diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index c8a32a4..7fb4cb2 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -1,8 +1,24 @@
-
+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(nlogn)
+# Space Complexity: O(n)
+def heapsort(list)
+  return list if list.length <= 1
+
+  # create heap
+  heap = MinHeap.new
+  list.each do |element|
+    heap.add(element, element)
+  end
+
+  # sort list by pulling off item from heap
+  # and replacing current list indices
+  i = 0
+  while i < list.length
+    list[i] = heap.remove
+    i += 1
+  end
+
+  return list
 end
\ No newline at end of file
diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..70bc434 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -14,18 +14,36 @@ def initialize
   end
 
   # This method adds a HeapNode instance to the heap
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(logn), worst case we have to swap through each level of a balanced tree
+  #                           meaning the height of the tree which is logn where n is the number
+  #                           of nodes in our tree
+  # Space Complexity: O(logn), due to the recursive calls through the heap_up helper method
   def add(key, value = key)
-    raise NotImplementedError, "Method not implemented yet..."
+    # insert new node to the bottom of the heap 
+    # by placing it at the end of the array
+    @store.push(HeapNode.new(key, value))
+
+    heap_up(@store.length - 1) if @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(logn) since worst case we have to go through each level, 
+  # n being number of nodes in the heap
+  # Space Complexity: O(1) since not using recursion
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+    return if @store.empty?
+    
+    # swap last item in heap with smallest value
+    swap(0, -1)
+
+    # remove smallest value
+    removedNode = @store.pop
+
+    # maintain heap structure
+    heap_down() if @store.length > 1
+    
+    return removedNode.value
   end
 
 
@@ -44,10 +62,10 @@ 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..."
+    return true if @store.length == 0
   end
 
   private
@@ -55,19 +73,44 @@ 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(logn)
+  # Space complexity: O(logn), n is halved with each recursive call
   def heap_up(index)
+    # base case to exit recursion
+    return if index == 0
     
+    parentIndex = (index - 1) / 2
+
+    if @store[parentIndex].key > @store[index].key
+      swap(index, parentIndex)
+      heap_up(parentIndex)
+    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..."
+  def heap_down(index=0)
+    return if @store.empty?
+
+    while ((2 * index) + 1) < @store.length # so long as we have a left child, continue to swap
+      rightIndex = (2 * index) + 2
+      leftIndex = (2 * index) + 1
+      smallerIndex = leftIndex
+      if (rightIndex < @store.length) && (@store[rightIndex].key < @store[leftIndex].key)
+        smallerIndex = rightIndex
+      end
+
+      if @store[index].key < @store[smallerIndex].key
+        break
+      else
+        swap(index, smallerIndex)
+      end
+      index = smallerIndex
+    end
   end
 
+
   # If you want a swap method... you're welcome
   def swap(index_1, index_2)
     temp = @store[index_1]
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 = []