From 0fafcef7c91984418a6b77c9e26eed4fe7e9516f Mon Sep 17 00:00:00 2001
From: peachmakkoli <lee.higgins.dev@gmail.com>
Date: Mon, 5 Oct 2020 21:25:22 -0700
Subject: [PATCH 1/3] completes add and heap_up methods

---
 lib/min_heap.rb | 17 +++++++++++++----
 1 file changed, 13 insertions(+), 4 deletions(-)

diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..dac7992 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -14,10 +14,11 @@ def initialize
   end
 
   # This method adds a HeapNode instance to the heap
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(log n), where n is the number of nodes in the complete binary tree
+  # Space Complexity: O(log n), due to recursive calls of the heap_up method
   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
@@ -58,7 +59,15 @@ def empty?
   # Time complexity: ?
   # Space complexity: ?
   def heap_up(index)
-    
+    return if !index || !@store[index]
+
+    parent = (index - 1) / 2
+
+    if @store[index].key < @store[parent].key
+      swap(index, parent)
+      return if parent == 0
+      heap_up(parent)
+    end
   end
 
   # This helper method takes an index and 

From ce862f66bac8ff924af2926bf52a155b8b1a2ada Mon Sep 17 00:00:00 2001
From: peachmakkoli <lee.higgins.dev@gmail.com>
Date: Mon, 5 Oct 2020 21:46:45 -0700
Subject: [PATCH 2/3] completes remove and heap_down methods

---
 lib/min_heap.rb | 35 +++++++++++++++++++++++++++--------
 1 file changed, 27 insertions(+), 8 deletions(-)

diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index dac7992..f28cf4e 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -14,7 +14,7 @@ def initialize
   end
 
   # This method adds a HeapNode instance to the heap
-  # Time Complexity: O(log n), where n is the number of nodes in the complete binary tree
+  # Time Complexity: O(log n), where n is the number of nodes in a heap (a complete binary tree has log n levels)
   # Space Complexity: O(log n), due to recursive calls of the heap_up method
   def add(key, value = key)
     @store << HeapNode.new(key, value)
@@ -23,10 +23,16 @@ def add(key, value = key)
 
   # This method removes and returns an element from the heap
   #   maintaining the heap structure
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(log n), where n is the number of nodes in a heap (a complete binary tree has log n levels)
+  # Space Complexity: O(log n), due to recursive calls of the heap_down method
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+    return if @store.empty? 
+
+    swap(0, @store.length - 1)
+    result = @store.pop
+    
+    heap_down(0) unless @store.empty?
+    return result.value
   end
 
 
@@ -45,10 +51,10 @@ def to_s
   end
 
   # This method returns true if the heap is empty
-  # Time complexity: ?
-  # Space complexity: ?
+  # Time complexity: O(n), where n is the number of nodes
+  # Space complexity: O(1)
   def empty?
-    raise NotImplementedError, "Method not implemented yet..."
+    return @store.empty?
   end
 
   private
@@ -74,7 +80,20 @@ def heap_up(index)
   #  moves it up the heap if it's smaller
   #  than it's parent node.
   def heap_down(index)
-    raise NotImplementedError, "Method not implemented yet..."
+    left_child = index * 2 + 1
+    right_child = index * 2 + 2
+    return if !@store[left_child] 
+
+    min_child = @store[right_child] ? find_min_child(left_child, right_child) : left_child 
+
+    if @store[index].key > @store[min_child].key
+      swap(index, min_child)
+      heap_down(min_child)
+    end
+  end
+
+  def find_min_child(left_child, right_child)
+    @store[left_child].key <= @store[right_child].key ? left_child : right_child
   end
 
   # If you want a swap method... you're welcome

From 8bf31d7a467811fd7cae152333b0faccfb84ae9a Mon Sep 17 00:00:00 2001
From: peachmakkoli <lee.higgins.dev@gmail.com>
Date: Mon, 5 Oct 2020 22:05:30 -0700
Subject: [PATCH 3/3] completes heapsort method

---
 lib/heap_sort.rb      | 22 ++++++++++++++++++----
 test/heapsort_test.rb |  2 +-
 2 files changed, 19 insertions(+), 5 deletions(-)

diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index 6b692e4..b21d0fc 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -1,8 +1,22 @@
-
+require_relative "min_heap"
 
 # This method uses a heap to sort an array.
-# Time Complexity:  ?
-# Space Complexity: ?
+# Time Complexity: O(n log n), where n is the number of nodes and because this method adds the elements to a heap, then places them back in the array in order
+# Space Complexity: O(log n), due to recursive calls of the heap_up and heap_down methods within the add and remove methods
 def heapsort(list)
-  raise NotImplementedError, "Method not implemented yet..."
+  return list if list.empty? || list.length < 2
+    
+  min_heap = MinHeap.new
+  list.each do |value|
+    min_heap.add(value)
+  end
+
+  i = 0
+
+  while i < list.length
+    list[i] = min_heap.remove
+    i += 1
+  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 = []