diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index c8a32a4..5d1d7a3 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -1,8 +1,23 @@
-
+require_relative "min_heap.rb"
 
 # This method uses a heap to sort an array.
-# Time Complexity:  ?
-# Space Complexity: ?
-def heap_sort(list)
-  raise NotImplementedError, "Method not implemented yet..."
-end
\ No newline at end of file
+# Time Complexity:  O(log n), where n is the number of elements in the array, because both the add() and remove() methods are recursive
+# Space Complexity: O(log n), where n is the number of elements in the array, because both the add() and remove() methods are recursive
+def heapsort(list)
+  heap = MinHeap.new
+
+  list.each do |val|
+    heap.add(val)
+  end
+
+  sorted_array = []
+
+  i = 0
+  while i < list.length
+    removed_node = heap.remove
+    sorted_array << removed_node
+    i += 1
+  end
+
+  return sorted_array
+end
diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..841ab27 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -8,27 +8,31 @@ def initialize(key, value)
 end
 
 class MinHeap
-
   def initialize
     @store = []
   end
 
   # This method adds a HeapNode instance to the heap
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(log n), n is the number of nodes in the heap
+  # Space Complexity: O(log n), n is the number of nodes in the heap, this is a recursive function
   def add(key, value = key)
-    raise NotImplementedError, "Method not implemented yet..."
+    new_node = HeapNode.new(key, value)
+    @store << new_node
+    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), n is the number of nodes in the heap
+  # Space Complexity: O(log n), n is the number of nodes in the heap, this is a recursive function
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+    return if @store.length == 0
+    swap(0, -1)
+    removed_node = @store.pop
+    heap_down(0)
+    return removed_node.value
   end
 
-
   # Used for Testing
   def to_s
     return "[]" if @store.empty?
@@ -39,15 +43,19 @@ def to_s
     end
 
     output += @store.last.value + "]"
-      
+
     return output
   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 in the heap
+  # Space complexity: O(1)
   def empty?
-    raise NotImplementedError, "Method not implemented yet..."
+    if @store.length == 0
+      return true
+    end
+
+    return false
   end
 
   private
@@ -55,17 +63,44 @@ 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), where n is the number of nodes in the heap
+  # Space complexity: O(log n), where n is the number of nodes in the heap because this is recursive
   def heap_up(index)
-    
+    return if index == 0
+
+    parent_index = (index - 1) / 2
+    if @store[parent_index].key > @store[index].key
+      swap(index, parent_index)
+      heap_up(parent_index)
+    end
+    return
   end
 
-  # This helper method takes an index and 
+  # 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..."
+    left_child = index * 2 + 1
+    right_child = index * 2 + 2
+
+    if @store[left_child].nil?
+      #could use the length
+      return
+    end
+    if @store[right_child].nil?
+      if @store[index].key > @store[left_child].key
+        swap(index, left_child)
+      end
+      return
+    end
+
+    if @store[left_child].key < @store[right_child].key
+      swap(left_child, index)
+      heap_down(left_child)
+    else
+      swap(right_child, index)
+      heap_down(right_child)
+    end
   end
 
   # If you want a swap method... you're welcome
@@ -74,4 +109,4 @@ def swap(index_1, index_2)
     @store[index_1] = @store[index_2]
     @store[index_2] = temp
   end
-end
\ No newline at end of file
+end
diff --git a/test/heapsort_test.rb b/test/heapsort_test.rb
index 34402ac..9964e33 100644
--- a/test/heapsort_test.rb
+++ b/test/heapsort_test.rb
@@ -1,8 +1,8 @@
 require_relative "test_helper"
 
-xdescribe "heapsort" do
+describe "heapsort" do
   it "sorts an empty array" do
-    # Arrange 
+    # Arrange
     list = []
 
     # Act
@@ -13,7 +13,7 @@
   end
 
   it "can sort a 1-element array" do
-    # Arrange 
+    # Arrange
     list = [5]
 
     # Act
@@ -22,9 +22,9 @@
     # Assert
     expect(result).must_equal [5]
   end
-  
+
   it "can sort a 5-element array" do
-    # Arrange 
+    # Arrange
     list = [5, 27, 3, 16, -50]
 
     # Act
@@ -32,5 +32,5 @@
 
     # Assert
     expect(result).must_equal [-50, 3, 5, 16, 27]
-  end  
-end
\ No newline at end of file
+  end
+end