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Merge pull request #458 from virtual-labs/header_and_footer
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Replaced the missing special character
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@mrudhvika940
mrudhvika940 authored May 6, 2020
2 parents 53a58fd + 3502226 commit 0af891d
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17 changes: 9 additions & 8 deletions src/lab/exp4/Theory.html
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Expand Up @@ -175,7 +175,7 @@ <h2>Application of linked lists is to polynomials</h2>
<li>Let f(x) = Σ<sup>d</sup><sub>i=0</sub> a<sub>i</sub>x<sup>i</sup>.
<br/> The quantity d is called as the degree of the polynomial, with the assumption that a<sub>d</sub> not equal to 0. A polynomial of degree d may however have missing terms i.e., powers j such that 0 &lt;= j &lt; d and a<sub>j</sub> = 0.
<br/> The standard operations on a polynomial are addition and multiplication. If we store the coefficient ofeach term of the polynomials in an array of size d + 1, then these operations can be supported in a straightforwardway. However, for sparse polynomails, i.e., polynomials where there are few non-zero coefficients, this is not efficient. One possible solution is to use linked lists to store degree, coefficient pairs for non-zero coefficients. With this representation, it makes it easier if we keep the list of such pairs in decreasing order of degrees. A polynomial is a sum of terms. Each term consists of a coefficient and a (common) variable raised to an exponent. We consider only integer exponents, for now.
<br/> Example: 4x<sup>3</sup> + 5x – 10.</li>
<br/> Example: 4x<sup>3</sup> + 5x − 10.</li>
<br/>
<li>How to represent a polynomial? Issues in representation, should not waste space, should be easy to use it for operating on polynomials. Any case, we need to store the coefficient and the exponent.
<br/> struct node
Expand All @@ -196,16 +196,16 @@ <h2>Application of linked lists is to polynomials</h2>
<br/>

<li> Adding polynomials :
<br/> (3x<sup>5</sup> – 9x<sup>3</sup> + 4x<sup>2</sup>) + (–8x<sup>5</sup> + 8x<sup>3</sup> + 2)
<br/> = 3x<sup>5</sup> – 8x<sup>5</sup> – 9x<sup>3</sup> + 8x<sup>3</sup> + 4x<sup>2</sup> + 2
<br/> = –5x<sup>5</sup> – x<sup>3</sup> + 4x<sup>2</sup> + 2 </li>
<br/> (3x<sup>5</sup> − 9x<sup>3</sup> + 4x<sup>2</sup>) + (−8x<sup>5</sup> + 8x<sup>3</sup> + 2)
<br/> = 3x<sup>5</sup> − 8x<sup>5</sup> − 9x<sup>3</sup> + 8x<sup>3</sup> + 4x<sup>2</sup> + 2
<br/> = −5x<sup>5</sup> − x<sup>3</sup> + 4x<sup>2</sup> + 2 </li>

<br/>
<li>Multiplying polynomials:
<br/> (2x – 3)(2x<sup>2</sup> + 3x – 2)
<br/> = 2x(2x<sup>2</sup> + 3x – 2) – 3(2x<sup>2</sup> + 3x – 2)
<br/> = 4x<sup>3</sup> + 6x<sup>2</sup> – 4x – 6x<sup>2</sup> – 9x+ 6
<br/> = 4x<sup>3</sup> – 13x+ 6
<br/> (2x − 3)(2x<sup>2</sup> + 3x − 2)
<br/> = 2x(2x<sup>2</sup> + 3x − 2) − 3(2x<sup>2</sup> + 3x − 2)
<br/> = 4x<sup>3</sup> + 6x<sup>2</sup> − 4x − 6x<sup>2</sup> − 9x+ 6
<br/> = 4x<sup>3</sup> − 13x+ 6

</li>
</ul>
Expand Down Expand Up @@ -338,4 +338,5 @@ <h4>Follow Us</h4>




</body><!-- jQuery --></html>
3 changes: 2 additions & 1 deletion src/lab/exp9/Theory.html
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Expand Up @@ -177,7 +177,7 @@ <h1 class="text-h1-lightblue">Spanning Trees in Graphs</h1>
<p><i>
<b>Algorithm Prims(G,v)</b><br/>
Add v to T;<br/>
While T has less than n – 1 edges do<br/>
While T has less than n − 1 edges do<br/>
w = vertex s.t. (v,w) has the smallest weight amongst edges with one endpoint in T and another not in T.<br/>
Add (v,w) to T.<br/>
end-while<br/>
Expand Down Expand Up @@ -313,4 +313,5 @@ <h4>Follow Us</h4>




</body><!-- jQuery --></html>

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