diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index c8a32a4..5356787 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -1,8 +1,106 @@
 
 
+# # This method uses a heap to sort an array.
+#  # Time Complexity: O(n log n) to add elements to a heap and swap them in order at each level
+#  # Space Complexity: O(n) since you're adding all the elements to a heap here
+def heapsort(list)
+	return [] if list.empty?
+
+  min_heap = MinHeap.new()
+
+  list.each do |item|
+		min_heap.add(item)
+	end
+
+	sorted_array = []
+
+	list.length.times do
+		sorted_item = min_heap.remove()
+		sorted_array << sorted_item
+	end
+
+	return sorted_array
+end
+
+def swap(list, index_1, index_2)
+	temp = list[index_1]
+	list[index_1] = list[index_2]
+	list[index_2] = temp
+end
+
+
+
+# Challenge If you can, do this method in O(1) space complexity.
 # 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) to add elements to a heap and swap them in order at each level
+# Space Complexity: O(1)
+def heapsort_in_place(list)
+	return [] if list.empty?
+
+	# Build heap (rearrange array)
+	build_max_heap(list)
+
+	unsorted_last_index = list.length - 1
+
+	while unsorted_last_index > 0
+		# Move current root (largest) to end
+		swap(list, 0, unsorted_last_index)
+
+		# Max heapify the reduced heap
+		max_heapify(list, unsorted_last_index, 0)
+
+		# The end is sorted
+		unsorted_last_index -= 1
+	end
+
+	return list
+end
+
+
+def build_max_heap(list)
+	# Range of internal nodes is 0 to (n/2 - 1) and range of leaves is (n/2) to (n - 1)
+	i = list.length / 2 - 1
+
+	while i >= 0 do
+		# Starting from half of array (non-leaf nodes), heapify (make a max heap, moving up)
+		max_heapify(list, list.length, i)
+		i -= 1
+	end
+
+	return list
+end
+
+# Compare current node to left and right child nodes, and swap to keep max heap structure
+def max_heapify(list, size, root)
+	root_larger_than_children = false
+
+	while !root_larger_than_children
+		largest = root
+
+		left_child_index = (root * 2) + 1
+		right_child_index = (root * 2) + 2
+
+		left_child_exists = (left_child_index <= (size - 1))
+		right_child_exists = (right_child_index <= (size - 1))
+
+		# If left child is larger than root, make left child the largest
+		if left_child_exists && list[left_child_index] > list[largest]
+			largest = left_child_index
+		end
+
+		# If right child is larger than largest so far, make right child the largest
+		if right_child_exists && list[right_child_index] > list[largest]
+			largest = right_child_index
+		end
+
+		# If largest now is not root, swap
+		if largest != root
+			swap(list, largest, root)
+
+			root = largest
+			next
+		end
+
+		root_larger_than_children = true
+	end
 end
\ No newline at end of file
diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..8e8c8e0 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) to swap for each level
+  # Space Complexity: O(log n) for the call stack in heap_up??
   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) to swap for each level
+  # Space Complexity: O(log n) for the call stack in heap_down??
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+    return nil if @store.empty?
+
+		swap(0, @store.length - 1)
+		result = @store.pop
+
+		# resort min-heap
+		heap_down(0)
+
+		return result.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..."
+    return @store.length == 0
   end
 
   private
@@ -55,19 +65,58 @@ 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) to swap for each level
+  # Space complexity: O(log n) for the call stack
   def heap_up(index)
-    
+    return if index == 0
+
+    parent_index = (index - 1) / 2
+
+    if @store[index].key < @store[parent_index].key
+			swap(index, parent_index)
+			# re-sort min-heap
+			heap_up(parent_index)
+		end
   end
 
   # This helper method takes an index and 
-  #  moves it up the heap if it's smaller
-  #  than it's parent node.
+  #  moves it down the heap if it's larger
+  #  than it's children node.
   def heap_down(index)
-    raise NotImplementedError, "Method not implemented yet..."
+		return if is_a_leaf(index)
+
+		smallest_child_index = min_child_index(index)
+
+		if @store[index].key > @store[smallest_child_index].key
+			swap(index, smallest_child_index)
+			# resort min-heap
+			heap_down(smallest_child_index)
+		end
   end
 
+	# Helper method returns true if the given index is on the last level / is a leaf
+	def is_a_leaf(index)
+		left_child_index = (index * 2 ) + 1 
+		last_index = @store.length - 1
+
+		return left_child_index > last_index
+	end
+
+	# Helper method returns the index of the smallest child
+	def min_child_index(index)
+		left_child_index = (index * 2) + 1
+		right_child_index = (index * 2) + 2
+
+		left_child_is_last_leaf = (left_child_index == @store.length - 1)
+
+		if ( left_child_is_last_leaf ) || 
+			( @store[left_child_index].key < @store[right_child_index].key ) 
+			return left_child_index
+		else 
+			return right_child_index
+		end
+	end
+
   # If you want a swap method... you're welcome
   def swap(index_1, index_2)
     temp = @store[index_1]
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 = []