diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index 6b692e4..bfcdafe 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -1,8 +1,21 @@
-
+require_relative "./min_heap"
 
 # This method uses a heap to sort an array.
-# Time Complexity:  ?
-# Space Complexity: ?
+# Time Complexity:  O n(log n)
+# Space Complexity: O(n) returning_array + internal heap array = O(2n) = O(n)?
 def heapsort(list)
-  raise NotImplementedError, "Method not implemented yet..."
+  heap = MinHeap.new
+
+  #make the minheap tree 
+  list.each do |item|
+    #add method will sort as adding item to heap
+    heap.add(item)
+  end
+
+  returning_list = []
+  (list.length).times do |i|
+    #remove method will pop/return the root aka smallest value 
+    returning_list << heap.remove
+  end
+  return returning_list
 end
\ No newline at end of file
diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..1b38a89 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -8,26 +8,36 @@ 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(1)
+  # 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(1)
+  # Space Complexity: O(log n)
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
-  end
+    if @store.empty?
+      return nil 
+    end
+    
+    #removing the root element 
+    swap(0, @store.length - 1)
+    result = @store.pop
 
+    #re-arranging heap 
+    heap_down(0) unless @store.empty?
+    return result.value 
+  end
 
   # Used for Testing
   def to_s
@@ -39,15 +49,15 @@ 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..."
+    @store.empty?
   end
 
   private
@@ -55,17 +65,42 @@ 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(1)
+  # Space complexity: O(log n)
   def heap_up(index)
-    
+    parent = (index - 1) / 2
+    return if index == 0
+
+    if @store[parent].key > @store[index].key
+      swap(parent, index)
+      heap_up(parent)
+    else #if @store[parent].key < @store[index].key
+      return
+    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.
   def heap_down(index)
-    raise NotImplementedError, "Method not implemented yet..."
+    right = 2 * index + 2
+    left = 2 * index + 1
+    return if left >= @store.length #return if no child exists 
+
+    #initilize smaller in case right index doesn't exist 
+    smaller = left 
+    #determine which is smaller 
+    if @store[right]
+      smaller = @store[left].key > @store[right].key ? right : left
+    end 
+
+    #swap 
+    if @store[smaller].key < @store[index].key
+      swap(smaller, index)
+      heap_down(smaller)
+    else #if @store[smaller].key > @store[index].key
+      return 
+    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..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 = []