diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index c8a32a4..bff6b58 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -1,8 +1,24 @@
-
+require 'pry'
+require_relative 'min_heap'
 
 # This method uses a heap to sort an array.
-# Time Complexity:  ?
-# Space Complexity: ?
+# Time Complexity:  O(n) followed by O(log n) beacause going through entire array for first operation
+# Space Complexity: I am attempting to do it in O(1)
 def heap_sort(list)
-  raise NotImplementedError, "Method not implemented yet..."
+  if list.nil? || list.empty? || list.length == 1
+    return list
+  end
+
+  min_heap = MinHeap.new
+
+  until list.empty?
+    min_heap.add(list.pop)
+  end
+
+  until min_heap.empty?
+    retrieved = min_heap.remove
+    list.push(retrieved)
+  end
+
+  return list
 end
\ No newline at end of file
diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..99a7e4d 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -1,3 +1,4 @@
+require 'pry'
 class HeapNode
   attr_reader :key, :value
 
@@ -14,18 +15,26 @@ def initialize
   end
 
   # This method adds a HeapNode instance to the heap
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(log n) bc it's a tree 
+  # Space Complexity: O(1)
   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: ?
-  def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+  # Time Complexity: O(log n) bc it's a tree
+  # Space Complexity: O(n log n) bc of recursive calls
+  def remove
+    index = 0
+    return nil if @store.empty?
+
+    swap(0, -1)
+    return_value = @store.pop 
+    heap_down(index)
+
+    return return_value.value
   end
 
 
@@ -44,28 +53,52 @@ def to_s
   end
 
   # This method returns true if the heap is empty
-  # Time complexity: ?
-  # Space complexity: ?
+  # Time complexity: O(1) - Uncertain if Ruby under the hood implements an array in the strictest sense, then by inference it allocates a certain number of spaces to an array and retrieving the length would be constant. Otherwise it is O(n) due to check each element until it becomes nil.
+  # Space complexity: O(1)
   def empty?
-    raise NotImplementedError, "Method not implemented yet..."
+    return @store.empty?
   end
 
   private
 
   # 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: ?
+  # 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: O(logn)
+  # Space complexity: Constant
   def heap_up(index)
-    
+    while index > 0
+      parent_index = ((index - 1) / 2)
+      if @store[parent_index].key > @store[index].key
+        swap(parent_index, index)
+        index = parent_index
+      else
+        return
+      end
+    end
   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..."
+    child_index_left = ((index * 2) + 1)
+    child_index_right = ((index * 2) + 2)
+
+    #if there are no children, return
+    if @store[child_index_left].nil?
+      return 
+    elsif @store[child_index_right].nil?
+      swap(index, child_index_left)
+    else 
+      if @store[child_index_left].key < @store[child_index_right].key  
+        swap(index, child_index_left)
+        heap_down(child_index_left)
+      else
+        swap(index, child_index_right)
+        heap_down(child_index_right)
+      end
+    end
   end
 
   # If you want a swap method... you're welcome
diff --git a/test/min_heap_test.rb b/test/min_heap_test.rb
index 186d4c2..7bfe97c 100644
--- a/test/min_heap_test.rb
+++ b/test/min_heap_test.rb
@@ -78,4 +78,34 @@
   # Another assert
   expect(removed).must_equal "Pasta"
   end
+end
+
+describe "heap sort" do 
+  it "can handle a null list"  do 
+    result = heap_sort(nil)
+    assert_nil(result)
+  end
+
+  it "can handle an empty list" do 
+    list = []
+    result = heap_sort(list)
+
+    assert_empty(result)
+  end
+
+  it "can handle a list with one element" do 
+    list = [10]
+    result = heap_sort(list)
+
+    expect(result).must_equal list
+  end
+
+  it "can sort a list in ascending order using heap sort" do
+    list = [5, 3, 1, 7]
+    min_result = [1, 3, 5, 7]
+
+    sorted_result = heap_sort(list)
+    
+    expect(sorted_result).must_equal(min_result)
+  end
 end
\ No newline at end of file