80%BB%E7%BB%93"><span class="nav-text">$23.12.9$ 考试总结</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#%E5%88%86%E6%95%B0-60-%EF%BC%88-50-10-0-0"><span class="nav-text">分数 : $60$ （$50+10+0+0$)</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#A-stick"><span class="nav-text">A. stick</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#B-game"><span class="nav-text">B. game</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#C-noip"><span class="nav-text">C.  noip</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#D-remove"><span class="nav-text">D. remove</span></a><ol class="nav-child"><li class="nav-item nav-level-6"><a class="nav-link" href="#%E5%88%9D%E5%A7%8B%E5%8C%96"><span class="nav-text">初始化 :</span></a></li><li class="nav-item nav-level-6"><a class="nav-link" href="#%E8%BD%AC%E7%A7%BB"><span class="nav-text">转移</span></a></li><li class="nav-item nav-level-6"><a class="nav-link" href="#g"><span class="nav-text">g?</span></a></li><li class="nav-item nav-level-6"><a class="nav-link" href="#%E7%A6%BB%E6%95%A3%E5%8C%96%E5%90%8E-O-n-4"><span class="nav-text">离散化后 $O(n^4)$</span></a></li></ol></li></ol></li></ol></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#%E9%97%AE%E9%A2%98%EF%BC%9A"><span class="nav-text">问题：</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%89%8B%E6%8A%84%E6%96%A9%E6%89%8B%EF%BC%8C%E4%BD%BF%E7%94%A8CV%E5%A4%A7%E5%8F%91%E3%80%82"><span class="nav-text">手抄斩手，使用CV大发。</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#O2-%E8%A6%81%E7%9C%8B%E8%BF%94%E5%9B%9E%E5%80%BC%E3%80%82"><span class="nav-text">$O2$ 要看返回值。</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E5%AF%B9%E6%8B%8D%E6%95%B0%E6%8D%AE%E8%A6%81%E6%8A%8A%E6%97%B6%E9%97%B4%E5%8D%A1%E5%88%B0%E6%BB%A1%EF%BC%8C%E4%B8%8D%E8%83%BD%E6%94%BE%E6%B0%B4%E3%80%82"><span class="nav-text">对拍数据要把时间卡到满，不能放水。</span></a></li></ol></li></ol></li></ol></li></ol></li></ol>
+        <ol class="nav"><li class="nav-item nav-level-1"><a class="nav-link" href="#23129-%E8%80%83%E8%AF%95%E6%80%BB%E7%BB%93"><span class="nav-text"> 23.12.923.12.923.12.9 考试总结</span></a><ol class="nav-child"><li class="nav-item nav-level-3"><a class="nav-link" href="#%E5%88%86%E6%95%B0-60-501000"><span class="nav-text"> 分数 : 606060 （50+10+0+050+10+0+050+10+0+0)</span></a></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#a-stick"><span class="nav-text"> A. stick</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#b-game"><span class="nav-text"> B. game</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#c-noip"><span class="nav-text"> C.  noip</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#d-remove"><span class="nav-text"> D. remove</span></a><ol class="nav-child"><li class="nav-item nav-level-6"><a class="nav-link" href="#%E5%88%9D%E5%A7%8B%E5%8C%96"><span class="nav-text"> 初始化 :</span></a></li><li class="nav-item nav-level-6"><a class="nav-link" href="#%E8%BD%AC%E7%A7%BB"><span class="nav-text"> 转移</span></a></li><li class="nav-item nav-level-6"><a class="nav-link" href="#g"><span class="nav-text"> g?</span></a></li><li class="nav-item nav-level-6"><a class="nav-link" href="#%E7%A6%BB%E6%95%A3%E5%8C%96%E5%90%8E-on4"><span class="nav-text"> 离散化后 O(n4)O(n^4)O(n4)</span></a></li></ol></li></ol></li></ol></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#%E9%97%AE%E9%A2%98"><span class="nav-text"> 问题：</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%89%8B%E6%8A%84%E6%96%A9%E6%89%8B%E4%BD%BF%E7%94%A8cv%E5%A4%A7%E5%8F%91"><span class="nav-text"> 手抄斩手，使用CV大发。</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#o2-%E8%A6%81%E7%9C%8B%E8%BF%94%E5%9B%9E%E5%80%BC"><span class="nav-text"> O2O2O2 要看返回值。</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E5%AF%B9%E6%8B%8D%E6%95%B0%E6%8D%AE%E8%A6%81%E6%8A%8A%E6%97%B6%E9%97%B4%E5%8D%A1%E5%88%B0%E6%BB%A1%E4%B8%8D%E8%83%BD%E6%94%BE%E6%B0%B4"><span class="nav-text"> 对拍数据要把时间卡到满，不能放水。</span></a></li></ol></li></ol></li></ol></li></ol></li></ol>
     </div>
 </div>
 
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-                    <p>﻿## 1. 状态<br>$\ \ \ \ $区间$DP$的状态一般 <code>设 f[l][r] 表示区间 [l][r] ....</code>。但有些时候可以直接设 $f_i$ 表示 $[1,i]$…。</p>
-<p>$\ \ \ \ $转移的时候会依靠断点，即 $f[l][r]&#x3D;min&#x2F;max${$f[l][k]+f[k+1][r]$}。</p>
-<p>$\ \ \ \ $常见的优化有两种 : </p>
+                    <p>## 1. 状态<br />
+$\ \ \ \ <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>区间</mtext></mrow><annotation encoding="application/x-tex">区间</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">区</span><span class="mord cjk_fallback">间</span></span></span></span>DP$的状态一般 <code>设 f[l][r] 表示区间 [l][r] ....</code>。但有些时候可以直接设 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">f_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> 表示 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mn>1</mn><mo separator="true">,</mo><mi>i</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[1,i]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">[</span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">i</span><span class="mclose">]</span></span></span></span>…。</p>
+<p>$\ \ \ \ $转移的时候会依靠断点，即 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mo stretchy="false">[</mo><mi>l</mi><mo stretchy="false">]</mo><mo stretchy="false">[</mo><mi>r</mi><mo stretchy="false">]</mo><mo>=</mo><mi>m</mi><mi>i</mi><mi>n</mi><mi mathvariant="normal">/</mi><mi>m</mi><mi>a</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">f[l][r]=min/max</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mopen">[</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mclose">]</span><span class="mopen">[</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mclose">]</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span><span class="mord">/</span><span class="mord mathnormal">m</span><span class="mord mathnormal">a</span><span class="mord mathnormal">x</span></span></span></span>{<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mo stretchy="false">[</mo><mi>l</mi><mo stretchy="false">]</mo><mo stretchy="false">[</mo><mi>k</mi><mo stretchy="false">]</mo><mo>+</mo><mi>f</mi><mo stretchy="false">[</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo stretchy="false">]</mo><mo stretchy="false">[</mo><mi>r</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">f[l][k]+f[k+1][r]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mopen">[</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mclose">]</span><span class="mopen">[</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mclose">]</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mopen">[</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">]</span><span class="mopen">[</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mclose">]</span></span></span></span>}。</p>
+<p>$\ \ \ \ $常见的优化有两种 :</p>
 <ul>
-<li><pre><code>     	1. 四边形不等式
+<li>
+<pre><code>   	1. 四边形不等式
 </code></pre>
 </li>
-<li><pre><code>     	2. 递推
+<li>
+<pre><code>   	2. 递推
 </code></pre>
 </li>
 </ul>
-<h2 id="2-例题"><a href="#2-例题" class="headerlink" title="2.例题"></a>2.例题</h2><ol>
-<li><h5 id="表达式的亿种可能性"><a href="#表达式的亿种可能性" class="headerlink" title="表达式的亿种可能性"></a>表达式的亿种可能性</h5><blockquote>
+<h2 id="2例题"><a class="markdownIt-Anchor" href="#2例题"></a> 2.例题</h2>
+<ol>
+<li>
+<h5 id="表达式的亿种可能性"><a class="markdownIt-Anchor" href="#表达式的亿种可能性"></a> 表达式的亿种可能性</h5>
+<blockquote>
 <p>直接算是不行的，我们要去乘上每一个数的代价。</p>
 <p>原因是 加法和减法可以交换顺序。</p>
-<p><em>eg.</em> : $(1+1)+2\ &#x3D;\ 1+(1+2)$</p>
+<p><em>eg.</em> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mo>+</mo><mn>2</mn><mtext> </mtext><mo>=</mo><mtext> </mtext><mn>1</mn><mo>+</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(1+1)+2\ =\ 1+(1+2)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">2</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span></span></span></span></p>
 <p>乘法具有分配率。</p>
 </blockquote>
 </li>
-<li><h5 id="有味道的数字"><a href="#有味道的数字" class="headerlink" title="有味道的数字"></a>有味道的数字</h5><blockquote>
-<p>爆搜发现 $max\ ans\ &#x3D;\ 11$ , 且 $当且仅当\ n&#x3D;3\ 或\ n&#x3D;7\ $ 时，$ans&#x3D;-1$。</p>
-<p>用 $f[i]\ (f:vector)$ 存 $ans_n\ &#x3D;\ i$ 的 $n$。</p>
+<li>
+<h5 id="有味道的数字"><a class="markdownIt-Anchor" href="#有味道的数字"></a> 有味道的数字</h5>
+<blockquote>
+<p>爆搜发现 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi><mi>a</mi><mi>x</mi><mtext> </mtext><mi>a</mi><mi>n</mi><mi>s</mi><mtext> </mtext><mo>=</mo><mtext> </mtext><mn>11</mn></mrow><annotation encoding="application/x-tex">max\ ans\ =\ 11</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">a</span><span class="mord mathnormal">x</span><span class="mspace"> </span><span class="mord mathnormal">a</span><span class="mord mathnormal">n</span><span class="mord mathnormal">s</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord">1</span></span></span></span> , 且 $当且仅当\ n=3\ 或\ n=7\ $ 时，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo>−</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">ans=-1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">a</span><span class="mord mathnormal">n</span><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">−</span><span class="mord">1</span></span></span></span>。</p>
+<p>用 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mo stretchy="false">[</mo><mi>i</mi><mo stretchy="false">]</mo><mtext> </mtext><mo stretchy="false">(</mo><mi>f</mi><mo>:</mo><mi>v</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">f[i]\ (f:vector)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mopen">[</span><span class="mord mathnormal">i</span><span class="mclose">]</span><span class="mspace"> </span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mord mathnormal">e</span><span class="mord mathnormal">c</span><span class="mord mathnormal">t</span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mclose">)</span></span></span></span> 存 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><mi>n</mi><msub><mi>s</mi><mi>n</mi></msub><mtext> </mtext><mo>=</mo><mtext> </mtext><mi>i</mi></mrow><annotation encoding="application/x-tex">ans_n\ =\ i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord mathnormal">a</span><span class="mord mathnormal">n</span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">i</span></span></span></span> 的 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span>。</p>
 </blockquote>
 </li>
-<li><h5 id="守卫"><a href="#守卫" class="headerlink" title="守卫"></a>守卫</h5><blockquote>
+<li>
+<h5 id="守卫"><a class="markdownIt-Anchor" href="#守卫"></a> 守卫</h5>
+<blockquote>
 <p>题目具有迷惑性，容易想成单调栈。</p>
 <p>但发现加入点后需要一段区间的信息。</p>
-<p>所以直接区间 $DP$。</p>
-<p>枚举 $r$ ,  $l\ &#x3D;\ r\ \rightarrow\ 1$，递推。</p>
+<p>所以直接区间 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span>。</p>
+<p>枚举 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi></mrow><annotation encoding="application/x-tex">r</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span></span></span></span> ,  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mtext> </mtext><mo>=</mo><mtext> </mtext><mi>r</mi><mtext> </mtext><mo>→</mo><mtext> </mtext><mn>1</mn></mrow><annotation encoding="application/x-tex">l\ =\ r\ \rightarrow\ 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">→</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span>，递推。</p>
 </blockquote>
 </li>
-<li><h5 id="祖玛游戏-单调栈"><a href="#祖玛游戏-单调栈" class="headerlink" title="祖玛游戏 &amp;&amp; 单调栈"></a>祖玛游戏 &amp;&amp; 单调栈</h5><blockquote>
-<p>**打不过 (二维状态表示不完全) 就加入 (把表示不完全的信息加入状态)**。</p>
+<li>
+<h5 id="祖玛游戏-单调栈"><a class="markdownIt-Anchor" href="#祖玛游戏-单调栈"></a> 祖玛游戏 &amp;&amp; 单调栈</h5>
+<blockquote>
+<p><strong>打不过 (二维状态表示不完全) 就加入 (把表示不完全的信息加入状态)</strong>。</p>
 <p><strong>实在不行还能加辅助数组</strong>。</p>
-<p>**如果循环有后效性，或者循环讨论复杂，用 $dfs$**。</p>
+<p><strong>如果循环有后效性，或者循环讨论复杂，用 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi><mi>f</mi><mi>s</mi></mrow><annotation encoding="application/x-tex">dfs</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord mathnormal">s</span></span></span></span></strong>。</p>
 <p>思想来源于二分 ： 把原问题转换为可行性问题</p>
 </blockquote>
 </li>
-<li><h5 id="括号序列"><a href="#括号序列" class="headerlink" title="括号序列"></a>括号序列</h5><blockquote>
+<li>
+<h5 id="括号序列"><a class="markdownIt-Anchor" href="#括号序列"></a> 括号序列</h5>
+<blockquote>
 <p>算重了怎么办？ 学习 $Catalan $ <em>!</em></p>
-<p>我们知道<br>$$<br>C_{n+1}&#x3D;C_0C_n+C_1C_{n-1}+C_2C_{n-2}+…+C_{n-1}C_1+C_nC_0\ (注意这里没有重复)<br>$$<br>同理 , <img  
+<p>我们知道</p>
+<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>C</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><msub><mi>C</mi><mn>0</mn></msub><msub><mi>C</mi><mi>n</mi></msub><mo>+</mo><msub><mi>C</mi><mn>1</mn></msub><msub><mi>C</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>C</mi><mn>2</mn></msub><msub><mi>C</mi><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow></msub><mo>+</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo>+</mo><msub><mi>C</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><msub><mi>C</mi><mn>1</mn></msub><mo>+</mo><msub><mi>C</mi><mi>n</mi></msub><msub><mi>C</mi><mn>0</mn></msub><mtext> </mtext><mo stretchy="false">(</mo><mtext>注意这里没有重复</mtext><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">C_{n+1}=C_0C_n+C_1C_{n-1}+C_2C_{n-2}+...+C_{n-1}C_1+C_nC_0\ (注意这里没有重复)
+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.891661em;vertical-align:-0.208331em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.891661em;vertical-align:-0.208331em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.891661em;vertical-align:-0.208331em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.891661em;vertical-align:-0.208331em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace"> </span><span class="mopen">(</span><span class="mord cjk_fallback">注</span><span class="mord cjk_fallback">意</span><span class="mord cjk_fallback">这</span><span class="mord cjk_fallback">里</span><span class="mord cjk_fallback">没</span><span class="mord cjk_fallback">有</span><span class="mord cjk_fallback">重</span><span class="mord cjk_fallback">复</span><span class="mclose">)</span></span></span></span></span></p>
+<p>同理 , <img  
                        lazyload
                        alt="image"
                        data-src="https://cdn.luogu.com.cn/upload/image_hosting/iyn4t3lm.png"
-                       
+                        alt="" 
                  ></p>
 </blockquote>
 </li>
 </ol>
-<hr>
-<hr>
-<h2 id="3-好题"><a href="#3-好题" class="headerlink" title="3. 好题"></a>3. 好题</h2><ol>
-<li><p><a class="link"   target="_blank" rel="noopener" href="https://vj.imken.moe/problem/HDU-2476/origin" >HDU - 2476 <i class="fas fa-external-link-alt"></i></a></p>
+<hr />
+<hr />
+<h2 id="3-好题"><a class="markdownIt-Anchor" href="#3-好题"></a> 3. 好题</h2>
+<ol>
+<li>
+<p><a class="link"   target="_blank" rel="noopener" href="https://vj.imken.moe/problem/HDU-2476/origin" >HDU - 2476 <i class="fas fa-external-link-alt"></i></a></p>
 <blockquote>
 <p>(空 -&gt; B) - (A -&gt; B)</p>
 </blockquote>
 </li>
-<li><p><a class="link"   target="_blank" rel="noopener" href="https://vj.imken.moe/problem/CodeForces-149D/origin" >CodeForces - 149D <i class="fas fa-external-link-alt"></i></a></p>
+<li>
+<p><a class="link"   target="_blank" rel="noopener" href="https://vj.imken.moe/problem/CodeForces-149D/origin" >CodeForces - 149D <i class="fas fa-external-link-alt"></i></a></p>
 <blockquote>
 <p>高维状态 ：</p>
-<p>$f_{l,r,x,y}$ 表示 区间$[l,r]$中，左端点是$x$,右端点是$y$的方案数。(左右端点均hash过)。</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi></mrow></msub></mrow><annotation encoding="application/x-tex">f_{l,r,x,y}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.03588em;">y</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span> 表示 区间<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[l,r]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">[</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mclose">]</span></span></span></span>中，左端点是<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span>,右端点是<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span>的方案数。(左右端点均hash过)。</p>
 </blockquote>
 </li>
-<li><p><a class="link"   target="_blank" rel="noopener" href="https://www.luogu.com.cn/problem/P3147" >262144  P<i class="fas fa-external-link-alt"></i></a></p>
+<li>
+<p><a class="link"   target="_blank" rel="noopener" href="https://www.luogu.com.cn/problem/P3147" >262144  P<i class="fas fa-external-link-alt"></i></a></p>
 <blockquote>
-<p>状态不同于普通区间$DP$，类倍增，设的是<br>$$<br>f_{i,k}\ 表示\ 从\ i\ 开始直到合出\ k\ 所需的最小长度。<br>$$</p>
+<p>状态不同于普通区间<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span>，类倍增，设的是</p>
+<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>k</mi></mrow></msub><mtext> 表示 从 </mtext><mi>i</mi><mtext> 开始直到合出 </mtext><mi>k</mi><mtext> 所需的最小长度。</mtext></mrow><annotation encoding="application/x-tex">f_{i,k}\ 表示\ 从\ i\ 开始直到合出\ k\ 所需的最小长度。
+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace"> </span><span class="mord cjk_fallback">表</span><span class="mord cjk_fallback">示</span><span class="mspace"> </span><span class="mord cjk_fallback">从</span><span class="mspace"> </span><span class="mord mathnormal">i</span><span class="mspace"> </span><span class="mord cjk_fallback">开</span><span class="mord cjk_fallback">始</span><span class="mord cjk_fallback">直</span><span class="mord cjk_fallback">到</span><span class="mord cjk_fallback">合</span><span class="mord cjk_fallback">出</span><span class="mspace"> </span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace"> </span><span class="mord cjk_fallback">所</span><span class="mord cjk_fallback">需</span><span class="mord cjk_fallback">的</span><span class="mord cjk_fallback">最</span><span class="mord cjk_fallback">小</span><span class="mord cjk_fallback">长</span><span class="mord cjk_fallback">度</span><span class="mord cjk_fallback">。</span></span></span></span></span></p>
 </blockquote>
 </li>
 <li></li>
 </ol>
-<hr>
-<h2 id="4-总结"><a href="#4-总结" class="headerlink" title="4.总结"></a>4.总结</h2><blockquote>
+<hr />
+<h2 id="4总结"><a class="markdownIt-Anchor" href="#4总结"></a> 4.总结</h2>
+<blockquote>
 <p>状态的根本问题是 : <strong>如何用最简洁的信息使得答案能够被(不重复)，不遗漏的算出来。</strong></p>
-<p>即使是 $f_{l,r}$ 也是逃不过的。</p>
-<p>区间 $DP$ 一般满足 <code>一些局部最优解能凑出全局最优解</code>，不行的话就得加维度。</p>
+<p>即使是 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi></mrow></msub></mrow><annotation encoding="application/x-tex">f_{l,r}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span> 也是逃不过的。</p>
+<p>区间 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span> 一般满足 <code>一些局部最优解能凑出全局最优解</code>，不行的话就得加维度。</p>
 </blockquote>
 
                 </div>
@@ -455,7 +480,7 @@ <h2 id="4-总结"><a href="#4-总结" class="headerlink" title="4.总结"></a>4.
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@@ -493,7 +518,7 @@ <h2 id="4-总结"><a href="#4-总结" class="headerlink" title="4.总结"></a>4.
             <div class="pc-post-toc left-toc">
                 <div class="post-toc-wrap border-box">
     <div class="post-toc border-box">
-        <ol class="nav"><li class="nav-item nav-level-2"><a class="nav-link" href="#2-%E4%BE%8B%E9%A2%98"><span class="nav-text">2.例题</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E8%A1%A8%E8%BE%BE%E5%BC%8F%E7%9A%84%E4%BA%BF%E7%A7%8D%E5%8F%AF%E8%83%BD%E6%80%A7"><span class="nav-text">表达式的亿种可能性</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%9C%89%E5%91%B3%E9%81%93%E7%9A%84%E6%95%B0%E5%AD%97"><span class="nav-text">有味道的数字</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E5%AE%88%E5%8D%AB"><span class="nav-text">守卫</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E7%A5%96%E7%8E%9B%E6%B8%B8%E6%88%8F-%E5%8D%95%E8%B0%83%E6%A0%88"><span class="nav-text">祖玛游戏 &amp;&amp; 单调栈</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%8B%AC%E5%8F%B7%E5%BA%8F%E5%88%97"><span class="nav-text">括号序列</span></a></li></ol></li></ol></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#3-%E5%A5%BD%E9%A2%98"><span class="nav-text">3. 好题</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#4-%E6%80%BB%E7%BB%93"><span class="nav-text">4.总结</span></a></li></ol>
+        <ol class="nav"><li class="nav-item nav-level-2"><a class="nav-link" href="#2%E4%BE%8B%E9%A2%98"><span class="nav-text"> 2.例题</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E8%A1%A8%E8%BE%BE%E5%BC%8F%E7%9A%84%E4%BA%BF%E7%A7%8D%E5%8F%AF%E8%83%BD%E6%80%A7"><span class="nav-text"> 表达式的亿种可能性</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%9C%89%E5%91%B3%E9%81%93%E7%9A%84%E6%95%B0%E5%AD%97"><span class="nav-text"> 有味道的数字</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E5%AE%88%E5%8D%AB"><span class="nav-text"> 守卫</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E7%A5%96%E7%8E%9B%E6%B8%B8%E6%88%8F-%E5%8D%95%E8%B0%83%E6%A0%88"><span class="nav-text"> 祖玛游戏 &amp;&amp; 单调栈</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%8B%AC%E5%8F%B7%E5%BA%8F%E5%88%97"><span class="nav-text"> 括号序列</span></a></li></ol></li></ol></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#3-%E5%A5%BD%E9%A2%98"><span class="nav-text"> 3. 好题</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#4%E6%80%BB%E7%BB%93"><span class="nav-text"> 4.总结</span></a></li></ol>
     </div>
 </div>
 
@@ -671,7 +696,7 @@ <h2 id="4-总结"><a href="#4-总结" class="headerlink" title="4.总结"></a>4.
             <div class="tablet-post-toc">
                 <div class="post-toc-wrap border-box">
     <div class="post-toc border-box">
-        <ol class="nav"><li class="nav-item nav-level-2"><a class="nav-link" href="#2-%E4%BE%8B%E9%A2%98"><span class="nav-text">2.例题</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E8%A1%A8%E8%BE%BE%E5%BC%8F%E7%9A%84%E4%BA%BF%E7%A7%8D%E5%8F%AF%E8%83%BD%E6%80%A7"><span class="nav-text">表达式的亿种可能性</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%9C%89%E5%91%B3%E9%81%93%E7%9A%84%E6%95%B0%E5%AD%97"><span class="nav-text">有味道的数字</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E5%AE%88%E5%8D%AB"><span class="nav-text">守卫</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E7%A5%96%E7%8E%9B%E6%B8%B8%E6%88%8F-%E5%8D%95%E8%B0%83%E6%A0%88"><span class="nav-text">祖玛游戏 &amp;&amp; 单调栈</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%8B%AC%E5%8F%B7%E5%BA%8F%E5%88%97"><span class="nav-text">括号序列</span></a></li></ol></li></ol></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#3-%E5%A5%BD%E9%A2%98"><span class="nav-text">3. 好题</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#4-%E6%80%BB%E7%BB%93"><span class="nav-text">4.总结</span></a></li></ol>
+        <ol class="nav"><li class="nav-item nav-level-2"><a class="nav-link" href="#2%E4%BE%8B%E9%A2%98"><span class="nav-text"> 2.例题</span></a><ol class="nav-child"><li class="nav-item nav-level-5"><a class="nav-link" href="#%E8%A1%A8%E8%BE%BE%E5%BC%8F%E7%9A%84%E4%BA%BF%E7%A7%8D%E5%8F%AF%E8%83%BD%E6%80%A7"><span class="nav-text"> 表达式的亿种可能性</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%9C%89%E5%91%B3%E9%81%93%E7%9A%84%E6%95%B0%E5%AD%97"><span class="nav-text"> 有味道的数字</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E5%AE%88%E5%8D%AB"><span class="nav-text"> 守卫</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E7%A5%96%E7%8E%9B%E6%B8%B8%E6%88%8F-%E5%8D%95%E8%B0%83%E6%A0%88"><span class="nav-text"> 祖玛游戏 &amp;&amp; 单调栈</span></a></li><li class="nav-item nav-level-5"><a class="nav-link" href="#%E6%8B%AC%E5%8F%B7%E5%BA%8F%E5%88%97"><span class="nav-text"> 括号序列</span></a></li></ol></li></ol></li></ol></li><li class="nav-item nav-level-2"><a class="nav-link" href="#3-%E5%A5%BD%E9%A2%98"><span class="nav-text"> 3. 好题</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#4%E6%80%BB%E7%BB%93"><span class="nav-text"> 4.总结</span></a></li></ol>
     </div>
 </div>
 
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index f7d858f7e..31bf83f01 100644
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+++ "b/2024/01/10/\345\233\276\350\256\272/index.html"
@@ -2,6 +2,7 @@
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+    <link rel="stylesheet" href="https://lib.baomitu.com/KaTeX/latest/katex.min.css">
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@@ -222,12 +223,12 @@
         
         
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-                <i class="icon fas fa-file-word"></i>&nbsp;<span>679 字</span>
+                <i class="icon fas fa-file-word"></i>&nbsp;<span>852 字</span>
             </span>
         
         
             <span class="meta-info-item post-min2read">
-                <i class="icon fas fa-clock"></i>&nbsp;<span>2 分钟</span>
+                <i class="icon fas fa-clock"></i>&nbsp;<span>3 分钟</span>
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@@ -248,53 +249,62 @@
                 <div class="post-content keep-markdown-body">
                     
 
-                    <h1 id="图论"><a href="#图论" class="headerlink" title="图论"></a>图论</h1><hr>
-<h2 id="0-有感而发"><a href="#0-有感而发" class="headerlink" title="$0.$有感而发"></a>$0.$有感而发</h2><blockquote>
-<p>  <em>眼睛瞎了有利于打Dijkstra。</em> by NotDeep</p>
-<p>  <em>如果这题我不会做，那么一定是图论。</em> by NotDeep</p>
+                    <h1 id="图论"><a class="markdownIt-Anchor" href="#图论"></a> 图论</h1>
+<hr />
+<h2 id="0有感而发"><a class="markdownIt-Anchor" href="#0有感而发"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0.</mn></mrow><annotation encoding="application/x-tex">0.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span><span class="mord">.</span></span></span></span>有感而发</h2>
+<blockquote>
+<p><em>眼睛瞎了有利于打Dijkstra。</em> by NotDeep</p>
+<p><em>如果这题我不会做，那么一定是图论。</em> by NotDeep</p>
 </blockquote>
-<hr>
-<h2 id="1-基本算法"><a href="#1-基本算法" class="headerlink" title="$1.$ 基本算法"></a>$1.$ 基本算法</h2><p>​	$Case\ 1:$ <strong>Dijkstra</strong></p>
+<hr />
+<h2 id="1-基本算法"><a class="markdownIt-Anchor" href="#1-基本算法"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1.</mn></mrow><annotation encoding="application/x-tex">1.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord">.</span></span></span></span> 基本算法</h2>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>1</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 1:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">1</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> <strong>Dijkstra</strong></p>
 <p>​		本质是 $贪心\ +\ DP $。</p>
 <p>​		适用于非负权权图，保证当前取出的节点的最短路是<strong>确定的</strong>，是未确定最短路的节点中<strong>最小的</strong>。</p>
-<p>​		常见题型 ： 补图，非负权图上用 <em>ta</em> ( $SPFA$已死 )。</p>
-<p>​	$Case\ 2:$ <strong>Floyd</strong></p>
-<p>​		通过 $O(n^3)$ 的时间求出任意两点的最短路。<strong>可以在负权图上使用。</strong></p>
+<p>​		常见题型 ： 补图，非负权图上用 <em>ta</em> ( <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mi>P</mi><mi>F</mi><mi>A</mi></mrow><annotation encoding="application/x-tex">SPFA</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mord mathnormal">A</span></span></span></span>已死 )。</p>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>2</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 2:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">2</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> <strong>Floyd</strong></p>
+<p>​		通过 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mn>3</mn></msup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(n^3)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span> 的时间求出任意两点的最短路。<strong>可以在负权图上使用。</strong></p>
 <p>​		可以求 <strong>最小环</strong>,<strong>传递闭包</strong>。</p>
 <p>​		下面对最小环进行说明:</p>
 <figure class="highlight c++"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//g[i][j]表示 i-&gt;j 的最短路,f[i][j]表示i-&gt;j的 边的长度</span></span><br><span class="line"><span class="comment">//把最短路拆成 (i-j) + (i&gt;k,k-&gt;j)</span></span><br><span class="line"><span class="comment">//用 dji 可以做到 O(m(n+m)log m)</span></span><br><span class="line"><span class="keyword">for</span>(<span class="type">int</span> k=<span class="number">1</span>;k&lt;=n;k++)</span><br><span class="line">&#123;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=k<span class="number">-1</span>;i++)</span><br><span class="line">        <span class="keyword">for</span>(<span class="type">int</span> j=i+<span class="number">1</span>;j&lt;=k<span class="number">-1</span>;j++)</span><br><span class="line">            ans=<span class="built_in">min</span>(ans,f[i][k]+f[k][j]+g[i][j]);</span><br><span class="line">	<span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n;i++)</span><br><span class="line">		<span class="keyword">for</span>(<span class="type">int</span> j=<span class="number">1</span>;j&lt;=n;j++)</span><br><span class="line">            g[i][j]=<span class="built_in">min</span>(g[i][k]+g[k][j],g[i][j]);</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
-
-<p>​	$Case\ 3:$ <strong>Bellman–Ford</strong></p>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>3</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 3:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">3</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> <strong>Bellman–Ford</strong></p>
 <p>​		从 <strong>边</strong> 的角度考虑最短路：</p>
 <p>​			最短路的边的个数 <strong>最多</strong> 是 n-1。</p>
 <p>​		如果 <strong>边数</strong> 大于了 n-1 , 说明原图上有负环。</p>
-<p>​		通过 $for(i&#x3D;1\ \rightarrow\ n)\ \ \ for([u,v] \in E)\ \ 松弛$ 可以让每一条边都走过。</p>
-<p>​		但实际上跑不满，所以有了 $SPFA$。</p>
-<p>​	$Case\ 4:$ <strong>SPFA</strong></p>
-<p>​		对$Case\ 3$的广搜优化，可以判负环。最坏 $O(nm)$。</p>
+<p>​		通过 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mi>o</mi><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mtext> </mtext><mo>→</mo><mtext> </mtext><mi>n</mi><mo stretchy="false">)</mo><mtext>   </mtext><mi>f</mi><mi>o</mi><mi>r</mi><mo stretchy="false">(</mo><mo stretchy="false">[</mo><mi>u</mi><mo separator="true">,</mo><mi>v</mi><mo stretchy="false">]</mo><mo>∈</mo><mi>E</mi><mo stretchy="false">)</mo><mtext>  松弛</mtext></mrow><annotation encoding="application/x-tex">for(i=1\ \rightarrow\ n)\ \ \ for([u,v] \in E)\ \ 松弛</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mopen">(</span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">→</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">n</span><span class="mclose">)</span><span class="mspace"> </span><span class="mspace"> </span><span class="mspace"> </span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mopen">(</span><span class="mopen">[</span><span class="mord mathnormal">u</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mclose">]</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mclose">)</span><span class="mspace"> </span><span class="mspace"> </span><span class="mord cjk_fallback">松</span><span class="mord cjk_fallback">弛</span></span></span></span> 可以让每一条边都走过。</p>
+<p>​		但实际上跑不满，所以有了 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mi>P</mi><mi>F</mi><mi>A</mi></mrow><annotation encoding="application/x-tex">SPFA</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mord mathnormal">A</span></span></span></span>。</p>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>4</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 4:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">4</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> <strong>SPFA</strong></p>
+<p>​		对<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>3</mn></mrow><annotation encoding="application/x-tex">Case\ 3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">3</span></span></span></span>的广搜优化，可以判负环。最坏 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mi>n</mi><mi>m</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(nm)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mord mathnormal">m</span><span class="mclose">)</span></span></span></span>。</p>
 <p>​		优化点<a class="link"   target="_blank" rel="noopener" href="https://www.luogu.com.cn/blog/Parabola/spfa-hacker-orzorz" >这儿<i class="fas fa-external-link-alt"></i></a>。</p>
-<hr>
-<h2 id="2-常见思路"><a href="#2-常见思路" class="headerlink" title="$2.$ 常见思路"></a>$2.$ 常见思路</h2><p>​	$Case\ 1:$ 分层图最短路</p>
-<p>​	$Case\ 2:$ Bellman–Ford 找负环</p>
-<p>​	$Case\ 3:$ 跑完最短路后，在 最短路图(<strong>DAG</strong>) 上$DP$。</p>
-<p>​	$Case\ 4:$ 多维最短路</p>
-<p>​	$Case\ 5:$ 拆贡献&#x2F;拆来源&#x2F;YY长啥样</p>
-<hr>
-<h2 id="3-魔改将至"><a href="#3-魔改将至" class="headerlink" title="$3.$ 魔改将至"></a>$3.$ 魔改将至</h2><p>​	$Case\ 1:$ 贪心</p>
-<p>​		以$摄像头问题2$为例：</p>
-<p>​			对于一段区间 $[l,r]$ 我们连接一条 $l \rightarrow r+1$ 的边，在连接 $i \rightarrow i-1\ ,i\in n$ 。</p>
-<p>​			令 $dist_i$ 表示覆盖区间 $[1,i-1]$ 的代价，再跑最短路即可。</p>
-<p>​	$Case\ 2:$ $DP$</p>
+<hr />
+<h2 id="2-常见思路"><a class="markdownIt-Anchor" href="#2-常见思路"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2.</mn></mrow><annotation encoding="application/x-tex">2.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">2</span><span class="mord">.</span></span></span></span> 常见思路</h2>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>1</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 1:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">1</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> 分层图最短路</p>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>2</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 2:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">2</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> Bellman–Ford 找负环</p>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>3</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 3:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">3</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> 跑完最短路后，在 最短路图(<strong>DAG</strong>) 上<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span>。</p>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>4</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 4:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">4</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> 多维最短路</p>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>5</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 5:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">5</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> 拆贡献/拆来源/YY长啥样</p>
+<hr />
+<h2 id="3-魔改将至"><a class="markdownIt-Anchor" href="#3-魔改将至"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3.</mn></mrow><annotation encoding="application/x-tex">3.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">3</span><span class="mord">.</span></span></span></span> 魔改将至</h2>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>1</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 1:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">1</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> 贪心</p>
+<p>​		以<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>摄像头问题</mtext><mn>2</mn></mrow><annotation encoding="application/x-tex">摄像头问题2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">摄</span><span class="mord cjk_fallback">像</span><span class="mord cjk_fallback">头</span><span class="mord cjk_fallback">问</span><span class="mord cjk_fallback">题</span><span class="mord">2</span></span></span></span>为例：</p>
+<p>​			对于一段区间 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[l,r]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">[</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mclose">]</span></span></span></span> 我们连接一条 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mo>→</mo><mi>r</mi><mo>+</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">l \rightarrow r+1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span> 的边，在连接 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi><mo>→</mo><mi>i</mi><mo>−</mo><mn>1</mn><mtext> </mtext><mo separator="true">,</mo><mi>i</mi><mo>∈</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">i \rightarrow i-1\ ,i\in n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.74285em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em;"></span><span class="mord">1</span><span class="mspace"> </span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span> 。</p>
+<p>​			令 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi><mi>i</mi><mi>s</mi><msub><mi>t</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">dist_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">i</span><span class="mord mathnormal">s</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> 表示覆盖区间 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mn>1</mn><mo separator="true">,</mo><mi>i</mi><mo>−</mo><mn>1</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[1,i-1]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">[</span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">]</span></span></span></span> 的代价，再跑最短路即可。</p>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>2</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 2:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">2</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span></p>
 <p>​		以 <a class="link"   target="_blank" rel="noopener" href="https://codeforces.com/problemset/problem/1216/F" >Wi-Fi<i class="fas fa-external-link-alt"></i></a> 为例：</p>
-<p>​			我们把每种操作转换为 带权区间覆盖 ， 就转回了 $摄像头2$。</p>
-<hr>
+<p>​			我们把每种操作转换为 带权区间覆盖 ， 就转回了 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>摄像头</mtext><mn>2</mn></mrow><annotation encoding="application/x-tex">摄像头2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">摄</span><span class="mord cjk_fallback">像</span><span class="mord cjk_fallback">头</span><span class="mord">2</span></span></span></span>。</p>
+<hr />
 <div STYLE="page-break-after: always;"></div>
-
-<h2 id="4-题目详解"><a href="#4-题目详解" class="headerlink" title="$4.$ 题目详解"></a>$4.$ 题目详解</h2><h4 id="1-P4366"><a href="#1-P4366" class="headerlink" title="$1.$ $P4366$"></a>$1.$ <a class="link"   target="_blank" rel="noopener" href="https://www.luogu.com.cn/problem/P4366" >$P4366$<i class="fas fa-external-link-alt"></i></a></h4><p>​	卡 $O(m\log m)$ 的 dji 的题目少的很，遇见就要珍惜。</p>
-<p>​	考虑异或性质：<br>$$<br>x \oplus z&#x3D;(x\oplus y) \oplus (y\oplus z)&lt;&#x3D;x\oplus y+y\oplus z<br>$$<br>​	对于每个节点，拆成 32 个节点: ${v|v&#x3D;x \oplus2^k,k\in N,v\leq n}$，边数就会缩短成 $n\log n+m$。</p>
-<h4 id="2-神秘力量"><a href="#2-神秘力量" class="headerlink" title="$2.$ 神秘力量"></a>$2.$ <a class="link"   target="_blank" rel="noopener" href="http://oi.nks.edu.cn:19360/zh/Problem/Details?cid=2627&tid=Q" >神秘力量<i class="fas fa-external-link-alt"></i></a></h4><p>​	先对补图进行概念阐述：</p>
-<p>​		完全图-现有图&#x3D;现有图的补图</p>
-<p>​	维护时可以用堆乱搞或用链表维护。分别为 $O(m \log m)$ 和 $O(n)$。</p>
+<h2 id="4-题目详解"><a class="markdownIt-Anchor" href="#4-题目详解"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4.</mn></mrow><annotation encoding="application/x-tex">4.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">4</span><span class="mord">.</span></span></span></span> 题目详解</h2>
+<h4 id="1-p4366"><a class="markdownIt-Anchor" href="#1-p4366"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1.</mn></mrow><annotation encoding="application/x-tex">1.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord">.</span></span></span></span> <a target="_blank" rel="noopener" href="https://www.luogu.com.cn/problem/P4366"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mn>4366</mn></mrow><annotation encoding="application/x-tex">P4366</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mord">4</span><span class="mord">3</span><span class="mord">6</span><span class="mord">6</span></span></span></span></a></h4>
+<p>​	卡 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mi>m</mi><mi>log</mi><mo>⁡</mo><mi>m</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(m\log m)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord mathnormal">m</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">m</span><span class="mclose">)</span></span></span></span> 的 dji 的题目少的很，遇见就要珍惜。</p>
+<p>​	考虑异或性质：</p>
+<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>x</mi><mo>⊕</mo><mi>z</mi><mo>=</mo><mo stretchy="false">(</mo><mi>x</mi><mo>⊕</mo><mi>y</mi><mo stretchy="false">)</mo><mo>⊕</mo><mo stretchy="false">(</mo><mi>y</mi><mo>⊕</mo><mi>z</mi><mo stretchy="false">)</mo><mo>&lt;</mo><mo>=</mo><mi>x</mi><mo>⊕</mo><mi>y</mi><mo>+</mo><mi>y</mi><mo>⊕</mo><mi>z</mi></mrow><annotation encoding="application/x-tex">x \oplus z=(x\oplus y) \oplus (y\oplus z)&lt;=x\oplus y+y\oplus z
+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⊕</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⊕</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⊕</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⊕</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&lt;</span></span><span class="base"><span class="strut" style="height:0.36687em;vertical-align:0em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⊕</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.7777700000000001em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.7777700000000001em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⊕</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span></span></span></span></span></p>
+<p>​	对于每个节点，拆成 32 个节点: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">{</mo><mi>v</mi><mi mathvariant="normal">∣</mi><mi>v</mi><mo>=</mo><mi>x</mi><mo>⊕</mo><msup><mn>2</mn><mi>k</mi></msup><mo separator="true">,</mo><mi>k</mi><mo>∈</mo><mi>N</mi><mo separator="true">,</mo><mi>v</mi><mo>≤</mo><mi>n</mi><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">\{v|v=x \oplus2^k,k\in N,v\leq n\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">{</span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mord">∣</span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⊕</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.043548em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">n</span><span class="mclose">}</span></span></span></span>，边数就会缩短成 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>+</mo><mi>m</mi></mrow><annotation encoding="application/x-tex">n\log n+m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">m</span></span></span></span>。</p>
+<h4 id="2-神秘力量"><a class="markdownIt-Anchor" href="#2-神秘力量"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2.</mn></mrow><annotation encoding="application/x-tex">2.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">2</span><span class="mord">.</span></span></span></span> <a class="link"   target="_blank" rel="noopener" href="http://oi.nks.edu.cn:19360/zh/Problem/Details?cid=2627&amp;tid=Q" >神秘力量<i class="fas fa-external-link-alt"></i></a></h4>
+<p>​	先对补图进行概念阐述：</p>
+<p>​		完全图-现有图=现有图的补图</p>
+<p>​	维护时可以用堆乱搞或用链表维护。分别为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mi>m</mi><mi>log</mi><mo>⁡</mo><mi>m</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(m \log m)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord mathnormal">m</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">m</span><span class="mclose">)</span></span></span></span> 和 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span></span>。</p>
 
                 </div>
 
@@ -410,7 +420,7 @@ <h4 id="2-神秘力量"><a href="#2-神秘力量" class="headerlink" title="$2.$
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@@ -448,7 +458,7 @@ <h4 id="2-神秘力量"><a href="#2-神秘力量" class="headerlink" title="$2.$
             <div class="pc-post-toc left-toc">
                 <div class="post-toc-wrap border-box">
     <div class="post-toc border-box">
-        <ol class="nav"><li class="nav-item nav-level-1"><a class="nav-link" href="#%E5%9B%BE%E8%AE%BA"><span class="nav-text">图论</span></a><ol class="nav-child"><li class="nav-item nav-level-2"><a class="nav-link" href="#0-%E6%9C%89%E6%84%9F%E8%80%8C%E5%8F%91"><span class="nav-text">$0.$有感而发</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#1-%E5%9F%BA%E6%9C%AC%E7%AE%97%E6%B3%95"><span class="nav-text">$1.$ 基本算法</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#2-%E5%B8%B8%E8%A7%81%E6%80%9D%E8%B7%AF"><span class="nav-text">$2.$ 常见思路</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#3-%E9%AD%94%E6%94%B9%E5%B0%86%E8%87%B3"><span class="nav-text">$3.$ 魔改将至</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#4-%E9%A2%98%E7%9B%AE%E8%AF%A6%E8%A7%A3"><span class="nav-text">$4.$ 题目详解</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#1-P4366"><span class="nav-text">$1.$ $P4366$</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#2-%E7%A5%9E%E7%A7%98%E5%8A%9B%E9%87%8F"><span class="nav-text">$2.$ 神秘力量</span></a></li></ol></li></ol></li></ol></li></ol>
+        <ol class="nav"><li class="nav-item nav-level-1"><a class="nav-link" href="#%E5%9B%BE%E8%AE%BA"><span class="nav-text"> 图论</span></a><ol class="nav-child"><li class="nav-item nav-level-2"><a class="nav-link" href="#0%E6%9C%89%E6%84%9F%E8%80%8C%E5%8F%91"><span class="nav-text"> 0.0.0.有感而发</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#1-%E5%9F%BA%E6%9C%AC%E7%AE%97%E6%B3%95"><span class="nav-text"> 1.1.1. 基本算法</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#2-%E5%B8%B8%E8%A7%81%E6%80%9D%E8%B7%AF"><span class="nav-text"> 2.2.2. 常见思路</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#3-%E9%AD%94%E6%94%B9%E5%B0%86%E8%87%B3"><span class="nav-text"> 3.3.3. 魔改将至</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#4-%E9%A2%98%E7%9B%AE%E8%AF%A6%E8%A7%A3"><span class="nav-text"> 4.4.4. 题目详解</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#1-p4366"><span class="nav-text"> 1.1.1. P4366P4366P4366</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#2-%E7%A5%9E%E7%A7%98%E5%8A%9B%E9%87%8F"><span class="nav-text"> 2.2.2. 神秘力量</span></a></li></ol></li></ol></li></ol></li></ol>
     </div>
 </div>
 
@@ -626,7 +636,7 @@ <h4 id="2-神秘力量"><a href="#2-神秘力量" class="headerlink" title="$2.$
             <div class="tablet-post-toc">
                 <div class="post-toc-wrap border-box">
     <div class="post-toc border-box">
-        <ol class="nav"><li class="nav-item nav-level-1"><a class="nav-link" href="#%E5%9B%BE%E8%AE%BA"><span class="nav-text">图论</span></a><ol class="nav-child"><li class="nav-item nav-level-2"><a class="nav-link" href="#0-%E6%9C%89%E6%84%9F%E8%80%8C%E5%8F%91"><span class="nav-text">$0.$有感而发</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#1-%E5%9F%BA%E6%9C%AC%E7%AE%97%E6%B3%95"><span class="nav-text">$1.$ 基本算法</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#2-%E5%B8%B8%E8%A7%81%E6%80%9D%E8%B7%AF"><span class="nav-text">$2.$ 常见思路</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#3-%E9%AD%94%E6%94%B9%E5%B0%86%E8%87%B3"><span class="nav-text">$3.$ 魔改将至</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#4-%E9%A2%98%E7%9B%AE%E8%AF%A6%E8%A7%A3"><span class="nav-text">$4.$ 题目详解</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#1-P4366"><span class="nav-text">$1.$ $P4366$</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#2-%E7%A5%9E%E7%A7%98%E5%8A%9B%E9%87%8F"><span class="nav-text">$2.$ 神秘力量</span></a></li></ol></li></ol></li></ol></li></ol>
+        <ol class="nav"><li class="nav-item nav-level-1"><a class="nav-link" href="#%E5%9B%BE%E8%AE%BA"><span class="nav-text"> 图论</span></a><ol class="nav-child"><li class="nav-item nav-level-2"><a class="nav-link" href="#0%E6%9C%89%E6%84%9F%E8%80%8C%E5%8F%91"><span class="nav-text"> 0.0.0.有感而发</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#1-%E5%9F%BA%E6%9C%AC%E7%AE%97%E6%B3%95"><span class="nav-text"> 1.1.1. 基本算法</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#2-%E5%B8%B8%E8%A7%81%E6%80%9D%E8%B7%AF"><span class="nav-text"> 2.2.2. 常见思路</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#3-%E9%AD%94%E6%94%B9%E5%B0%86%E8%87%B3"><span class="nav-text"> 3.3.3. 魔改将至</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#4-%E9%A2%98%E7%9B%AE%E8%AF%A6%E8%A7%A3"><span class="nav-text"> 4.4.4. 题目详解</span></a><ol class="nav-child"><li class="nav-item nav-level-4"><a class="nav-link" href="#1-p4366"><span class="nav-text"> 1.1.1. P4366P4366P4366</span></a></li><li class="nav-item nav-level-4"><a class="nav-link" href="#2-%E7%A5%9E%E7%A7%98%E5%8A%9B%E9%87%8F"><span class="nav-text"> 2.2.2. 神秘力量</span></a></li></ol></li></ol></li></ol></li></ol>
     </div>
 </div>
 
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+++ b/404.html
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-                            图论
-$0.$有感而发
-  眼睛瞎了有利于打Dijkstra。 by NotDeep
-  如果这题我不会做，那么一定是图论。 by NotDeep
+                             图论
 
+ 0.0.0.有感而发
 
-$1.$ 基本算法​	$Case\ 1:$ Dijkstra
-​		本质是 $贪心\ +\ DP ...
+眼睛瞎了有利于打Dijkstra。 by NotDeep
+如果这题我不会做，那么一定是图论。 by NotDeep
+
+
+ 1.1.1. 基本算法
+​	Case 1:Case\ 1:Case 1: Dijkstra
+...
                         
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-                            ﻿## 1. 状态$\ \ \ \ $区间$DP$的状态一般 设 f[l][r] 表示区间 [l][r] ....。但有些时候可以直接设 $f_i$ 表示 $[1,i]$…。
-$\ \ \ \ $转移的时候会依靠断点，即 $f[l][r]&#x3D;...
+                            ## 1. 状态
+$\ \ \ \ 区间区间区间DP$的状态一般 设 f[l][r] 表示区间 [l][r] ....。但有些时候可以直接设 fif_ifi​ 表示 [1,i][1,i][1,i]…。
+$\ \ \ \ $转移的时候会依靠断点，即 f...
                         
                     </div>
 
@@ -391,11 +396,12 @@ <h3 class="home-post-title border-box">
 
                     <div class="home-post-content keep-markdown-body">
                         
-                            $23.12.9$ 考试总结分数 : $60$ （$50+10+0+0$)A. stick
-先是一个数字，然后一串$0$，最后一串$8$。贪就完了。
-注意模数是 $998244$8$53$。挂分 $50pts$
-B. game
-正解爆搜。少打 bre...
+                             23.12.923.12.923.12.9 考试总结
+ 分数 : 606060 （50+10+0+050+10+0+050+10+0+0)
+ A. stick
+
+先是一个数字，然后一串000，最后一串888。贪就完了。
+注意模数是 99824499...
                         
                     </div>
 
@@ -443,13 +449,14 @@ <h3 class="home-post-title border-box">
 
                     <div class="home-post-content keep-markdown-body">
                         
-                            $CSP$ 游记Day 0
-晚上去了酒店，和另外几个人一起复习了 $Tarjan$ ，然后就睡了。
-睡觉前想着 $2.5h$ 写前两个题，后两个题打下暴力，应该能拿  一等。
+                             CSPCSPCSP 游记
+ Day 0
+
+晚上去了酒店，和另外几个人一起复习了 TarjanTarjanTarjan ，然后就睡了。
+睡觉前想着 2.5h2.5h2.5h 写前两个题，后两个题打下暴力，应该能拿  一等。
 
-Day 1 + 上午
-$7\ :\ 40$
-早上起来的最早，但发现自己感...
+ Day 1 + 上午
+...
                         
                     </div>
 
@@ -497,18 +504,19 @@ <h3 class="home-post-title border-box">
 
                     <div class="home-post-content keep-markdown-body">
                         
-                            DP总结$线性DP$
-定义:
-具有线性”阶段”划分的$DP$被称为线性$DP$。
+                             DP总结
+ 线性DP线性DP线性DP
+
+
+ 定义:
+
+具有线性&quot;阶段&quot;划分的DPDPDP被称为线性DPDPDP。
 
 
-经典模型
-$LIS$ , $LCS$ , $LCIS$(最长公共上升子序列) , $最长公共子序列$ , $数字三角形$。
 
+ 经典模型
 
-例题：
-LCS题意：
-求两个字符串中...
+LISLISLIS , LCSLCSLCS , LCISLCISLCIS(最长公共上升子序列)...
                         
                     </div>
 
diff --git a/search.xml b/search.xml
index 70c2baa10..3baa2f03d 100644
--- a/search.xml
+++ b/search.xml
@@ -1,340 +1,308 @@
 <?xml version="1.0" encoding="utf-8"?>
 <search>
-  <entry>
-    <title>23.12.9考试总结</title>
-    <url>/2023/12/09/23.12.9%20%E8%80%83%E8%AF%95%E6%80%BB%E7%BB%93/</url>
-    <content><![CDATA[<h1 id="23-12-9-考试总结"><a href="#23-12-9-考试总结" class="headerlink" title="$23.12.9$ 考试总结"></a>$23.12.9$ 考试总结</h1><h3 id="分数-60-（-50-10-0-0"><a href="#分数-60-（-50-10-0-0" class="headerlink" title="分数 : $60$ （$50+10+0+0$)"></a>分数 : $60$ （$50+10+0+0$)</h3><h2 id="A-stick"><a href="#A-stick" class="headerlink" title="A. stick"></a>A. stick</h2><hr>
-<p>先是一个数字，然后一串$0$，最后一串$8$。贪就完了。</p>
-<p>注意模数是 $998244$<font color=red size=26>8</font>$53$。挂分 $50pts$</p>
-<h2 id="B-game"><a href="#B-game" class="headerlink" title="B. game"></a>B. game</h2><hr>
-<p>正解爆搜。少打 <code>break</code>挂 $90pts$。</p>
-<p>答案很多，所以 $yes$ 跑得很快。</p>
-<p>最坏情况$5\times 6$，此时$O(1^4\times2^{14}\times3^{16})$。</p>
-<p>注意到数据很小，考虑可行性剪枝即可。</p>
-<p>来自 <a class="link"   href="http://f7.163.com/" >永远的7日之都<i class="fas fa-external-link-alt"></i></a> :</p>
-<p><img  
-                       lazyload
-                       alt="image"
-                       data-src="https://www.z4a.net/images/2023/12/11/375a1f3119b0cb2173b9acd3a689e50071d0bfe4.jpg1256w_708h_web-article-pic.web"
-                       
-                 ></p>
-<h2 id="C-noip"><a href="#C-noip" class="headerlink" title="C.  noip"></a>C.  <strong>noip</strong></h2><hr>
-<p>万恶的 $O2$，$RE\ \ 0$。</p>
-<p>字典序从大到小搜索,$DP$ 预处理 $每个后缀首字母确定的情况下所能得到的最大权值$ ，判断当前是否 $\geq\ x$ $(可行性剪枝)$。</p>
-<blockquote>
-<p>学的是 $DP作为部分$ 的思路。</p>
-</blockquote>
-<h2 id="D-remove"><a href="#D-remove" class="headerlink" title="D. remove"></a>D. remove</h2><hr>
-<p>区间 $DP$。求<br>$$<br>min<br>\left{<br>\begin{aligned}<br>a \times k + b\times\sum\limits_{i&#x3D;1}^{k} \Big (max_i-min_i\Big)<br>\end{aligned}<br>\right}<br>$$</p>
-<p>设方程 $f_{l,r,max,min}$ 表示 消除区间 $[l,r]$ 使其剩下的最大值为 <code>max</code> ，最小值为 <code>min</code> 的最小代价。$g_{l,r}$ 表示 区间$[l,r]$中全消的最小代价。</p>
-<p>所以</p>
-<blockquote>
-<ol>
-<li><h6 id="初始化"><a href="#初始化" class="headerlink" title="初始化 :"></a>初始化 :</h6></li>
-</ol>
-<p>$g_{l,r}&#x3D;min${$f_{l,r,max,min}+a+b\times (r-l)^2$}</p>
-<ol start="2">
-<li><h6 id="转移"><a href="#转移" class="headerlink" title="转移"></a>转移</h6></li>
-</ol>
-<p>左边空或右边空 :</p>
-<ul>
-<li>$f_{l,r,max,min}&#x3D;\min{g_{l,k} + f_{k+1,r,max,min}}$</li>
-<li>$f_{l,r,max,min}&#x3D;\min{g_{k+1,r} + f_{l,k,max,min}}$</li>
-</ul>
-<p>两边都空</p>
-<ul>
-<li>$f_{l,r,max,min}&#x3D;\min{f_{l,r,max,min} + f_{k+1,r,max,min}}$</li>
-</ul>
-<p>端点刷表</p>
-<ul>
-<li>$f_{l,r+1,max(max,w_l),min(min,w_r)}&#x3D;f_{l,r,max,min}$</li>
-</ul>
-<ol start="3">
-<li><h6 id="g"><a href="#g" class="headerlink" title="g?"></a>g?</h6><p> $g_{l,r}&#x3D;min${$f_{l,r,max,min}+a+b\times(max-min)^2$}</p>
-</li>
-<li><h6 id="离散化后-O-n-4"><a href="#离散化后-O-n-4" class="headerlink" title="离散化后 $O(n^4)$"></a>离散化后 $O(n^4)$</h6></li>
-</ol>
-</blockquote>
-<hr>
-<h2 id="问题："><a href="#问题：" class="headerlink" title="问题："></a>问题：</h2><ol>
-<li><h5 id="手抄斩手，使用CV大发。"><a href="#手抄斩手，使用CV大发。" class="headerlink" title="手抄斩手，使用CV大发。"></a>手抄斩手，使用CV大发。</h5></li>
-<li><h5 id="O2-要看返回值。"><a href="#O2-要看返回值。" class="headerlink" title="$O2$ 要看返回值。"></a>$O2$ 要看返回值。</h5></li>
-<li><h5 id="对拍数据要把时间卡到满，不能放水。"><a href="#对拍数据要把时间卡到满，不能放水。" class="headerlink" title="对拍数据要把时间卡到满，不能放水。"></a>对拍数据要把时间卡到满，不能放水。</h5></li>
-</ol>
-]]></content>
-  </entry>
-  <entry>
-    <title>CSP总结</title>
-    <url>/2023/10/24/CSP/</url>
-    <content><![CDATA[<h1 id="CSP-游记"><a href="#CSP-游记" class="headerlink" title="$CSP$ 游记"></a>$CSP$ 游记</h1><h3 id="Day-0"><a href="#Day-0" class="headerlink" title="Day 0"></a>Day 0</h3><blockquote>
-<p>晚上去了酒店，和另外几个人一起复习了 $Tarjan$ ，然后就睡了。</p>
-<p>睡觉前想着 $2.5h$ 写前两个题，后两个题打下暴力，应该能拿  <strong>一等</strong>。</p>
-</blockquote>
-<h3 id="Day-1-上午"><a href="#Day-1-上午" class="headerlink" title="Day 1 + 上午"></a>Day 1 + 上午</h3><blockquote>
-<p>$7\ :\ 40$</p>
-<p>早上起来的最早，但发现自己感冒了。喝了只 $蒲地蓝$ ，还戴上了 $开喉剑$ 。</p>
-<p>心里有种不祥的预感，感觉 $T3$ 会是与式子有关的 大模拟。</p>
-<p>$\ $</p>
-<p>$8\ :\ 30$</p>
-<p>到一中集了合，拍了张照。果老师讲了些关于低级失误的事。</p>
-<p>$\ $</p>
-<p>$8\ :\ 30$</p>
-<p>进了考场，发现座位设计非常 <code>反人类</code>，腿稍稍往前放一点就会碰到膝盖。</p>
-<p>题面与压缩包出现了分离，<del>监考老师也搞了很久</del>。</p>
-<p>$\ $</p>
-<p>$8\ :\ 55$</p>
-<p>$T1$ 感觉像约瑟夫，但 手搓样例 后发现每次会消掉 $\lfloor \frac{n-1} {3} \rfloor$ 个，$while(n)$ 即可。</p>
-<p>对于第二个问，有一个显然的性质:</p>
-<blockquote>
-<p>在 $n$ 消掉前，他一定在末尾。</p>
-</blockquote>
-<p>所以$while(n)$时判断一下 $(n-1)%3&#x3D;&#x3D;1$ 即可。</p>
-<p>$\ $</p>
-<p>$9\ :\ 30$</p>
-<p>把 $T1$ 的对拍打了一下，然后发现 $T2$ 是贪心水题，$15min$ 切了。</p>
-<p>$\ $</p>
-<p>$9\ :\ 50$</p>
-<p>发现 $T3$ 是二次函数求值，回想起了去年 $T2$ 用 $sqrt$ 爆精度，就筛了 $1e6$ 内的质数。</p>
-<p>然后模拟即可。</p>
-<p>$\ $</p>
-<p>$11\ :\ 00$</p>
-<p>把前三个题看了一遍，发现没问题，开冲 $T4$。</p>
-<p>$\ $</p>
-<p>$12\ :\ 00$</p>
-<p>考试结束，预估</p>
-<p>$100\ +\ 100\ +\ 100\ +\ 10\ &#x3D;\ 310  $ ， 感觉<strong>一等</strong>没问题。</p>
-</blockquote>
-<h3 id="Day-1-下午"><a href="#Day-1-下午" class="headerlink" title="Day 1 + 下午"></a>Day 1 + 下午</h3><blockquote>
-<p>$2\ :\ 30$ </p>
-<p>进入了考场，$pdf$ 的密码老师没找到，延迟了 $5min$。</p>
-<p>$\ $</p>
-<p>$3\ :\ 00$</p>
-<p>发现 $T1$ 是水题，枚举所有状态再反过来判断即可。</p>
-<p>$\ $</p>
-<p>$3\ :\ 35$</p>
-<p>$T2$ 先打了一个 $O(n^3)$ 的暴力，然后发现枚举右端点太费时间，优化成了 $O(n^2)$</p>
-<p>$\ $</p>
-<p>$3\ :\ 55$</p>
-<p>看了一下 $T4$ ，感觉像 <code>树上DP</code> ，但没推出来，转去了 $T3$。</p>
-<p>$\ $</p>
-<p>$6\ :\ 00$</p>
-<p>一直在调 $T3$ ，感觉灵魂出窍。</p>
-<p>$对其原则$ 很好做，但 $4$ 操作难调得死，最后修修补补的过了大样例。</p>
-<p><del><strong>考完发现没有初始化</strong></del>。</p>
-<p>$\ $</p>
-<p>估分 $100\ +\ 50\ +\ +\ ?\ +\ 0\ &#x3D;\ 150^+$</p>
-</blockquote>
-<h2 id="反思"><a href="#反思" class="headerlink" title="反思"></a>反思</h2><blockquote>
-<p>比赛节奏感觉可以，$S$ 组 $T4$ 没看出来感觉很可惜。</p>
-<p>听说 $J$ 组的 $T4$ 是分层图最短路，考场上自己没去想。</p>
-<p>$S$ 组 $T3$ 能拿多少是多少，得一等的希望就在他身上了。</p>
-</blockquote>
-]]></content>
-  </entry>
   <entry>
     <title>DP再次总结</title>
     <url>/2024/01/10/DP_2/</url>
-    <content><![CDATA[<p>﻿## 1. 状态<br>$\ \ \ \ $区间$DP$的状态一般 <code>设 f[l][r] 表示区间 [l][r] ....</code>。但有些时候可以直接设 $f_i$ 表示 $[1,i]$…。</p>
-<p>$\ \ \ \ $转移的时候会依靠断点，即 $f[l][r]&#x3D;min&#x2F;max${$f[l][k]+f[k+1][r]$}。</p>
-<p>$\ \ \ \ $常见的优化有两种 : </p>
+    <content><![CDATA[<p>## 1. 状态<br />
+$\ \ \ \ <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>区间</mtext></mrow><annotation encoding="application/x-tex">区间</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">区</span><span class="mord cjk_fallback">间</span></span></span></span>DP$的状态一般 <code>设 f[l][r] 表示区间 [l][r] ....</code>。但有些时候可以直接设 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">f_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> 表示 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mn>1</mn><mo separator="true">,</mo><mi>i</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[1,i]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">[</span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">i</span><span class="mclose">]</span></span></span></span>…。</p>
+<p>$\ \ \ \ $转移的时候会依靠断点，即 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mo stretchy="false">[</mo><mi>l</mi><mo stretchy="false">]</mo><mo stretchy="false">[</mo><mi>r</mi><mo stretchy="false">]</mo><mo>=</mo><mi>m</mi><mi>i</mi><mi>n</mi><mi mathvariant="normal">/</mi><mi>m</mi><mi>a</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">f[l][r]=min/max</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mopen">[</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mclose">]</span><span class="mopen">[</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mclose">]</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span><span class="mord">/</span><span class="mord mathnormal">m</span><span class="mord mathnormal">a</span><span class="mord mathnormal">x</span></span></span></span>{<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mo stretchy="false">[</mo><mi>l</mi><mo stretchy="false">]</mo><mo stretchy="false">[</mo><mi>k</mi><mo stretchy="false">]</mo><mo>+</mo><mi>f</mi><mo stretchy="false">[</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo stretchy="false">]</mo><mo stretchy="false">[</mo><mi>r</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">f[l][k]+f[k+1][r]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mopen">[</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mclose">]</span><span class="mopen">[</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mclose">]</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mopen">[</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">]</span><span class="mopen">[</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mclose">]</span></span></span></span>}。</p>
+<p>$\ \ \ \ $常见的优化有两种 :</p>
 <ul>
-<li><pre><code>     	1. 四边形不等式
+<li>
+<pre><code>   	1. 四边形不等式
 </code></pre>
 </li>
-<li><pre><code>     	2. 递推
+<li>
+<pre><code>   	2. 递推
 </code></pre>
 </li>
 </ul>
-<h2 id="2-例题"><a href="#2-例题" class="headerlink" title="2.例题"></a>2.例题</h2><ol>
-<li><h5 id="表达式的亿种可能性"><a href="#表达式的亿种可能性" class="headerlink" title="表达式的亿种可能性"></a>表达式的亿种可能性</h5><blockquote>
+<h2 id="2例题"><a class="markdownIt-Anchor" href="#2例题"></a> 2.例题</h2>
+<ol>
+<li>
+<h5 id="表达式的亿种可能性"><a class="markdownIt-Anchor" href="#表达式的亿种可能性"></a> 表达式的亿种可能性</h5>
+<blockquote>
 <p>直接算是不行的，我们要去乘上每一个数的代价。</p>
 <p>原因是 加法和减法可以交换顺序。</p>
-<p><em>eg.</em> : $(1+1)+2\ &#x3D;\ 1+(1+2)$</p>
+<p><em>eg.</em> : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mo>+</mo><mn>2</mn><mtext> </mtext><mo>=</mo><mtext> </mtext><mn>1</mn><mo>+</mo><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(1+1)+2\ =\ 1+(1+2)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">2</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span></span></span></span></p>
 <p>乘法具有分配率。</p>
 </blockquote>
 </li>
-<li><h5 id="有味道的数字"><a href="#有味道的数字" class="headerlink" title="有味道的数字"></a>有味道的数字</h5><blockquote>
-<p>爆搜发现 $max\ ans\ &#x3D;\ 11$ , 且 $当且仅当\ n&#x3D;3\ 或\ n&#x3D;7\ $ 时，$ans&#x3D;-1$。</p>
-<p>用 $f[i]\ (f:vector)$ 存 $ans_n\ &#x3D;\ i$ 的 $n$。</p>
+<li>
+<h5 id="有味道的数字"><a class="markdownIt-Anchor" href="#有味道的数字"></a> 有味道的数字</h5>
+<blockquote>
+<p>爆搜发现 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi><mi>a</mi><mi>x</mi><mtext> </mtext><mi>a</mi><mi>n</mi><mi>s</mi><mtext> </mtext><mo>=</mo><mtext> </mtext><mn>11</mn></mrow><annotation encoding="application/x-tex">max\ ans\ =\ 11</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">a</span><span class="mord mathnormal">x</span><span class="mspace"> </span><span class="mord mathnormal">a</span><span class="mord mathnormal">n</span><span class="mord mathnormal">s</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord">1</span></span></span></span> , 且 $当且仅当\ n=3\ 或\ n=7\ $ 时，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><mi>n</mi><mi>s</mi><mo>=</mo><mo>−</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">ans=-1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">a</span><span class="mord mathnormal">n</span><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">−</span><span class="mord">1</span></span></span></span>。</p>
+<p>用 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mo stretchy="false">[</mo><mi>i</mi><mo stretchy="false">]</mo><mtext> </mtext><mo stretchy="false">(</mo><mi>f</mi><mo>:</mo><mi>v</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">f[i]\ (f:vector)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mopen">[</span><span class="mord mathnormal">i</span><span class="mclose">]</span><span class="mspace"> </span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mord mathnormal">e</span><span class="mord mathnormal">c</span><span class="mord mathnormal">t</span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mclose">)</span></span></span></span> 存 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><mi>n</mi><msub><mi>s</mi><mi>n</mi></msub><mtext> </mtext><mo>=</mo><mtext> </mtext><mi>i</mi></mrow><annotation encoding="application/x-tex">ans_n\ =\ i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord mathnormal">a</span><span class="mord mathnormal">n</span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">i</span></span></span></span> 的 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span>。</p>
 </blockquote>
 </li>
-<li><h5 id="守卫"><a href="#守卫" class="headerlink" title="守卫"></a>守卫</h5><blockquote>
+<li>
+<h5 id="守卫"><a class="markdownIt-Anchor" href="#守卫"></a> 守卫</h5>
+<blockquote>
 <p>题目具有迷惑性，容易想成单调栈。</p>
 <p>但发现加入点后需要一段区间的信息。</p>
-<p>所以直接区间 $DP$。</p>
-<p>枚举 $r$ ,  $l\ &#x3D;\ r\ \rightarrow\ 1$，递推。</p>
+<p>所以直接区间 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span>。</p>
+<p>枚举 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>r</mi></mrow><annotation encoding="application/x-tex">r</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span></span></span></span> ,  <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mtext> </mtext><mo>=</mo><mtext> </mtext><mi>r</mi><mtext> </mtext><mo>→</mo><mtext> </mtext><mn>1</mn></mrow><annotation encoding="application/x-tex">l\ =\ r\ \rightarrow\ 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">→</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span>，递推。</p>
 </blockquote>
 </li>
-<li><h5 id="祖玛游戏-单调栈"><a href="#祖玛游戏-单调栈" class="headerlink" title="祖玛游戏 &amp;&amp; 单调栈"></a>祖玛游戏 &amp;&amp; 单调栈</h5><blockquote>
-<p>**打不过 (二维状态表示不完全) 就加入 (把表示不完全的信息加入状态)**。</p>
+<li>
+<h5 id="祖玛游戏-单调栈"><a class="markdownIt-Anchor" href="#祖玛游戏-单调栈"></a> 祖玛游戏 &amp;&amp; 单调栈</h5>
+<blockquote>
+<p><strong>打不过 (二维状态表示不完全) 就加入 (把表示不完全的信息加入状态)</strong>。</p>
 <p><strong>实在不行还能加辅助数组</strong>。</p>
-<p>**如果循环有后效性，或者循环讨论复杂，用 $dfs$**。</p>
+<p><strong>如果循环有后效性，或者循环讨论复杂，用 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi><mi>f</mi><mi>s</mi></mrow><annotation encoding="application/x-tex">dfs</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord mathnormal">s</span></span></span></span></strong>。</p>
 <p>思想来源于二分 ： 把原问题转换为可行性问题</p>
 </blockquote>
 </li>
-<li><h5 id="括号序列"><a href="#括号序列" class="headerlink" title="括号序列"></a>括号序列</h5><blockquote>
+<li>
+<h5 id="括号序列"><a class="markdownIt-Anchor" href="#括号序列"></a> 括号序列</h5>
+<blockquote>
 <p>算重了怎么办？ 学习 $Catalan $ <em>!</em></p>
-<p>我们知道<br>$$<br>C_{n+1}&#x3D;C_0C_n+C_1C_{n-1}+C_2C_{n-2}+…+C_{n-1}C_1+C_nC_0\ (注意这里没有重复)<br>$$<br>同理 , <img  
+<p>我们知道</p>
+<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>C</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><msub><mi>C</mi><mn>0</mn></msub><msub><mi>C</mi><mi>n</mi></msub><mo>+</mo><msub><mi>C</mi><mn>1</mn></msub><msub><mi>C</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>C</mi><mn>2</mn></msub><msub><mi>C</mi><mrow><mi>n</mi><mo>−</mo><mn>2</mn></mrow></msub><mo>+</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo>+</mo><msub><mi>C</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msub><msub><mi>C</mi><mn>1</mn></msub><mo>+</mo><msub><mi>C</mi><mi>n</mi></msub><msub><mi>C</mi><mn>0</mn></msub><mtext> </mtext><mo stretchy="false">(</mo><mtext>注意这里没有重复</mtext><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">C_{n+1}=C_0C_n+C_1C_{n-1}+C_2C_{n-2}+...+C_{n-1}C_1+C_nC_0\ (注意这里没有重复)
+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.891661em;vertical-align:-0.208331em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">+</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.891661em;vertical-align:-0.208331em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.891661em;vertical-align:-0.208331em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.891661em;vertical-align:-0.208331em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.301108em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.208331em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.30110799999999993em;"><span style="top:-2.5500000000000003em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace"> </span><span class="mopen">(</span><span class="mord cjk_fallback">注</span><span class="mord cjk_fallback">意</span><span class="mord cjk_fallback">这</span><span class="mord cjk_fallback">里</span><span class="mord cjk_fallback">没</span><span class="mord cjk_fallback">有</span><span class="mord cjk_fallback">重</span><span class="mord cjk_fallback">复</span><span class="mclose">)</span></span></span></span></span></p>
+<p>同理 , <img  
                        lazyload
                        alt="image"
                        data-src="https://cdn.luogu.com.cn/upload/image_hosting/iyn4t3lm.png"
-                       
+                        alt="" 
                  ></p>
 </blockquote>
 </li>
 </ol>
-<hr>
-<hr>
-<h2 id="3-好题"><a href="#3-好题" class="headerlink" title="3. 好题"></a>3. 好题</h2><ol>
-<li><p><a class="link"   href="https://vj.imken.moe/problem/HDU-2476/origin" >HDU - 2476 <i class="fas fa-external-link-alt"></i></a></p>
+<hr />
+<hr />
+<h2 id="3-好题"><a class="markdownIt-Anchor" href="#3-好题"></a> 3. 好题</h2>
+<ol>
+<li>
+<p><a class="link"   href="https://vj.imken.moe/problem/HDU-2476/origin" >HDU - 2476 <i class="fas fa-external-link-alt"></i></a></p>
 <blockquote>
 <p>(空 -&gt; B) - (A -&gt; B)</p>
 </blockquote>
 </li>
-<li><p><a class="link"   href="https://vj.imken.moe/problem/CodeForces-149D/origin" >CodeForces - 149D <i class="fas fa-external-link-alt"></i></a></p>
+<li>
+<p><a class="link"   href="https://vj.imken.moe/problem/CodeForces-149D/origin" >CodeForces - 149D <i class="fas fa-external-link-alt"></i></a></p>
 <blockquote>
 <p>高维状态 ：</p>
-<p>$f_{l,r,x,y}$ 表示 区间$[l,r]$中，左端点是$x$,右端点是$y$的方案数。(左右端点均hash过)。</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi></mrow></msub></mrow><annotation encoding="application/x-tex">f_{l,r,x,y}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.03588em;">y</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span> 表示 区间<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[l,r]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">[</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mclose">]</span></span></span></span>中，左端点是<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span>,右端点是<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span></span></span></span>的方案数。(左右端点均hash过)。</p>
 </blockquote>
 </li>
-<li><p><a class="link"   href="https://www.luogu.com.cn/problem/P3147" >262144  P<i class="fas fa-external-link-alt"></i></a></p>
+<li>
+<p><a class="link"   href="https://www.luogu.com.cn/problem/P3147" >262144  P<i class="fas fa-external-link-alt"></i></a></p>
 <blockquote>
-<p>状态不同于普通区间$DP$，类倍增，设的是<br>$$<br>f_{i,k}\ 表示\ 从\ i\ 开始直到合出\ k\ 所需的最小长度。<br>$$</p>
+<p>状态不同于普通区间<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span>，类倍增，设的是</p>
+<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>k</mi></mrow></msub><mtext> 表示 从 </mtext><mi>i</mi><mtext> 开始直到合出 </mtext><mi>k</mi><mtext> 所需的最小长度。</mtext></mrow><annotation encoding="application/x-tex">f_{i,k}\ 表示\ 从\ i\ 开始直到合出\ k\ 所需的最小长度。
+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace"> </span><span class="mord cjk_fallback">表</span><span class="mord cjk_fallback">示</span><span class="mspace"> </span><span class="mord cjk_fallback">从</span><span class="mspace"> </span><span class="mord mathnormal">i</span><span class="mspace"> </span><span class="mord cjk_fallback">开</span><span class="mord cjk_fallback">始</span><span class="mord cjk_fallback">直</span><span class="mord cjk_fallback">到</span><span class="mord cjk_fallback">合</span><span class="mord cjk_fallback">出</span><span class="mspace"> </span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace"> </span><span class="mord cjk_fallback">所</span><span class="mord cjk_fallback">需</span><span class="mord cjk_fallback">的</span><span class="mord cjk_fallback">最</span><span class="mord cjk_fallback">小</span><span class="mord cjk_fallback">长</span><span class="mord cjk_fallback">度</span><span class="mord cjk_fallback">。</span></span></span></span></span></p>
 </blockquote>
 </li>
 <li></li>
 </ol>
-<hr>
-<h2 id="4-总结"><a href="#4-总结" class="headerlink" title="4.总结"></a>4.总结</h2><blockquote>
+<hr />
+<h2 id="4总结"><a class="markdownIt-Anchor" href="#4总结"></a> 4.总结</h2>
+<blockquote>
 <p>状态的根本问题是 : <strong>如何用最简洁的信息使得答案能够被(不重复)，不遗漏的算出来。</strong></p>
-<p>即使是 $f_{l,r}$ 也是逃不过的。</p>
-<p>区间 $DP$ 一般满足 <code>一些局部最优解能凑出全局最优解</code>，不行的话就得加维度。</p>
+<p>即使是 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi></mrow></msub></mrow><annotation encoding="application/x-tex">f_{l,r}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span> 也是逃不过的。</p>
+<p>区间 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span> 一般满足 <code>一些局部最优解能凑出全局最优解</code>，不行的话就得加维度。</p>
 </blockquote>
 ]]></content>
   </entry>
   <entry>
-    <title>图论总结</title>
-    <url>/2024/01/10/%E5%9B%BE%E8%AE%BA/</url>
-    <content><![CDATA[<h1 id="图论"><a href="#图论" class="headerlink" title="图论"></a>图论</h1><hr>
-<h2 id="0-有感而发"><a href="#0-有感而发" class="headerlink" title="$0.$有感而发"></a>$0.$有感而发</h2><blockquote>
-<p>  <em>眼睛瞎了有利于打Dijkstra。</em> by NotDeep</p>
-<p>  <em>如果这题我不会做，那么一定是图论。</em> by NotDeep</p>
+    <title>23.12.9考试总结</title>
+    <url>/2023/12/09/23.12.9%20%E8%80%83%E8%AF%95%E6%80%BB%E7%BB%93/</url>
+    <content><![CDATA[<h1 id="23129-考试总结"><a class="markdownIt-Anchor" href="#23129-考试总结"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>23.12.9</mn></mrow><annotation encoding="application/x-tex">23.12.9</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">2</span><span class="mord">3</span><span class="mord">.</span><span class="mord">1</span><span class="mord">2</span><span class="mord">.</span><span class="mord">9</span></span></span></span> 考试总结</h1>
+<h3 id="分数-60-501000"><a class="markdownIt-Anchor" href="#分数-60-501000"></a> 分数 : <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>60</mn></mrow><annotation encoding="application/x-tex">60</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">6</span><span class="mord">0</span></span></span></span> （<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50</mn><mo>+</mo><mn>10</mn><mo>+</mo><mn>0</mn><mo>+</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">50+10+0+0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">5</span><span class="mord">0</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">1</span><span class="mord">0</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">0</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span></span></span></span>)</h3>
+<h2 id="a-stick"><a class="markdownIt-Anchor" href="#a-stick"></a> A. stick</h2>
+<hr />
+<p>先是一个数字，然后一串<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span></span></span></span>，最后一串<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>8</mn></mrow><annotation encoding="application/x-tex">8</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">8</span></span></span></span>。贪就完了。</p>
+<p>注意模数是 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>998244</mn></mrow><annotation encoding="application/x-tex">998244</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">9</span><span class="mord">9</span><span class="mord">8</span><span class="mord">2</span><span class="mord">4</span><span class="mord">4</span></span></span></span><font color=red size=26>8</font><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>53</mn></mrow><annotation encoding="application/x-tex">53</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">5</span><span class="mord">3</span></span></span></span>。挂分 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50</mn><mi>p</mi><mi>t</mi><mi>s</mi></mrow><annotation encoding="application/x-tex">50pts</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em;"></span><span class="mord">5</span><span class="mord">0</span><span class="mord mathnormal">p</span><span class="mord mathnormal">t</span><span class="mord mathnormal">s</span></span></span></span></p>
+<h2 id="b-game"><a class="markdownIt-Anchor" href="#b-game"></a> B. game</h2>
+<hr />
+<p>正解爆搜。少打 <code>break</code>挂 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>90</mn><mi>p</mi><mi>t</mi><mi>s</mi></mrow><annotation encoding="application/x-tex">90pts</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em;"></span><span class="mord">9</span><span class="mord">0</span><span class="mord mathnormal">p</span><span class="mord mathnormal">t</span><span class="mord mathnormal">s</span></span></span></span>。</p>
+<p>答案很多，所以 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi><mi>e</mi><mi>s</mi></mrow><annotation encoding="application/x-tex">yes</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mord mathnormal">e</span><span class="mord mathnormal">s</span></span></span></span> 跑得很快。</p>
+<p>最坏情况<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>5</mn><mo>×</mo><mn>6</mn></mrow><annotation encoding="application/x-tex">5\times 6</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">6</span></span></span></span>，此时<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mn>1</mn><mn>4</mn></msup><mo>×</mo><msup><mn>2</mn><mn>14</mn></msup><mo>×</mo><msup><mn>3</mn><mn>16</mn></msup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(1^4\times2^{14}\times3^{16})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord">1</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.897438em;vertical-align:-0.08333em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mord mtight">4</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord">3</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mord mtight">6</span></span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span>。</p>
+<p>注意到数据很小，考虑可行性剪枝即可。</p>
+<p>来自 <a class="link"   href="http://f7.163.com/" >永远的7日之都<i class="fas fa-external-link-alt"></i></a> :</p>
+<p><img  
+                       lazyload
+                       alt="image"
+                       data-src="https://www.z4a.net/images/2023/12/11/375a1f3119b0cb2173b9acd3a689e50071d0bfe4.jpg1256w_708h_web-article-pic.web"
+                        alt="" 
+                 ></p>
+<h2 id="c-noip"><a class="markdownIt-Anchor" href="#c-noip"></a> C.  <strong>noip</strong></h2>
+<hr />
+<p>万恶的 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mn>2</mn></mrow><annotation encoding="application/x-tex">O2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mord">2</span></span></span></span>，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>R</mi><mi>E</mi><mtext>  </mtext><mn>0</mn></mrow><annotation encoding="application/x-tex">RE\ \ 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mspace"> </span><span class="mspace"> </span><span class="mord">0</span></span></span></span>。</p>
+<p>字典序从大到小搜索,<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span> 预处理 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>每个后缀首字母确定的情况下所能得到的最大权值</mtext></mrow><annotation encoding="application/x-tex">每个后缀首字母确定的情况下所能得到的最大权值</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">每</span><span class="mord cjk_fallback">个</span><span class="mord cjk_fallback">后</span><span class="mord cjk_fallback">缀</span><span class="mord cjk_fallback">首</span><span class="mord cjk_fallback">字</span><span class="mord cjk_fallback">母</span><span class="mord cjk_fallback">确</span><span class="mord cjk_fallback">定</span><span class="mord cjk_fallback">的</span><span class="mord cjk_fallback">情</span><span class="mord cjk_fallback">况</span><span class="mord cjk_fallback">下</span><span class="mord cjk_fallback">所</span><span class="mord cjk_fallback">能</span><span class="mord cjk_fallback">得</span><span class="mord cjk_fallback">到</span><span class="mord cjk_fallback">的</span><span class="mord cjk_fallback">最</span><span class="mord cjk_fallback">大</span><span class="mord cjk_fallback">权</span><span class="mord cjk_fallback">值</span></span></span></span> ，判断当前是否 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>≥</mo><mtext> </mtext><mi>x</mi></mrow><annotation encoding="application/x-tex">\geq\ x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719400000000001em;vertical-align:-0.13597em;"></span><span class="mrel">≥</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">x</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mtext>可行性剪枝</mtext><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">(可行性剪枝)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord cjk_fallback">可</span><span class="mord cjk_fallback">行</span><span class="mord cjk_fallback">性</span><span class="mord cjk_fallback">剪</span><span class="mord cjk_fallback">枝</span><span class="mclose">)</span></span></span></span>。</p>
+<blockquote>
+<p>学的是 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi><mtext>作为部分</mtext></mrow><annotation encoding="application/x-tex">DP作为部分</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mord cjk_fallback">作</span><span class="mord cjk_fallback">为</span><span class="mord cjk_fallback">部</span><span class="mord cjk_fallback">分</span></span></span></span> 的思路。</p>
+</blockquote>
+<h2 id="d-remove"><a class="markdownIt-Anchor" href="#d-remove"></a> D. remove</h2>
+<hr />
+<p>区间 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span>。求</p>
+<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>m</mi><mi>i</mi><mi>n</mi><mrow><mo fence="true">{</mo><mtable rowspacing="0.24999999999999992em" columnalign="right" columnspacing=""><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mi>a</mi><mo>×</mo><mi>k</mi><mo>+</mo><mi>b</mi><mo>×</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>k</mi></munderover><mo fence="false">(</mo><mi>m</mi><mi>a</mi><msub><mi>x</mi><mi>i</mi></msub><mo>−</mo><mi>m</mi><mi>i</mi><msub><mi>n</mi><mi>i</mi></msub><mo fence="false">)</mo></mrow></mstyle></mtd></mtr></mtable><mo fence="true">}</mo></mrow></mrow><annotation encoding="application/x-tex">min
+\left\{
+\begin{aligned} 
+a \times k + b\times\sum\limits_{i=1}^{k} \Big (max_i-min_i\Big)
+\end{aligned}
+\right\}
+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:3.60004em;vertical-align:-1.55002em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.05002em;"><span style="top:-2.49999em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎩</span></span></span><span style="top:-2.20499em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-3.15001em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎨</span></span></span><span style="top:-4.00501em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.30002em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎧</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.55002em;"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.9568910000000002em;"><span style="top:-3.9568909999999997em;"><span class="pstrut" style="height:3.836113em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8361130000000003em;"><span style="top:-1.872331em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.277669em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="delimsizing size2">(</span></span><span class="mord mathnormal">m</span><span class="mord mathnormal">a</span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">i</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="delimsizing size2">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.4568910000000002em;"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.05002em;"><span style="top:-2.49999em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎭</span></span></span><span style="top:-2.20499em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-3.15001em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎬</span></span></span><span style="top:-4.00501em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎪</span></span></span><span style="top:-4.30002em;"><span class="pstrut" style="height:3.15em;"></span><span class="delimsizinginner delim-size4"><span>⎫</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.55002em;"><span></span></span></span></span></span></span></span></span></span></span></span></p>
+<p>设方程 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub></mrow><annotation encoding="application/x-tex">f_{l,r,max,min}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span> 表示 消除区间 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[l,r]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">[</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mclose">]</span></span></span></span> 使其剩下的最大值为 <code>max</code> ，最小值为 <code>min</code> 的最小代价。<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>g</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi></mrow></msub></mrow><annotation encoding="application/x-tex">g_{l,r}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span> 表示 区间<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[l,r]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">[</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mclose">]</span></span></span></span>中全消的最小代价。</p>
+<p>所以</p>
+<blockquote>
+<ol>
+<li>
+<h6 id="初始化"><a class="markdownIt-Anchor" href="#初始化"></a> 初始化 :</h6>
+</li>
+</ol>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>g</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi></mrow></msub><mo>=</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow><annotation encoding="application/x-tex">g_{l,r}=min</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span></span></span></span>{<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo>+</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>×</mo><mo stretchy="false">(</mo><mi>r</mi><mo>−</mo><mi>l</mi><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">f_{l,r,max,min}+a+b\times (r-l)^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>}</p>
+<ol start="2">
+<li>
+<h6 id="转移"><a class="markdownIt-Anchor" href="#转移"></a> 转移</h6>
+</li>
+</ol>
+<p>左边空或右边空 :</p>
+<ul>
+<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo>=</mo><mi>min</mi><mo>⁡</mo><mo stretchy="false">{</mo><msub><mi>g</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>k</mi></mrow></msub><mo>+</mo><msub><mi>f</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">f_{l,r,max,min}=\min\{g_{l,k} + f_{k+1,r,max,min}\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.036108em;vertical-align:-0.286108em;"></span><span class="mop">min</span><span class="mopen">{</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.036108em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mclose">}</span></span></span></span></li>
+<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo>=</mo><mi>min</mi><mo>⁡</mo><mo stretchy="false">{</mo><msub><mi>g</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn><mo separator="true">,</mo><mi>r</mi></mrow></msub><mo>+</mo><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>k</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">f_{l,r,max,min}=\min\{g_{k+1,r} + f_{l,k,max,min}\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.036108em;vertical-align:-0.286108em;"></span><span class="mop">min</span><span class="mopen">{</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.036108em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mclose">}</span></span></span></span></li>
+</ul>
+<p>两边都空</p>
+<ul>
+<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo>=</mo><mi>min</mi><mo>⁡</mo><mo stretchy="false">{</mo><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo>+</mo><msub><mi>f</mi><mrow><mi>k</mi><mo>+</mo><mn>1</mn><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">f_{l,r,max,min}=\min\{f_{l,r,max,min} + f_{k+1,r,max,min}\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.036108em;vertical-align:-0.286108em;"></span><span class="mop">min</span><span class="mopen">{</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.036108em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mclose">}</span></span></span></span></li>
+</ul>
+<p>端点刷表</p>
+<ul>
+<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo>+</mo><mn>1</mn><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo stretchy="false">(</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><msub><mi>w</mi><mi>l</mi></msub><mo stretchy="false">)</mo><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi><mo stretchy="false">(</mo><mi>m</mi><mi>i</mi><mi>n</mi><mo separator="true">,</mo><msub><mi>w</mi><mi>r</mi></msub><mo stretchy="false">)</mo></mrow></msub><mo>=</mo><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub></mrow><annotation encoding="application/x-tex">f_{l,r+1,max(max,w_l),min(min,w_r)}=f_{l,r,max,min}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.04964em;vertical-align:-0.3551999999999999em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.34480000000000005em;"><span style="top:-2.5198em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3448em;"><span style="top:-2.3487714285714287em;margin-left:-0.02691em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15122857142857138em;"><span></span></span></span></span></span></span><span class="mclose mtight">)</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span><span class="mopen mtight">(</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span><span class="mpunct mtight">,</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.16454285714285719em;"><span style="top:-2.357em;margin-left:-0.02691em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mclose mtight">)</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3551999999999999em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span></li>
+</ul>
+<ol start="3">
+<li>
+<h6 id="g"><a class="markdownIt-Anchor" href="#g"></a> g?</h6>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>g</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi></mrow></msub><mo>=</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow><annotation encoding="application/x-tex">g_{l,r}=min</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span></span></span></span>{<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo separator="true">,</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo separator="true">,</mo><mi>m</mi><mi>i</mi><mi>n</mi></mrow></msub><mo>+</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>×</mo><mo stretchy="false">(</mo><mi>m</mi><mi>a</mi><mi>x</mi><mo>−</mo><mi>m</mi><mi>i</mi><mi>n</mi><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">f_{l,r,max,min}+a+b\times(max-min)^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361079999999999em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight">x</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">m</span><span class="mord mathnormal mtight">i</span><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">a</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">b</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">m</span><span class="mord mathnormal">a</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>}</p>
+</li>
+<li>
+<h6 id="离散化后-on4"><a class="markdownIt-Anchor" href="#离散化后-on4"></a> 离散化后 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mn>4</mn></msup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(n^4)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></h6>
+</li>
+</ol>
 </blockquote>
-<hr>
-<h2 id="1-基本算法"><a href="#1-基本算法" class="headerlink" title="$1.$ 基本算法"></a>$1.$ 基本算法</h2><p>​	$Case\ 1:$ <strong>Dijkstra</strong></p>
-<p>​		本质是 $贪心\ +\ DP $。</p>
-<p>​		适用于非负权权图，保证当前取出的节点的最短路是<strong>确定的</strong>，是未确定最短路的节点中<strong>最小的</strong>。</p>
-<p>​		常见题型 ： 补图，非负权图上用 <em>ta</em> ( $SPFA$已死 )。</p>
-<p>​	$Case\ 2:$ <strong>Floyd</strong></p>
-<p>​		通过 $O(n^3)$ 的时间求出任意两点的最短路。<strong>可以在负权图上使用。</strong></p>
-<p>​		可以求 <strong>最小环</strong>,<strong>传递闭包</strong>。</p>
-<p>​		下面对最小环进行说明:</p>
-<figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="comment">//g[i][j]表示 i-&gt;j 的最短路,f[i][j]表示i-&gt;j的 边的长度</span></span><br><span class="line"><span class="comment">//把最短路拆成 (i-j) + (i&gt;k,k-&gt;j)</span></span><br><span class="line"><span class="comment">//用 dji 可以做到 O(m(n+m)log m)</span></span><br><span class="line"><span class="keyword">for</span>(<span class="type">int</span> k=<span class="number">1</span>;k&lt;=n;k++)</span><br><span class="line">&#123;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=k<span class="number">-1</span>;i++)</span><br><span class="line">        <span class="keyword">for</span>(<span class="type">int</span> j=i+<span class="number">1</span>;j&lt;=k<span class="number">-1</span>;j++)</span><br><span class="line">            ans=<span class="built_in">min</span>(ans,f[i][k]+f[k][j]+g[i][j]);</span><br><span class="line">	<span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n;i++)</span><br><span class="line">		<span class="keyword">for</span>(<span class="type">int</span> j=<span class="number">1</span>;j&lt;=n;j++)</span><br><span class="line">            g[i][j]=<span class="built_in">min</span>(g[i][k]+g[k][j],g[i][j]);</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
-
-<p>​	$Case\ 3:$ <strong>Bellman–Ford</strong></p>
-<p>​		从 <strong>边</strong> 的角度考虑最短路：</p>
-<p>​			最短路的边的个数 <strong>最多</strong> 是 n-1。</p>
-<p>​		如果 <strong>边数</strong> 大于了 n-1 , 说明原图上有负环。</p>
-<p>​		通过 $for(i&#x3D;1\ \rightarrow\ n)\ \ \ for([u,v] \in E)\ \ 松弛$ 可以让每一条边都走过。</p>
-<p>​		但实际上跑不满，所以有了 $SPFA$。</p>
-<p>​	$Case\ 4:$ <strong>SPFA</strong></p>
-<p>​		对$Case\ 3$的广搜优化，可以判负环。最坏 $O(nm)$。</p>
-<p>​		优化点<a class="link"   href="https://www.luogu.com.cn/blog/Parabola/spfa-hacker-orzorz" >这儿<i class="fas fa-external-link-alt"></i></a>。</p>
-<hr>
-<h2 id="2-常见思路"><a href="#2-常见思路" class="headerlink" title="$2.$ 常见思路"></a>$2.$ 常见思路</h2><p>​	$Case\ 1:$ 分层图最短路</p>
-<p>​	$Case\ 2:$ Bellman–Ford 找负环</p>
-<p>​	$Case\ 3:$ 跑完最短路后，在 最短路图(<strong>DAG</strong>) 上$DP$。</p>
-<p>​	$Case\ 4:$ 多维最短路</p>
-<p>​	$Case\ 5:$ 拆贡献&#x2F;拆来源&#x2F;YY长啥样</p>
-<hr>
-<h2 id="3-魔改将至"><a href="#3-魔改将至" class="headerlink" title="$3.$ 魔改将至"></a>$3.$ 魔改将至</h2><p>​	$Case\ 1:$ 贪心</p>
-<p>​		以$摄像头问题2$为例：</p>
-<p>​			对于一段区间 $[l,r]$ 我们连接一条 $l \rightarrow r+1$ 的边，在连接 $i \rightarrow i-1\ ,i\in n$ 。</p>
-<p>​			令 $dist_i$ 表示覆盖区间 $[1,i-1]$ 的代价，再跑最短路即可。</p>
-<p>​	$Case\ 2:$ $DP$</p>
-<p>​		以 <a class="link"   href="https://codeforces.com/problemset/problem/1216/F" >Wi-Fi<i class="fas fa-external-link-alt"></i></a> 为例：</p>
-<p>​			我们把每种操作转换为 带权区间覆盖 ， 就转回了 $摄像头2$。</p>
-<hr>
-<div STYLE="page-break-after: always;"></div>
-
-<h2 id="4-题目详解"><a href="#4-题目详解" class="headerlink" title="$4.$ 题目详解"></a>$4.$ 题目详解</h2><h4 id="1-P4366"><a href="#1-P4366" class="headerlink" title="$1.$ $P4366$"></a>$1.$ <a class="link"   href="https://www.luogu.com.cn/problem/P4366" >$P4366$<i class="fas fa-external-link-alt"></i></a></h4><p>​	卡 $O(m\log m)$ 的 dji 的题目少的很，遇见就要珍惜。</p>
-<p>​	考虑异或性质：<br>$$<br>x \oplus z&#x3D;(x\oplus y) \oplus (y\oplus z)&lt;&#x3D;x\oplus y+y\oplus z<br>$$<br>​	对于每个节点，拆成 32 个节点: ${v|v&#x3D;x \oplus2^k,k\in N,v\leq n}$，边数就会缩短成 $n\log n+m$。</p>
-<h4 id="2-神秘力量"><a href="#2-神秘力量" class="headerlink" title="$2.$ 神秘力量"></a>$2.$ <a class="link"   href="http://oi.nks.edu.cn:19360/zh/Problem/Details?cid=2627&tid=Q" >神秘力量<i class="fas fa-external-link-alt"></i></a></h4><p>​	先对补图进行概念阐述：</p>
-<p>​		完全图-现有图&#x3D;现有图的补图</p>
-<p>​	维护时可以用堆乱搞或用链表维护。分别为 $O(m \log m)$ 和 $O(n)$。</p>
+<hr />
+<h2 id="问题"><a class="markdownIt-Anchor" href="#问题"></a> 问题：</h2>
+<ol>
+<li>
+<h5 id="手抄斩手使用cv大发"><a class="markdownIt-Anchor" href="#手抄斩手使用cv大发"></a> 手抄斩手，使用CV大发。</h5>
+</li>
+<li>
+<h5 id="o2-要看返回值"><a class="markdownIt-Anchor" href="#o2-要看返回值"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mn>2</mn></mrow><annotation encoding="application/x-tex">O2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mord">2</span></span></span></span> 要看返回值。</h5>
+</li>
+<li>
+<h5 id="对拍数据要把时间卡到满不能放水"><a class="markdownIt-Anchor" href="#对拍数据要把时间卡到满不能放水"></a> 对拍数据要把时间卡到满，不能放水。</h5>
+</li>
+</ol>
 ]]></content>
   </entry>
   <entry>
     <title>DP总结</title>
     <url>/2023/07/22/DP%E6%80%BB%E7%BB%93/</url>
-    <content><![CDATA[<h1 id="DP总结"><a href="#DP总结" class="headerlink" title="DP总结"></a>DP总结</h1><h3 id="线性DP"><a href="#线性DP" class="headerlink" title="$线性DP$"></a>$线性DP$</h3><ul>
-<li><h4 id="定义"><a href="#定义" class="headerlink" title="定义:"></a>定义:</h4><blockquote>
-<p>具有线性”阶段”划分的$DP$被称为线性$DP$。</p>
+    <content><![CDATA[<h1 id="dp总结"><a class="markdownIt-Anchor" href="#dp总结"></a> DP总结</h1>
+<h3 id="线性dp"><a class="markdownIt-Anchor" href="#线性dp"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>线性</mtext><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">线性DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">线</span><span class="mord cjk_fallback">性</span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span></h3>
+<ul>
+<li>
+<h4 id="定义"><a class="markdownIt-Anchor" href="#定义"></a> 定义:</h4>
+<blockquote>
+<p>具有线性&quot;阶段&quot;划分的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span>被称为线性<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span>。</p>
 </blockquote>
 </li>
-<li><h4 id="经典模型"><a href="#经典模型" class="headerlink" title="经典模型"></a>经典模型</h4><blockquote>
-<p>$LIS$ , $LCS$ , $LCIS$(最长公共上升子序列) , $最长公共子序列$ , $数字三角形$。</p>
+<li>
+<h4 id="经典模型"><a class="markdownIt-Anchor" href="#经典模型"></a> 经典模型</h4>
+<blockquote>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>I</mi><mi>S</mi></mrow><annotation encoding="application/x-tex">LIS</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span></span></span></span> , <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>C</mi><mi>S</mi></mrow><annotation encoding="application/x-tex">LCS</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span></span></span></span> , <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>C</mi><mi>I</mi><mi>S</mi></mrow><annotation encoding="application/x-tex">LCIS</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span></span></span></span>(最长公共上升子序列) , <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>最长公共子序列</mtext></mrow><annotation encoding="application/x-tex">最长公共子序列</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">最</span><span class="mord cjk_fallback">长</span><span class="mord cjk_fallback">公</span><span class="mord cjk_fallback">共</span><span class="mord cjk_fallback">子</span><span class="mord cjk_fallback">序</span><span class="mord cjk_fallback">列</span></span></span></span> , <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>数字三角形</mtext></mrow><annotation encoding="application/x-tex">数字三角形</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">数</span><span class="mord cjk_fallback">字</span><span class="mord cjk_fallback">三</span><span class="mord cjk_fallback">角</span><span class="mord cjk_fallback">形</span></span></span></span>。</p>
 </blockquote>
 </li>
-<li><h4 id="例题："><a href="#例题：" class="headerlink" title="例题："></a>例题：</h4><ol>
-<li><h4 id="LCS"><a href="#LCS" class="headerlink" title="LCS"></a><a class="link"   href="https://www.luogu.com.cn/problem/AT_dp_f" >LCS<i class="fas fa-external-link-alt"></i></a></h4><h5 id="题意："><a href="#题意：" class="headerlink" title="题意："></a>题意：</h5><blockquote>
-<p>求两个字符串中<strong>字典序最小的</strong>$LCS$。</p>
+<li>
+<h4 id="例题"><a class="markdownIt-Anchor" href="#例题"></a> 例题：</h4>
+<ol>
+<li>
+<h4 id="lcs"><a class="markdownIt-Anchor" href="#lcs"></a> <a class="link"   href="https://www.luogu.com.cn/problem/AT_dp_f" >LCS<i class="fas fa-external-link-alt"></i></a></h4>
+<h5 id="题意"><a class="markdownIt-Anchor" href="#题意"></a> 题意：</h5>
+<blockquote>
+<p>求两个字符串中<strong>字典序最小的</strong><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>C</mi><mi>S</mi></mrow><annotation encoding="application/x-tex">LCS</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span></span></span></span>。</p>
 </blockquote>
-<h5 id="方法"><a href="#方法" class="headerlink" title="方法:"></a>方法:</h5><blockquote>
-<p>用 $vector$ 记录下每一个状态下的答案。</p>
+<h5 id="方法"><a class="markdownIt-Anchor" href="#方法"></a> 方法:</h5>
+<blockquote>
+<p>用 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</mi></mrow><annotation encoding="application/x-tex">vector</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.61508em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mord mathnormal">e</span><span class="mord mathnormal">c</span><span class="mord mathnormal">t</span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span></span></span></span> 记录下每一个状态下的答案。</p>
 </blockquote>
 </li>
-<li><h4 id="最长上升子序列-LIS"><a href="#最长上升子序列-LIS" class="headerlink" title="最长上升子序列(LIS)"></a><a class="link"   href="https://www.luogu.com.cn/problem/AT_chokudai_S001_h" >最长上升子序列(LIS)<i class="fas fa-external-link-alt"></i></a></h4><h5 id="题意：-1"><a href="#题意：-1" class="headerlink" title="题意："></a>题意：</h5><blockquote>
+<li>
+<h4 id="最长上升子序列lis"><a class="markdownIt-Anchor" href="#最长上升子序列lis"></a> <a class="link"   href="https://www.luogu.com.cn/problem/AT_chokudai_S001_h" >最长上升子序列(LIS)<i class="fas fa-external-link-alt"></i></a></h4>
+<h5 id="题意-2"><a class="markdownIt-Anchor" href="#题意-2"></a> 题意：</h5>
+<blockquote>
 <ul>
-<li>给定一个长为 <em>n</em> 的序列 $a_i$，求这个序列的最长单调上升子序列长度。</li>
-<li>要求 $O(n log_n)$ 。</li>
+<li>给定一个长为 <em>n</em> 的序列 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>a</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">a_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>，求这个序列的最长单调上升子序列长度。</li>
+<li>要求 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mi>n</mi><mi>l</mi><mi>o</mi><msub><mi>g</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(n log_n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">o</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span> 。</li>
 </ul>
 </blockquote>
-<h5 id="方法："><a href="#方法：" class="headerlink" title="方法："></a>方法：</h5><blockquote>
+<h5 id="方法-2"><a class="markdownIt-Anchor" href="#方法-2"></a> 方法：</h5>
+<blockquote>
 <p>在长度一定的情况下，若结尾元素更小，那么最终答案也就更优。</p>
-<p>所以我们维护一个数组表示当前的$LIS$，每一次插入当前元素。</p>
+<p>所以我们维护一个数组表示当前的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mi>I</mi><mi>S</mi></mrow><annotation encoding="application/x-tex">LIS</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">L</span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span></span></span></span>，每一次插入当前元素。</p>
 </blockquote>
-<h5 id="code"><a href="#code" class="headerlink" title="code :"></a>code :</h5><figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string">&lt;bits/stdc++.h&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">define</span> int long long</span></span><br><span class="line"><span class="meta">#<span class="keyword">define</span> rep(i,a,b) for(int i=(a);i&lt;=(b);++i)</span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N=<span class="number">1e6</span> +<span class="number">3</span>;</span><br><span class="line"><span class="type">int</span> n,m,a[N],f[N];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">signed</span> <span class="title">main</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">	cin&gt;&gt;n; <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n;i++) cin&gt;&gt;a[i];</span><br><span class="line">	<span class="built_in">memset</span>(f,<span class="number">0x3f</span>,<span class="keyword">sizeof</span> f);</span><br><span class="line">	<span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n;i++) *<span class="built_in">upper_bound</span>(f+<span class="number">1</span>,f+n+<span class="number">1</span>,a[i])=a[i];</span><br><span class="line">	<span class="type">int</span> res=<span class="number">1</span>; <span class="keyword">while</span>(f[res]!=f[<span class="number">0</span>]) res++;</span><br><span class="line">	cout&lt;&lt;res<span class="number">-1</span>&lt;&lt;endl;</span><br><span class="line">	<span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure></li>
+<h5 id="code"><a class="markdownIt-Anchor" href="#code"></a> code :</h5>
+<figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span><span class="string">&lt;bits/stdc++.h&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">define</span> int long long</span></span><br><span class="line"><span class="meta">#<span class="keyword">define</span> rep(i,a,b) for(int i=(a);i&lt;=(b);++i)</span></span><br><span class="line"><span class="keyword">using</span> <span class="keyword">namespace</span> std;</span><br><span class="line"></span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N=<span class="number">1e6</span> +<span class="number">3</span>;</span><br><span class="line"><span class="type">int</span> n,m,a[N],f[N];</span><br><span class="line"></span><br><span class="line"><span class="function"><span class="type">signed</span> <span class="title">main</span><span class="params">()</span></span></span><br><span class="line"><span class="function"></span>&#123;</span><br><span class="line">	cin&gt;&gt;n; <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n;i++) cin&gt;&gt;a[i];</span><br><span class="line">	<span class="built_in">memset</span>(f,<span class="number">0x3f</span>,<span class="keyword">sizeof</span> f);</span><br><span class="line">	<span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n;i++) *<span class="built_in">upper_bound</span>(f+<span class="number">1</span>,f+n+<span class="number">1</span>,a[i])=a[i];</span><br><span class="line">	<span class="type">int</span> res=<span class="number">1</span>; <span class="keyword">while</span>(f[res]!=f[<span class="number">0</span>]) res++;</span><br><span class="line">	cout&lt;&lt;res<span class="number">-1</span>&lt;&lt;endl;</span><br><span class="line">	<span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
+</li>
 </ol>
 </li>
 </ul>
-<h3 id="二维平面上的-DP-与-状态压缩-DP"><a href="#二维平面上的-DP-与-状态压缩-DP" class="headerlink" title="二维平面上的$DP$ 与 状态压缩$DP$"></a>二维平面上的$DP$ 与 状态压缩$DP$</h3><ul>
-<li><h5 id="怎样判断？"><a href="#怎样判断？" class="headerlink" title="怎样判断？"></a>怎样判断？</h5><blockquote>
+<h3 id="二维平面上的dp-与-状态压缩dp"><a class="markdownIt-Anchor" href="#二维平面上的dp-与-状态压缩dp"></a> 二维平面上的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span> 与 状态压缩<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span></h3>
+<ul>
+<li>
+<h5 id="怎样判断"><a class="markdownIt-Anchor" href="#怎样判断"></a> 怎样判断？</h5>
+<blockquote>
 <p>二维平面看题面。</p>
-<p>状态压缩的$n\le 22$。</p>
+<p>状态压缩的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>≤</mo><mn>22</mn></mrow><annotation encoding="application/x-tex">n\le 22</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719400000000001em;vertical-align:-0.13597em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">2</span><span class="mord">2</span></span></span></span>。</p>
 </blockquote>
 </li>
-<li><h4 id="例题：-1"><a href="#例题：-1" class="headerlink" title="例题："></a>例题：</h4><ol>
-<li><h4 id="Grid-2"><a href="#Grid-2" class="headerlink" title="Grid 2"></a><a class="link"   href="https://www.luogu.com.cn/problem/AT_dp_y" >Grid 2<i class="fas fa-external-link-alt"></i></a></h4><h5 id="题目："><a href="#题目：" class="headerlink" title="题目："></a>题目：</h5><blockquote>
-<p>给一个 <em>H</em>×<em>W</em> 的网格，每一步只能向右或向下走，给出 $n$ 个坐标，这些坐标对应的位置不能经过，求从左上角 (<em>1</em>,<em>1</em>)走到右下角 (<em>H</em>,<em>W</em>) 的方案数，答案对 $10^9+7$ 取模。</p>
+<li>
+<h4 id="例题-2"><a class="markdownIt-Anchor" href="#例题-2"></a> 例题：</h4>
+<ol>
+<li>
+<h4 id="grid-2"><a class="markdownIt-Anchor" href="#grid-2"></a> <a class="link"   href="https://www.luogu.com.cn/problem/AT_dp_y" >Grid 2<i class="fas fa-external-link-alt"></i></a></h4>
+<h5 id="题目"><a class="markdownIt-Anchor" href="#题目"></a> 题目：</h5>
+<blockquote>
+<p>给一个 <em>H</em>×<em>W</em> 的网格，每一步只能向右或向下走，给出 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span> 个坐标，这些坐标对应的位置不能经过，求从左上角 (<em>1</em>,<em>1</em>)走到右下角 (<em>H</em>,<em>W</em>) 的方案数，答案对 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><msup><mn>0</mn><mn>9</mn></msup><mo>+</mo><mn>7</mn></mrow><annotation encoding="application/x-tex">10^9+7</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.897438em;vertical-align:-0.08333em;"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">9</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">7</span></span></span></span> 取模。</p>
 </blockquote>
-<h5 id="思路："><a href="#思路：" class="headerlink" title="思路："></a>思路：</h5><blockquote>
-<p>首先对于 $f_{i,j}\ (1\le i\le H,1\le j\le W)$ 可行性显然，但空间不够。我们只能对着 $n$ 个坐标开数组。</p>
-<p>我们设方程 $f_i$  表示从 (<em>1,1</em>) 做到第<em>i</em>个坐标，且只经过第$i$个坐标的方案总数。</p>
+<h5 id="思路"><a class="markdownIt-Anchor" href="#思路"></a> 思路：</h5>
+<blockquote>
+<p>首先对于 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi></mrow></msub><mtext> </mtext><mo stretchy="false">(</mo><mn>1</mn><mo>≤</mo><mi>i</mi><mo>≤</mo><mi>H</mi><mo separator="true">,</mo><mn>1</mn><mo>≤</mo><mi>j</mi><mo>≤</mo><mi>W</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">f_{i,j}\ (1\le i\le H,1\le j\le W)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.036108em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace"> </span><span class="mopen">(</span><span class="mord">1</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.79549em;vertical-align:-0.13597em;"></span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mclose">)</span></span></span></span> 可行性显然，但空间不够。我们只能对着 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span> 个坐标开数组。</p>
+<p>我们设方程 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">f_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>  表示从 (<em>1,1</em>) 做到第<em>i</em>个坐标，且只经过第<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">i</span></span></span></span>个坐标的方案总数。</p>
 <p>那么，我们尝试使用容斥原理进行转移</p>
 <ul>
-<li>从 (<em>1,1</em>) 到 ($x_i,y_i$) 的方案数是 ${C_{x_i-1+y_i-1}^{x_i -1}}$ </li>
+<li>从 (<em>1,1</em>) 到 (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>x</mi><mi>i</mi></msub><mo separator="true">,</mo><msub><mi>y</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">x_i,y_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>) 的方案数是 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>C</mi><mrow><msub><mi>x</mi><mi>i</mi></msub><mo>−</mo><mn>1</mn><mo>+</mo><msub><mi>y</mi><mi>i</mi></msub><mo>−</mo><mn>1</mn></mrow><mrow><msub><mi>x</mi><mi>i</mi></msub><mo>−</mo><mn>1</mn></mrow></msubsup></mrow><annotation encoding="application/x-tex">{C_{x_i-1+y_i-1}^{x_i -1}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2984239999999998em;vertical-align:-0.402416em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8960079999999999em;"><span style="top:-2.433692em;margin-left:-0.07153em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mbin mtight">−</span><span class="mord mtight">1</span><span class="mbin mtight">+</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:-0.03588em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.1449000000000003em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3280857142857143em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.402416em;"><span></span></span></span></span></span></span></span></span></span></span></li>
 <li>从某一个坐标转移过来的方案数是 $\sum C_{x_i-x_j+y_i-y_j}^{x_i -x_j} $</li>
 </ul>
 </blockquote>
 </li>
-<li><h4 id="Matching"><a href="#Matching" class="headerlink" title="Matching"></a><a class="link"   href="https://vjudge.csgrandeur.cn/contest/569557#problem/O" >Matching<i class="fas fa-external-link-alt"></i></a></h4><h5 id="题目：-1"><a href="#题目：-1" class="headerlink" title="题目："></a>题目：</h5><blockquote>
-<p>给定 <em>N</em>，表示有 N 个男生和 N 个女生，再给你一个矩阵 a，如果$a_{i,j}$ 等于 1，表示 <em>i</em> 这个男生和 <em>j</em> 这个女生可以匹配成一对，否则不能。 问要匹配 N 对的方案数。答案对 $10^9+7$ 取模。</p>
+<li>
+<h4 id="matching"><a class="markdownIt-Anchor" href="#matching"></a> <a class="link"   href="https://vjudge.csgrandeur.cn/contest/569557#problem/O" >Matching<i class="fas fa-external-link-alt"></i></a></h4>
+<h5 id="题目-2"><a class="markdownIt-Anchor" href="#题目-2"></a> 题目：</h5>
+<blockquote>
+<p>给定 <em>N</em>，表示有 N 个男生和 N 个女生，再给你一个矩阵 a，如果<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>a</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi></mrow></msub></mrow><annotation encoding="application/x-tex">a_{i,j}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span> 等于 1，表示 <em>i</em> 这个男生和 <em>j</em> 这个女生可以匹配成一对，否则不能。 问要匹配 N 对的方案数。答案对 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><msup><mn>0</mn><mn>9</mn></msup><mo>+</mo><mn>7</mn></mrow><annotation encoding="application/x-tex">10^9+7</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.897438em;vertical-align:-0.08333em;"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">9</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">7</span></span></span></span> 取模。</p>
 </blockquote>
-<h5 id="思路：-1"><a href="#思路：-1" class="headerlink" title="思路："></a>思路：</h5><blockquote>
+<h5 id="思路-2"><a class="markdownIt-Anchor" href="#思路-2"></a> 思路：</h5>
+<blockquote>
 <p>状压男生，枚举女生</p>
 </blockquote>
 </li>
 </ol>
 </li>
 </ul>
-<h3 id="区间-DP"><a href="#区间-DP" class="headerlink" title="区间$DP$"></a>区间$DP$</h3><p>​	<strong>都离不开三重循环: $\sum\limits_{长度} \sum\limits_{左端点} \sum\limits_{转移的断点} f…$</strong></p>
+<h3 id="区间dp"><a class="markdownIt-Anchor" href="#区间dp"></a> 区间<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span></h3>
+<p>​	<strong>都离不开三重循环: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><munder><mo>∑</mo><mtext>长度</mtext></munder><munder><mo>∑</mo><mtext>左端点</mtext></munder><munder><mo>∑</mo><mtext>转移的断点</mtext></munder><mi>f</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi></mrow><annotation encoding="application/x-tex">\sum\limits_{长度} \sum\limits_{左端点} \sum\limits_{转移的断点} f...</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.744341em;vertical-align:-0.994336em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.750005em;"><span style="top:-2.105664em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord cjk_fallback mtight">长</span><span class="mord cjk_fallback mtight">度</span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.994336em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.750005em;"><span style="top:-2.105664em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord cjk_fallback mtight">左</span><span class="mord cjk_fallback mtight">端</span><span class="mord cjk_fallback mtight">点</span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.994336em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.750005em;"><span style="top:-2.105664em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord cjk_fallback mtight">转</span><span class="mord cjk_fallback mtight">移</span><span class="mord cjk_fallback mtight">的</span><span class="mord cjk_fallback mtight">断</span><span class="mord cjk_fallback mtight">点</span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">∑</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.994336em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span></span></span></span></strong></p>
 <ol>
-<li><h4 id="石子合并"><a href="#石子合并" class="headerlink" title="石子合并"></a><a href="luogu.com.cn/problem/P1880">石子合并</a></h4><h5 id="题目：-2"><a href="#题目：-2" class="headerlink" title="题目："></a>题目：</h5><blockquote>
+<li>
+<h4 id="石子合并"><a class="markdownIt-Anchor" href="#石子合并"></a> <a href="luogu.com.cn/problem/P1880">石子合并</a></h4>
+<h5 id="题目-3"><a class="markdownIt-Anchor" href="#题目-3"></a> 题目：</h5>
+<blockquote>
 <p>在一个圆形操场的四周摆放 <em>N</em> 堆石子，现要将石子有次序地合并成一堆，规定每次只能选相邻的 2 堆合并成新的一堆，并将新的一堆的石子数，记为该次合并的得分。</p>
 <p>试设计出一个算法,计算出将 N* 堆石子合并成 1 堆的最小得分和最大得分。</p>
 </blockquote>
-<h5 id="思路：-2"><a href="#思路：-2" class="headerlink" title="思路："></a>思路：</h5><blockquote>
+<h5 id="思路-3"><a class="markdownIt-Anchor" href="#思路-3"></a> 思路：</h5>
+<blockquote>
 <p>令<code>dp[i][j]</code>表示区间<code>[i,j]</code>的最小价值。</p>
 <p>不妨从终点考虑问题，即结果为两个子区间合并的最小值再加上合并需要的代价即可。</p>
 <p>枚举两个子区间，即枚举这个区间的中间点k，使这个区间被分为<code>[i,k]</code>和<code>[k+1,j]</code>两个区间，取一遍最小值加上合并的即为当前区间所求。</p>
@@ -342,34 +310,178 @@
 <p>所以<code>dp[i][j]=min(dp[i][j],dp[i][k]+dp[k+1][j]+sum[j]-sum[i-1])</code></p>
 </blockquote>
 </li>
-<li><h4 id="Deque"><a href="#Deque" class="headerlink" title="Deque"></a><a class="link"   href="https://vjudge.csgrandeur.cn/contest/569557#problem/L" >Deque<i class="fas fa-external-link-alt"></i></a></h4><h5 id="题目：-3"><a href="#题目：-3" class="headerlink" title="题目："></a>题目：</h5><blockquote>
-<p>给定 N 个数的序列 $A$。</p>
+<li>
+<h4 id="deque"><a class="markdownIt-Anchor" href="#deque"></a> <a class="link"   href="https://vjudge.csgrandeur.cn/contest/569557#problem/L" >Deque<i class="fas fa-external-link-alt"></i></a></h4>
+<h5 id="题目-4"><a class="markdownIt-Anchor" href="#题目-4"></a> 题目：</h5>
+<blockquote>
+<p>给定 N 个数的序列 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal">A</span></span></span></span>。</p>
 <p>A 和 B 轮流取数，每个人每次可以从序列<strong>头部</strong>或者<strong>尾部</strong>取走一个数（直到序列为空）。</p>
 <p>A 和 B 都希望自己取得的数的总和尽可能大。</p>
 <p>假设最优策略下，A 取得的数的总和是 X，B 取得的数的总和是 Y， 请输出 X-Y。</p>
 </blockquote>
-<h5 id="思路：-3"><a href="#思路：-3" class="headerlink" title="思路："></a>思路：</h5><blockquote>
-<p>显然游戏过程中剩下的数必然是连续的一段。设 $f_{i,j}$ 表示剩下下标为 $[i,j]$ 的数时，先手（并非当前的先手而是开始时的先手，下同）能取得的最大分数差。</p>
+<h5 id="思路-4"><a class="markdownIt-Anchor" href="#思路-4"></a> 思路：</h5>
+<blockquote>
+<p>显然游戏过程中剩下的数必然是连续的一段。设 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi></mrow></msub></mrow><annotation encoding="application/x-tex">f_{i,j}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span> 表示剩下下标为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mi>i</mi><mo separator="true">,</mo><mi>j</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[i,j]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">[</span><span class="mord mathnormal">i</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span><span class="mclose">]</span></span></span></span> 的数时，先手（并非当前的先手而是开始时的先手，下同）能取得的最大分数差。</p>
 <p>分两种情况讨论：</p>
 <ul>
-<li>已经取走的数为偶数个，此时先手取，$f_{i,j}$&#x3D;$max⁡$ ($f_{i+1,j}+a_i$,$f_{i,j-1}$,$f_{i,j-1}+a_j$)</li>
-<li>已经取走的数为奇数个，此时后手取，$f_{i,j}$&#x3D;$max$⁡ ($f_{i+1,j}-a_i$,$f_{i,j-1}$,$f_{i,j-1}-a_j$)</li>
+<li>已经取走的数为偶数个，此时先手取，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi></mrow></msub></mrow><annotation encoding="application/x-tex">f_{i,j}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span>=<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi><mi>a</mi><mi>x</mi><mtext>⁡</mtext></mrow><annotation encoding="application/x-tex">max⁡</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">a</span><span class="mord mathnormal">x</span><span class="mord">⁡</span></span></span></span> (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo>+</mo><mn>1</mn><mo separator="true">,</mo><mi>j</mi></mrow></msub><mo>+</mo><msub><mi>a</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">f_{i+1,j}+a_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>,<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">f_{i,j-1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span>,<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>+</mo><msub><mi>a</mi><mi>j</mi></msub></mrow><annotation encoding="application/x-tex">f_{i,j-1}+a_j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span>)</li>
+<li>已经取走的数为奇数个，此时后手取，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi></mrow></msub></mrow><annotation encoding="application/x-tex">f_{i,j}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span>=<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">max</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">m</span><span class="mord mathnormal">a</span><span class="mord mathnormal">x</span></span></span></span>⁡ (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo>+</mo><mn>1</mn><mo separator="true">,</mo><mi>j</mi></mrow></msub><mo>−</mo><msub><mi>a</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">f_{i+1,j}-a_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mbin mtight">+</span><span class="mord mtight">1</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>,<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi><mo>−</mo><mn>1</mn></mrow></msub></mrow><annotation encoding="application/x-tex">f_{i,j-1}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span>,<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>f</mi><mrow><mi>i</mi><mo separator="true">,</mo><mi>j</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>−</mo><msub><mi>a</mi><mi>j</mi></msub></mrow><annotation encoding="application/x-tex">f_{i,j-1}-a_j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.980548em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.716668em;vertical-align:-0.286108em;"></span><span class="mord"><span class="mord mathnormal">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.311664em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.286108em;"><span></span></span></span></span></span></span></span></span></span>)</li>
 </ul>
 </blockquote>
 </li>
 </ol>
-<h3 id="换根-DP"><a href="#换根-DP" class="headerlink" title="换根$DP$"></a>换根$DP$</h3><p>​	<strong>本质上只是把序列变成了树</strong></p>
+<h3 id="换根dp"><a class="markdownIt-Anchor" href="#换根dp"></a> 换根<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span></h3>
+<p>​	<strong>本质上只是把序列变成了树</strong></p>
 <ol>
-<li><h4 id="Subtree"><a href="#Subtree" class="headerlink" title="Subtree"></a><a class="link"   href="https://vjudge.csgrandeur.cn/contest/569557#problem/V" >Subtree<i class="fas fa-external-link-alt"></i></a></h4><h5 id="题目：-4"><a href="#题目：-4" class="headerlink" title="题目："></a>题目：</h5><blockquote>
-<p>有一个 <em>n</em> 个节点的树，对一些节点染色，使得所有被染色的节点是一个连通块。求对于 $1,2,3,…,n$每个节点，该节点被染色的方案个数。所有答案对 <em>M</em> 取模。</p>
+<li>
+<h4 id="subtree"><a class="markdownIt-Anchor" href="#subtree"></a> <a class="link"   href="https://vjudge.csgrandeur.cn/contest/569557#problem/V" >Subtree<i class="fas fa-external-link-alt"></i></a></h4>
+<h5 id="题目-5"><a class="markdownIt-Anchor" href="#题目-5"></a> 题目：</h5>
+<blockquote>
+<p>有一个 <em>n</em> 个节点的树，对一些节点染色，使得所有被染色的节点是一个连通块。求对于 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mn>3</mn><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo separator="true">,</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">1,2,3,...,n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8388800000000001em;vertical-align:-0.19444em;"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">3</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord">.</span><span class="mord">.</span><span class="mord">.</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">n</span></span></span></span>每个节点，该节点被染色的方案个数。所有答案对 <em>M</em> 取模。</p>
 </blockquote>
-<h5 id="思路：-4"><a href="#思路：-4" class="headerlink" title="思路："></a>思路：</h5><blockquote>
-<p>我们设$p_i$表示以$i$为跟的子树中的可行方案数,$q_i$表示$i$的父节点中除了$i$的方案数。</p>
-<p>那么，有$ans_i&#x3D;(q_i+1)*p_i$。</p>
+<h5 id="思路-5"><a class="markdownIt-Anchor" href="#思路-5"></a> 思路：</h5>
+<blockquote>
+<p>我们设<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>p</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">p_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>表示以<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">i</span></span></span></span>为跟的子树中的可行方案数,<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>q</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">q_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>表示<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">i</span></span></span></span>的父节点中除了<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">i</span></span></span></span>的方案数。</p>
+<p>那么，有<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><mi>n</mi><msub><mi>s</mi><mi>i</mi></msub><mo>=</mo><mo stretchy="false">(</mo><msub><mi>q</mi><mi>i</mi></msub><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mo>∗</mo><msub><mi>p</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">ans_i=(q_i+1)*p_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="mord mathnormal">a</span><span class="mord mathnormal">n</span><span class="mord"><span class="mord mathnormal">s</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:-0.03588em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord mathnormal">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>。</p>
 </blockquote>
 </li>
 </ol>
-<h3 id="DP-优化"><a href="#DP-优化" class="headerlink" title="$DP$优化"></a>$DP$优化</h3><p>​	<strong>根据方程运用相应的数据结构即可</strong>。</p>
+<h3 id="dp优化"><a class="markdownIt-Anchor" href="#dp优化"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span>优化</h3>
+<p>​	<strong>根据方程运用相应的数据结构即可</strong>。</p>
+]]></content>
+  </entry>
+  <entry>
+    <title>CSP总结</title>
+    <url>/2023/10/24/CSP/</url>
+    <content><![CDATA[<h1 id="csp-游记"><a class="markdownIt-Anchor" href="#csp-游记"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>S</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">CSP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span> 游记</h1>
+<h3 id="day-0"><a class="markdownIt-Anchor" href="#day-0"></a> Day 0</h3>
+<blockquote>
+<p>晚上去了酒店，和另外几个人一起复习了 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mi>a</mi><mi>r</mi><mi>j</mi><mi>a</mi><mi>n</mi></mrow><annotation encoding="application/x-tex">Tarjan</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord mathnormal">a</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal" style="margin-right:0.05724em;">j</span><span class="mord mathnormal">a</span><span class="mord mathnormal">n</span></span></span></span> ，然后就睡了。</p>
+<p>睡觉前想着 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2.5</mn><mi>h</mi></mrow><annotation encoding="application/x-tex">2.5h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord">2</span><span class="mord">.</span><span class="mord">5</span><span class="mord mathnormal">h</span></span></span></span> 写前两个题，后两个题打下暴力，应该能拿  <strong>一等</strong>。</p>
+</blockquote>
+<h3 id="day-1-上午"><a class="markdownIt-Anchor" href="#day-1-上午"></a> Day 1 + 上午</h3>
+<blockquote>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>7</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>40</mn></mrow><annotation encoding="application/x-tex">7\ :\ 40</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">7</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">4</span><span class="mord">0</span></span></span></span></p>
+<p>早上起来的最早，但发现自己感冒了。喝了只 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>蒲地蓝</mtext></mrow><annotation encoding="application/x-tex">蒲地蓝</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">蒲</span><span class="mord cjk_fallback">地</span><span class="mord cjk_fallback">蓝</span></span></span></span> ，还戴上了 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>开喉剑</mtext></mrow><annotation encoding="application/x-tex">开喉剑</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">开</span><span class="mord cjk_fallback">喉</span><span class="mord cjk_fallback">剑</span></span></span></span> 。</p>
+<p>心里有种不祥的预感，感觉 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>3</mn></mrow><annotation encoding="application/x-tex">T3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">3</span></span></span></span> 会是与式子有关的 大模拟。</p>
+<p>$\ $</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>8</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>30</mn></mrow><annotation encoding="application/x-tex">8\ :\ 30</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">8</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">3</span><span class="mord">0</span></span></span></span></p>
+<p>到一中集了合，拍了张照。果老师讲了些关于低级失误的事。</p>
+<p>$\ $</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>8</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>30</mn></mrow><annotation encoding="application/x-tex">8\ :\ 30</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">8</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">3</span><span class="mord">0</span></span></span></span></p>
+<p>进了考场，发现座位设计非常 <code>反人类</code>，腿稍稍往前放一点就会碰到膝盖。</p>
+<p>题面与压缩包出现了分离，<s>监考老师也搞了很久</s>。</p>
+<p>$\ $</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>8</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>55</mn></mrow><annotation encoding="application/x-tex">8\ :\ 55</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">8</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">5</span><span class="mord">5</span></span></span></span></p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>1</mn></mrow><annotation encoding="application/x-tex">T1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">1</span></span></span></span> 感觉像约瑟夫，但 手搓样例 后发现每次会消掉 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">⌊</mo><mfrac><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow><mn>3</mn></mfrac><mo stretchy="false">⌋</mo></mrow><annotation encoding="application/x-tex">\lfloor \frac{n-1} {3} \rfloor</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.190108em;vertical-align:-0.345em;"></span><span class="mopen">⌊</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.845108em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">3</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span><span class="mbin mtight">−</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose">⌋</span></span></span></span> 个，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi><mi>h</mi><mi>i</mi><mi>l</mi><mi>e</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">while(n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mord mathnormal">h</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span></span> 即可。</p>
+<p>对于第二个问，有一个显然的性质:</p>
+<blockquote>
+<p>在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span> 消掉前，他一定在末尾。</p>
+</blockquote>
+<p>所以<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi><mi>h</mi><mi>i</mi><mi>l</mi><mi>e</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">while(n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02691em;">w</span><span class="mord mathnormal">h</span><span class="mord mathnormal">i</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal">e</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span></span>时判断一下 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mi mathvariant="normal">%</mi><mn>3</mn><mo>=</mo><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">(n-1)\%3==1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">)</span><span class="mord">%</span><span class="mord">3</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span></span><span class="base"><span class="strut" style="height:0.36687em;vertical-align:0em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span> 即可。</p>
+<p>$\ $</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>9</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>30</mn></mrow><annotation encoding="application/x-tex">9\ :\ 30</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">9</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">3</span><span class="mord">0</span></span></span></span></p>
+<p>把 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>1</mn></mrow><annotation encoding="application/x-tex">T1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">1</span></span></span></span> 的对拍打了一下，然后发现 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>2</mn></mrow><annotation encoding="application/x-tex">T2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">2</span></span></span></span> 是贪心水题，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>15</mn><mi>m</mi><mi>i</mi><mi>n</mi></mrow><annotation encoding="application/x-tex">15min</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord">5</span><span class="mord mathnormal">m</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span></span></span></span> 切了。</p>
+<p>$\ $</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>9</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>50</mn></mrow><annotation encoding="application/x-tex">9\ :\ 50</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">9</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">5</span><span class="mord">0</span></span></span></span></p>
+<p>发现 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>3</mn></mrow><annotation encoding="application/x-tex">T3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">3</span></span></span></span> 是二次函数求值，回想起了去年 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>2</mn></mrow><annotation encoding="application/x-tex">T2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">2</span></span></span></span> 用 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>s</mi><mi>q</mi><mi>r</mi><mi>t</mi></mrow><annotation encoding="application/x-tex">sqrt</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.80952em;vertical-align:-0.19444em;"></span><span class="mord mathnormal">s</span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">t</span></span></span></span> 爆精度，就筛了 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mi>e</mi><mn>6</mn></mrow><annotation encoding="application/x-tex">1e6</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord mathnormal">e</span><span class="mord">6</span></span></span></span> 内的质数。</p>
+<p>然后模拟即可。</p>
+<p>$\ $</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>11</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>00</mn></mrow><annotation encoding="application/x-tex">11\ :\ 00</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord">1</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span><span class="mord">0</span></span></span></span></p>
+<p>把前三个题看了一遍，发现没问题，开冲 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>4</mn></mrow><annotation encoding="application/x-tex">T4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">4</span></span></span></span>。</p>
+<p>$\ $</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>12</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>00</mn></mrow><annotation encoding="application/x-tex">12\ :\ 00</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord">2</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span><span class="mord">0</span></span></span></span></p>
+<p>考试结束，预估</p>
+<p>$100\ +\ 100\ +\ 100\ +\ 10\ =\ 310  $ ， 感觉<strong>一等</strong>没问题。</p>
+</blockquote>
+<h3 id="day-1-下午"><a class="markdownIt-Anchor" href="#day-1-下午"></a> Day 1 + 下午</h3>
+<blockquote>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>30</mn></mrow><annotation encoding="application/x-tex">2\ :\ 30</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">2</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">3</span><span class="mord">0</span></span></span></span></p>
+<p>进入了考场，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mi>d</mi><mi>f</mi></mrow><annotation encoding="application/x-tex">pdf</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathnormal">p</span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span></span></span></span> 的密码老师没找到，延迟了 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>5</mn><mi>m</mi><mi>i</mi><mi>n</mi></mrow><annotation encoding="application/x-tex">5min</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord">5</span><span class="mord mathnormal">m</span><span class="mord mathnormal">i</span><span class="mord mathnormal">n</span></span></span></span>。</p>
+<p>$\ $</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>00</mn></mrow><annotation encoding="application/x-tex">3\ :\ 00</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">3</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span><span class="mord">0</span></span></span></span></p>
+<p>发现 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>1</mn></mrow><annotation encoding="application/x-tex">T1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">1</span></span></span></span> 是水题，枚举所有状态再反过来判断即可。</p>
+<p>$\ $</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>35</mn></mrow><annotation encoding="application/x-tex">3\ :\ 35</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">3</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">3</span><span class="mord">5</span></span></span></span></p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>2</mn></mrow><annotation encoding="application/x-tex">T2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">2</span></span></span></span> 先打了一个 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mn>3</mn></msup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(n^3)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span> 的暴力，然后发现枚举右端点太费时间，优化成了 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mn>2</mn></msup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(n^2)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></p>
+<p>$\ $</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>55</mn></mrow><annotation encoding="application/x-tex">3\ :\ 55</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">3</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">5</span><span class="mord">5</span></span></span></span></p>
+<p>看了一下 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>4</mn></mrow><annotation encoding="application/x-tex">T4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">4</span></span></span></span> ，感觉像 <code>树上DP</code> ，但没推出来，转去了 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>3</mn></mrow><annotation encoding="application/x-tex">T3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">3</span></span></span></span>。</p>
+<p>$\ $</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>6</mn><mtext> </mtext><mo>:</mo><mtext> </mtext><mn>00</mn></mrow><annotation encoding="application/x-tex">6\ :\ 00</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">6</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span><span class="mord">0</span></span></span></span></p>
+<p>一直在调 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>3</mn></mrow><annotation encoding="application/x-tex">T3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">3</span></span></span></span> ，感觉灵魂出窍。</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>对其原则</mtext></mrow><annotation encoding="application/x-tex">对其原则</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">对</span><span class="mord cjk_fallback">其</span><span class="mord cjk_fallback">原</span><span class="mord cjk_fallback">则</span></span></span></span> 很好做，但 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4</mn></mrow><annotation encoding="application/x-tex">4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">4</span></span></span></span> 操作难调得死，最后修修补补的过了大样例。</p>
+<p><s><strong>考完发现没有初始化</strong></s>。</p>
+<p>$\ $</p>
+<p>估分 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>100</mn><mtext> </mtext><mo>+</mo><mtext> </mtext><mn>50</mn><mtext> </mtext><mo>+</mo><mtext> </mtext><mo>+</mo><mtext> </mtext><mo stretchy="false">?</mo><mtext> </mtext><mo>+</mo><mtext> </mtext><mn>0</mn><mtext> </mtext><mo>=</mo><mtext> </mtext><mn>15</mn><msup><mn>0</mn><mo>+</mo></msup></mrow><annotation encoding="application/x-tex">100\ +\ 50\ +\ +\ ?\ +\ 0\ =\ 150^+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">1</span><span class="mord">0</span><span class="mord">0</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">5</span><span class="mord">0</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.77777em;vertical-align:-0.08333em;"></span><span class="mord">+</span><span class="mspace"> </span><span class="mclose">?</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.771331em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord">5</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.771331em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">+</span></span></span></span></span></span></span></span></span></span></span></p>
+</blockquote>
+<h2 id="反思"><a class="markdownIt-Anchor" href="#反思"></a> 反思</h2>
+<blockquote>
+<p>比赛节奏感觉可以，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi></mrow><annotation encoding="application/x-tex">S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span></span></span></span> 组 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>4</mn></mrow><annotation encoding="application/x-tex">T4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">4</span></span></span></span> 没看出来感觉很可惜。</p>
+<p>听说 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>J</mi></mrow><annotation encoding="application/x-tex">J</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.09618em;">J</span></span></span></span> 组的 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>4</mn></mrow><annotation encoding="application/x-tex">T4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">4</span></span></span></span> 是分层图最短路，考场上自己没去想。</p>
+<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi></mrow><annotation encoding="application/x-tex">S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span></span></span></span> 组 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi><mn>3</mn></mrow><annotation encoding="application/x-tex">T3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">3</span></span></span></span> 能拿多少是多少，得一等的希望就在他身上了。</p>
+</blockquote>
+]]></content>
+  </entry>
+  <entry>
+    <title>图论总结</title>
+    <url>/2024/01/10/%E5%9B%BE%E8%AE%BA/</url>
+    <content><![CDATA[<h1 id="图论"><a class="markdownIt-Anchor" href="#图论"></a> 图论</h1>
+<hr />
+<h2 id="0有感而发"><a class="markdownIt-Anchor" href="#0有感而发"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0.</mn></mrow><annotation encoding="application/x-tex">0.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span><span class="mord">.</span></span></span></span>有感而发</h2>
+<blockquote>
+<p><em>眼睛瞎了有利于打Dijkstra。</em> by NotDeep</p>
+<p><em>如果这题我不会做，那么一定是图论。</em> by NotDeep</p>
+</blockquote>
+<hr />
+<h2 id="1-基本算法"><a class="markdownIt-Anchor" href="#1-基本算法"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1.</mn></mrow><annotation encoding="application/x-tex">1.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord">.</span></span></span></span> 基本算法</h2>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>1</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 1:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">1</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> <strong>Dijkstra</strong></p>
+<p>​		本质是 $贪心\ +\ DP $。</p>
+<p>​		适用于非负权权图，保证当前取出的节点的最短路是<strong>确定的</strong>，是未确定最短路的节点中<strong>最小的</strong>。</p>
+<p>​		常见题型 ： 补图，非负权图上用 <em>ta</em> ( <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mi>P</mi><mi>F</mi><mi>A</mi></mrow><annotation encoding="application/x-tex">SPFA</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mord mathnormal">A</span></span></span></span>已死 )。</p>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>2</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 2:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">2</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> <strong>Floyd</strong></p>
+<p>​		通过 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mn>3</mn></msup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(n^3)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.064108em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span> 的时间求出任意两点的最短路。<strong>可以在负权图上使用。</strong></p>
+<p>​		可以求 <strong>最小环</strong>,<strong>传递闭包</strong>。</p>
+<p>​		下面对最小环进行说明:</p>
+<figure class="highlight c++"><table><tr><td class="code"><pre><span class="line"><span class="comment">//g[i][j]表示 i-&gt;j 的最短路,f[i][j]表示i-&gt;j的 边的长度</span></span><br><span class="line"><span class="comment">//把最短路拆成 (i-j) + (i&gt;k,k-&gt;j)</span></span><br><span class="line"><span class="comment">//用 dji 可以做到 O(m(n+m)log m)</span></span><br><span class="line"><span class="keyword">for</span>(<span class="type">int</span> k=<span class="number">1</span>;k&lt;=n;k++)</span><br><span class="line">&#123;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=k<span class="number">-1</span>;i++)</span><br><span class="line">        <span class="keyword">for</span>(<span class="type">int</span> j=i+<span class="number">1</span>;j&lt;=k<span class="number">-1</span>;j++)</span><br><span class="line">            ans=<span class="built_in">min</span>(ans,f[i][k]+f[k][j]+g[i][j]);</span><br><span class="line">	<span class="keyword">for</span>(<span class="type">int</span> i=<span class="number">1</span>;i&lt;=n;i++)</span><br><span class="line">		<span class="keyword">for</span>(<span class="type">int</span> j=<span class="number">1</span>;j&lt;=n;j++)</span><br><span class="line">            g[i][j]=<span class="built_in">min</span>(g[i][k]+g[k][j],g[i][j]);</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>3</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 3:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">3</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> <strong>Bellman–Ford</strong></p>
+<p>​		从 <strong>边</strong> 的角度考虑最短路：</p>
+<p>​			最短路的边的个数 <strong>最多</strong> 是 n-1。</p>
+<p>​		如果 <strong>边数</strong> 大于了 n-1 , 说明原图上有负环。</p>
+<p>​		通过 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi><mi>o</mi><mi>r</mi><mo stretchy="false">(</mo><mi>i</mi><mo>=</mo><mn>1</mn><mtext> </mtext><mo>→</mo><mtext> </mtext><mi>n</mi><mo stretchy="false">)</mo><mtext>   </mtext><mi>f</mi><mi>o</mi><mi>r</mi><mo stretchy="false">(</mo><mo stretchy="false">[</mo><mi>u</mi><mo separator="true">,</mo><mi>v</mi><mo stretchy="false">]</mo><mo>∈</mo><mi>E</mi><mo stretchy="false">)</mo><mtext>  松弛</mtext></mrow><annotation encoding="application/x-tex">for(i=1\ \rightarrow\ n)\ \ \ for([u,v] \in E)\ \ 松弛</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mopen">(</span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">→</span><span class="mspace"> </span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">n</span><span class="mclose">)</span><span class="mspace"> </span><span class="mspace"> </span><span class="mspace"> </span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mord mathnormal">o</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mopen">(</span><span class="mopen">[</span><span class="mord mathnormal">u</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mclose">]</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mclose">)</span><span class="mspace"> </span><span class="mspace"> </span><span class="mord cjk_fallback">松</span><span class="mord cjk_fallback">弛</span></span></span></span> 可以让每一条边都走过。</p>
+<p>​		但实际上跑不满，所以有了 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mi>P</mi><mi>F</mi><mi>A</mi></mrow><annotation encoding="application/x-tex">SPFA</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="mord mathnormal">A</span></span></span></span>。</p>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>4</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 4:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">4</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> <strong>SPFA</strong></p>
+<p>​		对<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>3</mn></mrow><annotation encoding="application/x-tex">Case\ 3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">3</span></span></span></span>的广搜优化，可以判负环。最坏 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mi>n</mi><mi>m</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(nm)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mord mathnormal">m</span><span class="mclose">)</span></span></span></span>。</p>
+<p>​		优化点<a class="link"   href="https://www.luogu.com.cn/blog/Parabola/spfa-hacker-orzorz" >这儿<i class="fas fa-external-link-alt"></i></a>。</p>
+<hr />
+<h2 id="2-常见思路"><a class="markdownIt-Anchor" href="#2-常见思路"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2.</mn></mrow><annotation encoding="application/x-tex">2.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">2</span><span class="mord">.</span></span></span></span> 常见思路</h2>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>1</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 1:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">1</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> 分层图最短路</p>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>2</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 2:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">2</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> Bellman–Ford 找负环</p>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>3</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 3:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">3</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> 跑完最短路后，在 最短路图(<strong>DAG</strong>) 上<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span>。</p>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>4</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 4:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">4</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> 多维最短路</p>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>5</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 5:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">5</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> 拆贡献/拆来源/YY长啥样</p>
+<hr />
+<h2 id="3-魔改将至"><a class="markdownIt-Anchor" href="#3-魔改将至"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3.</mn></mrow><annotation encoding="application/x-tex">3.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">3</span><span class="mord">.</span></span></span></span> 魔改将至</h2>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>1</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 1:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">1</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> 贪心</p>
+<p>​		以<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>摄像头问题</mtext><mn>2</mn></mrow><annotation encoding="application/x-tex">摄像头问题2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">摄</span><span class="mord cjk_fallback">像</span><span class="mord cjk_fallback">头</span><span class="mord cjk_fallback">问</span><span class="mord cjk_fallback">题</span><span class="mord">2</span></span></span></span>为例：</p>
+<p>​			对于一段区间 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mi>l</mi><mo separator="true">,</mo><mi>r</mi><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[l,r]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">[</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mclose">]</span></span></span></span> 我们连接一条 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>l</mi><mo>→</mo><mi>r</mi><mo>+</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">l \rightarrow r+1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span> 的边，在连接 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi><mo>→</mo><mi>i</mi><mo>−</mo><mn>1</mn><mtext> </mtext><mo separator="true">,</mo><mi>i</mi><mo>∈</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">i \rightarrow i-1\ ,i\in n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.65952em;vertical-align:0em;"></span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">→</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.74285em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.85396em;vertical-align:-0.19444em;"></span><span class="mord">1</span><span class="mspace"> </span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">n</span></span></span></span> 。</p>
+<p>​			令 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi><mi>i</mi><mi>s</mi><msub><mi>t</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">dist_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.84444em;vertical-align:-0.15em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal">i</span><span class="mord mathnormal">s</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.31166399999999994em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> 表示覆盖区间 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mn>1</mn><mo separator="true">,</mo><mi>i</mi><mo>−</mo><mn>1</mn><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">[1,i-1]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">[</span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">i</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">]</span></span></span></span> 的代价，再跑最短路即可。</p>
+<p>​	<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>a</mi><mi>s</mi><mi>e</mi><mtext> </mtext><mn>2</mn><mo>:</mo></mrow><annotation encoding="application/x-tex">Case\ 2:</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">a</span><span class="mord mathnormal">s</span><span class="mord mathnormal">e</span><span class="mspace"> </span><span class="mord">2</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">:</span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">DP</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">D</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span></p>
+<p>​		以 <a class="link"   href="https://codeforces.com/problemset/problem/1216/F" >Wi-Fi<i class="fas fa-external-link-alt"></i></a> 为例：</p>
+<p>​			我们把每种操作转换为 带权区间覆盖 ， 就转回了 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>摄像头</mtext><mn>2</mn></mrow><annotation encoding="application/x-tex">摄像头2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord cjk_fallback">摄</span><span class="mord cjk_fallback">像</span><span class="mord cjk_fallback">头</span><span class="mord">2</span></span></span></span>。</p>
+<hr />
+<div STYLE="page-break-after: always;"></div>
+<h2 id="4-题目详解"><a class="markdownIt-Anchor" href="#4-题目详解"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4.</mn></mrow><annotation encoding="application/x-tex">4.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">4</span><span class="mord">.</span></span></span></span> 题目详解</h2>
+<h4 id="1-p4366"><a class="markdownIt-Anchor" href="#1-p4366"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1.</mn></mrow><annotation encoding="application/x-tex">1.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span><span class="mord">.</span></span></span></span> <a href="https://www.luogu.com.cn/problem/P4366"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>P</mi><mn>4366</mn></mrow><annotation encoding="application/x-tex">P4366</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mord">4</span><span class="mord">3</span><span class="mord">6</span><span class="mord">6</span></span></span></span></a></h4>
+<p>​	卡 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mi>m</mi><mi>log</mi><mo>⁡</mo><mi>m</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(m\log m)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord mathnormal">m</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">m</span><span class="mclose">)</span></span></span></span> 的 dji 的题目少的很，遇见就要珍惜。</p>
+<p>​	考虑异或性质：</p>
+<p class='katex-block'><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>x</mi><mo>⊕</mo><mi>z</mi><mo>=</mo><mo stretchy="false">(</mo><mi>x</mi><mo>⊕</mo><mi>y</mi><mo stretchy="false">)</mo><mo>⊕</mo><mo stretchy="false">(</mo><mi>y</mi><mo>⊕</mo><mi>z</mi><mo stretchy="false">)</mo><mo>&lt;</mo><mo>=</mo><mi>x</mi><mo>⊕</mo><mi>y</mi><mo>+</mo><mi>y</mi><mo>⊕</mo><mi>z</mi></mrow><annotation encoding="application/x-tex">x \oplus z=(x\oplus y) \oplus (y\oplus z)&lt;=x\oplus y+y\oplus z
+</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⊕</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⊕</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⊕</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⊕</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&lt;</span></span><span class="base"><span class="strut" style="height:0.36687em;vertical-align:0em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⊕</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.7777700000000001em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.7777700000000001em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⊕</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span></span></span></span></span></p>
+<p>​	对于每个节点，拆成 32 个节点: <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">{</mo><mi>v</mi><mi mathvariant="normal">∣</mi><mi>v</mi><mo>=</mo><mi>x</mi><mo>⊕</mo><msup><mn>2</mn><mi>k</mi></msup><mo separator="true">,</mo><mi>k</mi><mo>∈</mo><mi>N</mi><mo separator="true">,</mo><mi>v</mi><mo>≤</mo><mi>n</mi><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">\{v|v=x \oplus2^k,k\in N,v\leq n\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">{</span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mord">∣</span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">⊕</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1.043548em;vertical-align:-0.19444em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.849108em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">∈</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.8777699999999999em;vertical-align:-0.19444em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">N</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">v</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">n</span><span class="mclose">}</span></span></span></span>，边数就会缩短成 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>+</mo><mi>m</mi></mrow><annotation encoding="application/x-tex">n\log n+m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathnormal">m</span></span></span></span>。</p>
+<h4 id="2-神秘力量"><a class="markdownIt-Anchor" href="#2-神秘力量"></a> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2.</mn></mrow><annotation encoding="application/x-tex">2.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">2</span><span class="mord">.</span></span></span></span> <a class="link"   href="http://oi.nks.edu.cn:19360/zh/Problem/Details?cid=2627&amp;tid=Q" >神秘力量<i class="fas fa-external-link-alt"></i></a></h4>
+<p>​	先对补图进行概念阐述：</p>
+<p>​		完全图-现有图=现有图的补图</p>
+<p>​	维护时可以用堆乱搞或用链表维护。分别为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mi>m</mi><mi>log</mi><mo>⁡</mo><mi>m</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(m \log m)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord mathnormal">m</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathnormal">m</span><span class="mclose">)</span></span></span></span> 和 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(n)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span></span>。</p>
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