diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index c8a32a4..c26acd4 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -1,8 +1,28 @@
-
+require_relative "min_heap"
 
 # This method uses a heap to sort an array.
-# Time Complexity:  ?
-# Space Complexity: ?
-def heap_sort(list)
-  raise NotImplementedError, "Method not implemented yet..."
-end
\ No newline at end of file
+# Time Complexity:  O(n log n)
+# Space Complexity: O(n) times the number of recursive operations required to finish sorting
+def heapsort(list)
+  return list if list == [] || list.length == 1
+
+  # initialize new heap
+  heap = MinHeap.new
+
+  # add each element in list to heap's store
+  list.each do |num|
+    key = num
+    value = num
+
+    heap.add(key, value)
+  end
+
+  sorted_list = []
+  # take each element out of heap's store, keep it in another array
+  list.length.times do
+    removed = heap.remove
+    sorted_list << removed
+  end
+
+  return sorted_list
+end
diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..7f022dc 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -8,26 +8,38 @@ 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(log n), where n is the number of nodes in the heap
+  # Space complexity: O(log n), where n is the number of nodes in the heap.  The reason it's O(log n) (and not O(1)) is
+  # because we're calling this method recursively.
   def add(key, value = key)
-    raise NotImplementedError, "Method not implemented yet..."
+    new_node = HeapNode.new(key, value)
+    @store << new_node
+
+    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), where n is the number of nodes in the heap
+  # Space complexity: O(log n), where n is the number of nodes in the heap.  The reason it's O(log n) (and not O(1)) is
+  # because we're calling this method recursively.
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
-  end
+    root = @store[0]
+    new_root = @store[@store.length - 1]
 
+    @store[@store.length - 1] = root
+    @store[0] = new_root
+
+    removed = @store.pop
+
+    heap_down(0)
+    return removed.value
+  end
 
   # Used for Testing
   def to_s
@@ -39,15 +51,16 @@ 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), because we're making a straight comparison
+  # Space complexity: O(1), because there are no extra variables that change with input size
   def empty?
-    raise NotImplementedError, "Method not implemented yet..."
+    return true if @store == []
+    return false
   end
 
   private
@@ -55,17 +68,51 @@ 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), where n is the number of nodes in the heap
+  # Space complexity: O(log n), where n is the number of nodes in the heap.  The reason it's O(log n) (and not O(1)) is
+  # because we're calling this method recursively.
   def heap_up(index)
-    
+    # get parent index based on child's position
+    parent_index = (index - 1) / 2
+
+    # return the array if there's no parent, or parent is less than or equal to child
+    return @store if parent_index < 0 || @store[index].key >= @store[parent_index].key
+
+    swap(parent_index, index)
+
+    # call recursively on child's new position
+    heap_up(parent_index)
   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..."
+    left_child = 2 * index + 1
+    right_child = 2 * index + 2
+    min_child = nil
+
+    # Return if there's no left child
+    return if left_child > @store.length - 1
+
+    # If there's no RIGHT child AND parent is greater than LEFT child...
+    # swap parent with left child
+    if @store[right_child].nil? && @store[index].key > @store[left_child].key
+      swap(index, left_child)
+      heap_down(index)
+    elsif @store[right_child] #Otherwise, which child is min?
+      if @store[right_child].key <= @store[left_child].key
+        min_child = @store.index(@store[right_child])
+      else
+        min_child = @store.index(@store[left_child])
+      end
+    end
+
+    # If parent is greater than minimum child, swap them
+    if min_child && @store[index].key > @store[min_child].key
+      swap(index, min_child)
+      heap_down(index)
+    end
   end
 
   # If you want a swap method... you're welcome
@@ -74,4 +121,4 @@ 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..9964e33 100644
--- a/test/heapsort_test.rb
+++ b/test/heapsort_test.rb
@@ -1,8 +1,8 @@
 require_relative "test_helper"
 
-xdescribe "heapsort" do
+describe "heapsort" do
   it "sorts an empty array" do
-    # Arrange 
+    # Arrange
     list = []
 
     # Act
@@ -13,7 +13,7 @@
   end
 
   it "can sort a 1-element array" do
-    # Arrange 
+    # Arrange
     list = [5]
 
     # Act
@@ -22,9 +22,9 @@
     # Assert
     expect(result).must_equal [5]
   end
-  
+
   it "can sort a 5-element array" do
-    # Arrange 
+    # Arrange
     list = [5, 27, 3, 16, -50]
 
     # Act
@@ -32,5 +32,5 @@
 
     # Assert
     expect(result).must_equal [-50, 3, 5, 16, 27]
-  end  
-end
\ No newline at end of file
+  end
+end