diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index c8a32a4..67835da 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -1,8 +1,19 @@
 
 
 # This method uses a heap to sort an array.
-# Time Complexity:  ?
-# Space Complexity: ?
+# Time Complexity:  n log(n)
+# Space Complexity: n
 def heap_sort(list)
-  raise NotImplementedError, "Method not implemented yet..."
+  heap = MinHeap.new
+
+  list.each do |element|
+    heap.add(element)
+  end
+
+  sorted_list = []
+  until heap.empty?
+    sorted_list.push(heap.remove)
+  end
+
+  return sorted_list
 end
\ No newline at end of file
diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..38a3559 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -14,18 +14,23 @@ def initialize
   end
 
   # This method adds a HeapNode instance to the heap
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: log n
+  # Space Complexity: 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: log n
+  # Space Complexity: log n
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+    return nil if @store.empty?
+    swap(0, @store.length - 1)
+    result = @store.pop
+    heap_down(0) unless @store.empty?
+    return result.value
   end
 
 
@@ -44,10 +49,10 @@ def to_s
   end
 
   # This method returns true if the heap is empty
-  # Time complexity: ?
-  # Space complexity: ?
+  # Time complexity: 1
+  # Space complexity: 1
   def empty?
-    raise NotImplementedError, "Method not implemented yet..."
+    return @store.empty?
   end
 
   private
@@ -55,17 +60,39 @@ 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: log n
+  # Space complexity: log n
   def heap_up(index)
-    
+    return nil if index == 0
+    parent = (index - 1) / 2
+    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.
+  # Time complexity: log n
+  # Space complexity: log n
   def heap_down(index)
-    raise NotImplementedError, "Method not implemented yet..."
+    left = (index * 2) + 1
+    right = (index * 2) + 2
+
+    return @store if @store[left].nil?
+    return nil if left >= @store.length
+    
+    if @store[left].key < @store[index].key
+      # recursive case - left node
+      swap(left, index)
+      heap_down(left)
+    end
+    if right < @store.length && @store[right].key < @store[index].key
+      # recursive case - right node
+      swap(right, index)
+      heap_down(right)
+    end
   end
 
   # If you want a swap method... you're welcome