From 8c4ad0385d37a16f24b9a6cdcf6893e7b657987b Mon Sep 17 00:00:00 2001
From: Julia Bouvier <juliabouv@gmail.com>
Date: Sun, 15 Mar 2020 18:16:35 -0700
Subject: [PATCH 1/2] Implemented min_heap

---
 lib/min_heap.rb | 55 +++++++++++++++++++++++++++++++++++++------------
 1 file changed, 42 insertions(+), 13 deletions(-)

diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..7210e9d 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -14,18 +14,24 @@ def initialize
   end
 
   # This method adds a HeapNode instance to the heap
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: log(n)
+  # Space Complexity: log(n)
   def add(key, value = key)
-    raise NotImplementedError, "Method not implemented yet..."
+    @store << HeapNode.new(key, value)
+    return 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: log(n)
+  # Space Complexity: log(n)
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+    return nil if @store.empty?
+    swap(0, @store.length - 1)
+
+    removed = @store.pop
+    heap_down(0) unless @store.empty?
+    return removed.value
   end
 
 
@@ -44,10 +50,10 @@ def to_s
   end
 
   # This method returns true if the heap is empty
-  # Time complexity: ?
-  # Space complexity: ?
+  # Time complexity: O(n)
+  # Space complexity: O(1)
   def empty?
-    raise NotImplementedError, "Method not implemented yet..."
+    return true if @store.length == 0
   end
 
   private
@@ -55,17 +61,40 @@ 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: log(n)
+  # Space complexity: log(n)
   def heap_up(index)
-    
+    parent_index = (index - 1) / 2
+    return nil if @store.empty?
+    return if index == 0 || @store[index].key >= @store[parent_index].key
+
+    swap(index, parent_index)
+    return 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.
   def heap_down(index)
-    raise NotImplementedError, "Method not implemented yet..."
+    lc_index = index * 2 + 1
+    rc_index = index * 2 + 2
+    return if @store[lc_index].nil? && @store[rc_index].nil?
+    return if index == @store.length - 1
+
+    if @store[rc_index].nil? && @store[lc_index].key <= @store[index].key
+      return swap(index, lc_index)
+    elsif @store[rc_index].nil? && @store[lc_index].key > @store[index].key
+      return
+    end
+
+    return unless @store[lc_index].key <= @store[index].key && @store[rc_index].key <= @store[index].key
+    if @store[lc_index].key <= @store[rc_index].key
+      swap(index, lc_index)
+      return heap_down(lc_index)
+    else
+      swap(index, rc_index)
+      return heap_down(rc_index)
+    end
   end
 
   # If you want a swap method... you're welcome

From b5084b8d28c1248ad92f46e935225d63c8383634 Mon Sep 17 00:00:00 2001
From: Julia Bouvier <juliabouv@gmail.com>
Date: Sun, 15 Mar 2020 18:39:21 -0700
Subject: [PATCH 2/2] Implemented heap_sort

---
 lib/heap_sort.rb      | 20 ++++++++++++++++----
 test/heapsort_test.rb |  2 +-
 2 files changed, 17 insertions(+), 5 deletions(-)

diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index c8a32a4..9eec07d 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -1,8 +1,20 @@
+require_relative "./min_heap"
 
 
 # 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:  n(log(n))
+# Space Complexity: O(1)
+def heapsort(list)
+  heap = MinHeap.new
+
+  until list.empty?
+    heap.add(list.pop)
+  end
+
+  index = 0
+  until heap.empty?
+    list[index] = heap.remove()
+    index += 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 = []