diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index c8a32a4..931adf1 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -1,8 +1,21 @@
 
 
 # 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)
+  heap = MinHeap.new
+  
+  list.each do |num|
+    heap.add(num)
+  end
+
+  result = []
+  i = 0
+  while i < list.length
+    result << heap.remove()
+    i += 1
+  end
+
+  return result
 end
\ No newline at end of file
diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..6cb20df 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -14,18 +14,26 @@ 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)
   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)
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+    # min heap always remove the smallest element
+    return nil if @store.empty?
+    # swap it with the last node, so we can just pop off the last node in the heap
+    swap(0, @store.length - 1)
+    result = @store.pop
+    
+    heap_down(0) unless @store.empty?
+    return result.value
   end
 
 
@@ -44,10 +52,10 @@ 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 @store.empty?
   end
 
   private
@@ -55,17 +63,46 @@ 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)
-    
+    return if index == 0 # root node
+    # compare the new node with its parent
+    # if out of order, swap
+    parent = (index - 1) / 2
+    if @store[index].key < @store[parent].key
+      swap(index, parent)
+      heap_up(parent)
+    end
+    return
   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..."
+    # will stop when it reached the leave node
+
+    return if index == @store.length 
+    left_child = 2 * index + 1
+    right_child = 2 * index + 2
+    # compare to the smallest child for min heap
+    if right_child < @store.length
+      if @store[left_child].key > @store[right_child].key
+        smallest_child = right_child
+      else
+        smallest_child = left_child
+      end
+
+      if @store[index].key > @store[smallest_child].key
+        swap(index, smallest_child)
+        heap_down(smallest_child)
+      end
+    elsif left_child < @store.length
+      if @store[index].key > @store[left_child].key
+        swap(index, left_child)
+      end
+    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 = []