From 73bed56fb256ce408445c87cb9b4d2bf00035c4f Mon Sep 17 00:00:00 2001
From: Li Dai <li.lea.dai@gmail.com>
Date: Thu, 29 Apr 2021 23:21:32 -0700
Subject: [PATCH 1/2] min_heap done

---
 lib/min_heap.rb | 59 ++++++++++++++++++++++++++++++++++++++-----------
 1 file changed, 46 insertions(+), 13 deletions(-)

diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..7f713b4 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -14,18 +14,25 @@ def initialize
   end
 
   # This method adds a HeapNode instance to the heap
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(log n): push O(1) + heap_up O(log n)
+  # Space Complexity: O(log n) : heap_up O(log n)
   def add(key, value = key)
-    raise NotImplementedError, "Method not implemented yet..."
+    @store << HeapNode.new(key, value)
+    heap_up(@store.length - 1)
   end
 
   # This method removes and returns an element from the heap
   #   maintaining the heap structure
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(log n): pop, swap O(1) + heap_down O(log n)
+  # Space Complexity: O(log n) from heap_down call stacks
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+    return nil if @store.empty?
+
+    swap(0, @store.length - 1)
+    removed_element = @store.pop
+    heap_down(0) unless @store.empty?
+
+    return removed_element.value
   end
 
 
@@ -44,10 +51,10 @@ def to_s
   end
 
   # This method returns true if the heap is empty
-  # Time complexity: ?
-  # Space complexity: ?
+  # Time complexity: O(1)
+  # Space complexity: O(1)
   def empty?
-    raise NotImplementedError, "Method not implemented yet..."
+    return @store.length == 0
   end
 
   private
@@ -55,17 +62,43 @@ def empty?
   # This helper method takes an index and
   #  moves it up the heap, if it is less than it's parent node.
   #  It could be **very** helpful for the add method.
-  # Time complexity: ?
-  # Space complexity: ?
+  # Time complexity: O(log n): swap - O(1), and we will do it up to O(log n) times
+  # Space complexity: O(log n) for call stacks
+  # min heap, the smallest node goes up to root
   def heap_up(index)
-    
+    parent_index = (index - 1) / 2
+    #base cases - stop when in order(parent < child) or reach root
+    return @store if @store[index].key > @store[parent_index].key || index == 0
+
+    swap(index, parent_index)
+    heap_up(parent_index)
+     
   end
 
   # This helper method takes an index and 
   #  moves it up the heap if it's smaller
   #  than it's parent node.
+  # swap parent with the smaller child
+  # Time complexity: O(log n): find_smaller_childs_index - O(1), swap - O(1), and we will do it up to O(log n) times
+  # Space complexity: O(log n) for call stacks
   def heap_down(index)
-    raise NotImplementedError, "Method not implemented yet..."
+    left_child = index * 2 + 1
+    right_child = index * 2 + 2
+    smaller_child = find_smaller_childs_index(left_child, right_child)
+    #base cases - node has no child or in order(parent < child) 
+    return @store if @store[smaller_child].nil? || @store[index].key < @store[smaller_child].key 
+
+    swap(index, smaller_child)
+    heap_down(smaller_child)
+
+  end
+
+  def find_smaller_childs_index(left_index, right_index)
+    if @store[right_index]
+      return @store[left_index].key > @store[right_index].key ? right_index : left_index
+    else
+      return left_index
+    end
   end
 
   # If you want a swap method... you're welcome

From 42c0649481f150bbc56514a7945fcc870b898b99 Mon Sep 17 00:00:00 2001
From: Li Dai <li.lea.dai@gmail.com>
Date: Fri, 30 Apr 2021 00:06:49 -0700
Subject: [PATCH 2/2] heap sort done

---
 lib/heap_sort.rb      | 18 ++++++++++++++----
 test/heapsort_test.rb |  2 +-
 2 files changed, 15 insertions(+), 5 deletions(-)

diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index c8a32a4..d6f1043 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -1,8 +1,18 @@
 
 
 # This method uses a heap to sort an array.
-# Time Complexity:  ?
-# Space Complexity: ?
-def heap_sort(list)
-  raise NotImplementedError, "Method not implemented yet..."
+# Time Complexity:  O(nlogn): add O(nlogn) + remove O(nlogn)
+# Space Complexity: O(n) for creating @store to store all the nodes
+def heapsort(list)
+  min_heap = MinHeap.new
+
+  list.each do |element|
+    min_heap.add(element)
+  end
+
+  list.map! do |element|
+    min_heap.remove
+  end
+
+  return list
 end
\ No newline at end of file
diff --git a/test/heapsort_test.rb b/test/heapsort_test.rb
index 34402ac..7ce79b7 100644
--- a/test/heapsort_test.rb
+++ b/test/heapsort_test.rb
@@ -1,6 +1,6 @@
 require_relative "test_helper"
 
-xdescribe "heapsort" do
+describe "heapsort" do
   it "sorts an empty array" do
     # Arrange 
     list = []