diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index c8a32a4..5a45828 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -1,8 +1,25 @@
-
+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..."
-end
\ No newline at end of file
+# Time Complexity:  O(nlogn + nlogn) = O(nlogn) where n is the size of the list
+# Space Complexity: O(n) where n is the size of the list
+def heapsort(list)
+  return list if list.length <= 1
+
+  heap = MinHeap.new
+
+  i = 0
+  while i < list.length
+    heap.add(list[i])
+    i += 1
+  end
+
+  i = 0
+  while i < list.length
+    removed = heap.remove()
+    list[i] = removed
+    i += 1
+  end
+
+  return list
+end
diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..c65a3eb 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -8,26 +8,37 @@ 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(logn) where n is the length of the @store
+  # Space Complexity: O(1)
   def add(key, value = key)
-    raise NotImplementedError, "Method not implemented yet..."
+    new_node = HeapNode.new(key, value)
+    @store.push(new_node)
+
+    if @store.length > 1
+      heap_up((@store.length - 1))
+    end
   end
 
   # This method removes and returns an element from the heap
   #   maintaining the heap structure
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(logn) where n is the length of the @store
+  # Space Complexity: O(1)
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
-  end
+    return nil if @store.length == 0
+
+    swap(0, -1)
+    removed = @store.pop
+    if @store.length > 1
+      heap_down(0)
+    end
 
+    return removed.value
+  end
 
   # Used for Testing
   def to_s
@@ -39,15 +50,19 @@ 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(1)
+  # Space complexity: O(1)
   def empty?
-    raise NotImplementedError, "Method not implemented yet..."
+    if @store.length == 0
+      return true
+    else
+      return false
+    end
   end
 
   private
@@ -55,17 +70,48 @@ 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(logn) where n is the length of the @store
+  # Space complexity: O(logn)
   def heap_up(index)
-    
+    return if index <= 0
+
+    parent_index = (index - 1) / 2
+
+    if @store[index].key < @store[parent_index].key
+      swap(index, parent_index)
+      index = parent_index
+      heap_up(index)
+    end
   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.
+
+  # Time complexity: O(logn) where n is the length of the @store
+  # Space complexity: O(logn)
   def heap_down(index)
-    raise NotImplementedError, "Method not implemented yet..."
+    left_child = (index * 2) + 1
+    right_child = (index * 2) + 2
+    smallest = 0
+
+    return if @store[left_child].nil?
+
+    if @store[right_child].nil?
+      smallest = left_child
+    else
+      if @store[left_child].key < @store[right_child].key
+        smallest = left_child
+      else
+        smallest = right_child
+      end
+    end
+
+    if @store[smallest].key < @store[index].key
+      swap(smallest, index)
+      index = smallest
+      return heap_down(index)
+    end
   end
 
   # If you want a swap method... you're welcome
@@ -74,4 +120,4 @@ 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