diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index c8a32a4..d80d851 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -1,8 +1,23 @@
-
+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:  O(n log n)
+# Space Complexity: O(n)
+def heapsort(list)
+  return [] if list.empty?
+  heap = MinHeap.new
+
+  list.each do |val|
+    heap.add(val)
+  end
+
+  sorted_list = []
+
+  i = 0 
+  until i == list.length
+    sorted_list << heap.remove
+    i += 1
+  end
+
+  sorted_list
 end
\ No newline at end of file
diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..03b26a7 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -14,18 +14,28 @@ def initialize
   end
 
   # This method adds a HeapNode instance to the heap
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(log n)
+  # Space Complexity: O(log n) - potential stack call for heap_up
   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: ?
+  # Time Complexity: O(log n)
+  # Space Complexity: O(log n) - potential head_down stack call
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+    return nil if @store.empty?
+
+    last_index = @store.length - 1
+    swap(0, last_index)
+    result = @store.pop
+
+    # start heap_down with the root(index 0)
+    heap_down(0) unless @store.empty?
+    result.value
   end
 
 
@@ -44,10 +54,10 @@ 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?
-    raise NotImplementedError, "Method not implemented yet..."
+    @store.nil?
   end
 
   private
@@ -55,17 +65,48 @@ 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(log n)
+  # Space complexity: O(log n)
   def heap_up(index)
-    
+    if index == 0 
+      # base case
+      return @store
+    else
+      # recursive step
+      parent = (index - 1) / 2
+
+      if @store[parent].key > @store[index].key
+        swap(parent,index)
+        heap_up(parent)
+      else
+        return @store
+      end
+    end
   end
 
-  # This helper method takes an index and 
-  #  moves it up the heap if it's smaller
-  #  than it's parent node.
+
+  # Time complexity: O(log n)
+  # Space complexity: O(log n)
   def heap_down(index)
-    raise NotImplementedError, "Method not implemented yet..."
+
+    return if index == (@store.length - 1)
+    left_child_index = (index * 2) + 1
+    right_child_index = (index * 3) + 2
+
+    return if !@store[left_child_index]
+
+    if @store[left_child_index].key < @store[index].key
+      if @store[right_child_index] && @store[right_child_index].key < @store[index].key
+        min_child = @store[left_child_index].key <= @store[right_child_index].key ? left_child_index : right_child_index
+        swap(index, min_child)
+        heap_down(min_child)
+      else
+        swap(index, left_child_index)
+        heap_down(left_child_index)
+      end
+    else
+      return
+    end
   end
 
   # If you want a swap method... you're welcome
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 = []