diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index c8a32a4..9437258 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -1,8 +1,50 @@
 
 
 # This method uses a heap to sort an array.
-# Time Complexity:  ?
-# Space Complexity: ?
+# Time Complexity:  O(n log n)
+# Space Complexity: O(1)
 def heap_sort(list)
-  raise NotImplementedError, "Method not implemented yet..."
+  n = list.size
+  return list if n < 2
+
+  # heap construction - reorganize original array into a maximum heap
+  # proceed from right to left, starting halfway back through the array
+  # O(n)
+  i = (n - 1) / 2
+  while i >= 0
+    heap_down(list, i, n)
+    i -= 1
+  end
+
+  # sort
+  # remove the largest remaining item from the heap and
+  # put it into the array position vacated as the heap shrinks
+  # O(n log n)
+  while n > 0
+    list[0], list[n - 1] = list[n - 1], list[0]
+
+    n -= 1
+    heap_down(list, 0, n)
+
+  end
+  list
+end
+
+
+# max heap heap_down method
+def heap_down(list, index, n)
+  while index * 2 + 1 < n
+    j = index * 2 + 1 # first child
+
+    if j < n - 1 && list[j] < list[j + 1] # greater of two children
+      j += 1
+    end
+
+    if list[index] > list[j] # stop if move will violate heap order
+      break
+    end
+
+    list[index], list[j] = list[j], list[index]
+    index = j
+  end
 end
\ No newline at end of file
diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..7910a33 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -14,18 +14,28 @@ def initialize
   end
 
   # This method adds a HeapNode instance to the heap
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(log n) - worst case, when need heap-up, O(1) - best case
+  # Space Complexity: O(log n) - worst case, when need heap-up, O(1) - best case
   def add(key, value = key)
-    raise NotImplementedError, "Method not implemented yet..."
+    new_node = HeapNode.new(key, value)
+    @store << new_node
+    heap_up(@store.size-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 if @store.empty?
+    if @store.size == 1
+      return @store.pop
+    end
+    # swap the first and the last element in the underlying array
+    @store[-1], @store[0] = @store[0], @store[-1]
+    removed = @store.pop
+    heap_down(0)
+    return removed.value
   end
 
 
@@ -44,10 +54,10 @@ 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..."
+    @store.empty?
   end
 
   private
@@ -55,17 +65,34 @@ 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)
-    
+    # base case
+    parent_index = (index - 1) / 2
+    return if parent_index < 0 || @store[index].key >= @store[parent_index].key
+
+    # swap
+    @store[index], @store[parent_index] = @store[parent_index], @store[index]
+    # recursive case
+    heap_up(parent_index)
   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..."
+    n = @store.size
+    while index * 2 + 1 < n
+      j = index * 2 + 1
+
+      j += 1 if j < n - 1 && @store[j + 1].key < @store[j].key
+
+      break if @store[index].key <= @store[j].key
+
+      @store[index], @store[j] = @store[j], @store[index]
+      index = j
+    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..271e711 100644
--- a/test/heapsort_test.rb
+++ b/test/heapsort_test.rb
@@ -1,12 +1,12 @@
 require_relative "test_helper"
 
-xdescribe "heapsort" do
+describe "heapsort" do
   it "sorts an empty array" do
     # Arrange 
     list = []
 
     # Act
-    result = heapsort(list)
+    result = heap_sort(list)
 
     # Assert
     expect(result).must_equal []
@@ -17,7 +17,7 @@
     list = [5]
 
     # Act
-    result = heapsort(list)
+    result = heap_sort(list)
 
     # Assert
     expect(result).must_equal [5]
@@ -28,7 +28,7 @@
     list = [5, 27, 3, 16, -50]
 
     # Act
-    result = heapsort(list)
+    result = heap_sort(list)
 
     # Assert
     expect(result).must_equal [-50, 3, 5, 16, 27]