From 1fc23032f399c6e05c51c7e3fc5159c900457960 Mon Sep 17 00:00:00 2001
From: Alice Boone <alicegbone@gmail.com>
Date: Thu, 6 May 2021 16:26:41 -0700
Subject: [PATCH 1/3]  Add, remove, empty, index

---
 lib/min_heap.rb | 25 +++++++++++++++++++++----
 1 file changed, 21 insertions(+), 4 deletions(-)

diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..28b8ffc 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -17,7 +17,10 @@ def initialize
   # Time Complexity: ?
   # Space Complexity: ?
   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
@@ -25,7 +28,14 @@ def add(key, value = key)
   # Time Complexity: ?
   # Space Complexity: ?
   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
 
 
@@ -34,6 +44,7 @@ def to_s
     return "[]" if @store.empty?
 
     output = "["
+
     (@store.length - 1).times do |index|
       output += @store[index].value + ", "
     end
@@ -47,7 +58,7 @@ def to_s
   # Time complexity: ?
   # Space complexity: ?
   def empty?
-    raise NotImplementedError, "Method not implemented yet..."
+    return @store.length == 0 ? true : false
   end
 
   private
@@ -58,7 +69,13 @@ def empty?
   # Time complexity: ?
   # Space complexity: ?
   def heap_up(index)
-    
+    return if index == 0
+
+    parent = (index - 1) / 2
+    if @store[index].key < @store[parent].key
+      swap(index, parent)
+      heap_up(parent)
+    end
   end
 
   # This helper method takes an index and 

From f24da256e77d167e34c34210cb6a2dc38f20ef03 Mon Sep 17 00:00:00 2001
From: Alice Boone <alicegbone@gmail.com>
Date: Thu, 6 May 2021 16:31:00 -0700
Subject: [PATCH 2/3] heap down

---
 lib/min_heap.rb | 22 +++++++++++++++++++++-
 1 file changed, 21 insertions(+), 1 deletion(-)

diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 28b8ffc..9bad16b 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -82,7 +82,27 @@ 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..."
+
+    right = 2 * index + 2
+    left = 2 * index + 1
+
+    if right < @store.length
+      if @store[left].key > @store[right].key
+        smaller = right
+      else
+        smaller = left
+      end
+
+      if @store[index].key > @store[smaller].key
+        swap(index, smaller)
+        heap_down(smaller)
+      end
+
+    elsif left < @store.length
+      if @store[index].key > @store[left].key
+        swap(index, left)
+      end
+    end
   end
 
   # If you want a swap method... you're welcome

From a4f8155158db9c79007d3e3714ed0220750d233c Mon Sep 17 00:00:00 2001
From: Alice Boone <alicegbone@gmail.com>
Date: Thu, 6 May 2021 16:36:50 -0700
Subject: [PATCH 3/3] heap sort

---
 lib/heap_sort.rb | 16 +++++++++++++---
 lib/min_heap.rb  | 16 ++++++++--------
 2 files changed, 21 insertions(+), 11 deletions(-)

diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index c8a32a4..e8e6474 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: ?
+# Time Complexity:  O(n log n)
+# Space Complexity: O(n)
 def heap_sort(list)
-  raise NotImplementedError, "Method not implemented yet..."
+  heap = MinHeap.new
+
+  list.each do |element|
+    heap.add(element)
+  end
+
+  list.each_with_index do |number, index|
+    list[index] = heap.remove()
+  end
+
+  return list
 end
\ No newline at end of file
diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 9bad16b..3445b38 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -14,8 +14,8 @@ def initialize
   end
 
   # This method adds a HeapNode instance to the heap
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(log n)
+  # Space Complexity: O(1)
   def add(key, value = key)
 
     @store << HeapNode.new(key, value)
@@ -25,8 +25,8 @@ 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)
+  # Space Complexity: O(log n)
   def remove()
     return nil if @store.empty?
 
@@ -55,8 +55,8 @@ 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?
     return @store.length == 0 ? true : false
   end
@@ -66,8 +66,8 @@ 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)
+  # Space complexity: O(log n)
   def heap_up(index)
     return if index == 0