diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index c8a32a4..386a804 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -1,8 +1,23 @@
 
 
 # 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)
+  
+  # swap first with the last
+  return list if list.empty?
+  heap = MinHeap.new  # create a min heap
+
+  list.each do |element|
+    heap.add(element)
+  end
+
+  sorted = []
+  i = 0
+  while i < list.length
+    sorted << heap.remove
+    i += 1
+  end
+  sorted
 end
\ No newline at end of file
diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..5f535c7 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -14,18 +14,25 @@ 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) - n is the number of elemnts in the heap
   def add(key, value = key)
-    raise NotImplementedError, "Method not implemented yet..."
+    # put the element to the back of the arr
+    @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..."
+    return nil if @store.empty?
+    swap(0, @store.length - 1) # swap the root & last node 
+    removed = @store.pop
+    heap_down(0) # heap-down
+    return removed.value
   end
 
 
@@ -44,10 +51,10 @@ 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.length == 0 ? true : false
   end
 
   private
@@ -55,17 +62,42 @@ 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(log n)
+  # Space complexity: O(log n)
   def heap_up(index)
-    
+    # compare the new node with its parent, if they are out of order swap and heap-up
+    # to find the parents: i - 1 /2
+    return if index == 0 # base case
+    parent = (index - 1) / 2 # find the parent
+
+    if @store[index].key < @store[parent].key
+      swap(index, parent)
+      heap_up(parent)
+    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..."
+    # compare root with its children 
+    # make a swap with its largest child
+    min_child = index #0
+    left_child = 2 * index  + 1 # 1
+    right_child = 2 * index + 2 # 3
+
+    if left_child < @store.length && @store[left_child].key < @store[min_child].key
+      swap(min_child, left_child)
+    end
+
+    if right_child < @store.length && @store[right_child].key < @store[min_child].key
+      swap(min_child, right_child)
+    end
+    
+    if min_child != index
+      swap(index, min_child)
+      heap_down(min_child)
+    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 = []