diff --git a/lib/heap_sort.rb b/lib/heap_sort.rb
index c8a32a4..9c83fd0 100644
--- a/lib/heap_sort.rb
+++ b/lib/heap_sort.rb
@@ -1,8 +1,67 @@
+require_relative 'min_heap'
+
+def swap(index1, index2, list)
+  list[index1], list[index2] = list[index2], list[index1]
+end
+
+# for max heap
+# this is helpful https://www.youtube.com/watch?v=2DmK_H7IdTo
+# this is also helpful: https://www.programiz.com/dsa/heap-sort
+# time: o(logn)
+# space: o(logn) - because of call stack?
+def heap_down(list, i, length)
+  left_child = (i * 2) + 1
+  right_child = (i * 2) + 2
+  max = i
+
+  if left_child < length && list[left_child] > list[max]
+    max = left_child
+  end
+
+  if right_child < length && list[right_child] > list[max]
+    max = right_child
+  end
+
+  if i != max
+    swap(i, max, list)
+    heap_down(list, max, length)
+  end
+  
+end
 
 
 # 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(nlogn)
+# Space Complexity: o(logn) - bc of call stack?
+def heapsort(list)
+  # heap = MinHeap.new()
+
+  # until list.empty?             # time: o(n)
+  #   heap.add(list.pop)          # time: o(logn) heap add, o(1) list.pop, space: o(n)
+  # end
+
+  # until heap.empty?             # time: ?
+  #   list.push(heap.remove)      # time: o(logn) heap remove, o(1) list.push, space: o(n)
+  # end
+
+  # return list
+
+  end_index = list.length - 1
+  while end_index >= 0                                              # time: o(n)
+    # heapify - build a max heap
+    # parent nodes start at length / 2
+    parent_index = end_index/2
+    while parent_index >= 0
+      heap_down(list, parent_index, end_index)                      # time: o(logn)
+      parent_index -= 1 
+    end
+
+    # move largest element to the end
+    swap(0, end_index, list)
+
+    # don't include sorted portion in further heap down
+    end_index -= 1
+  end
+
+  return list
+end
diff --git a/lib/min_heap.rb b/lib/min_heap.rb
index 6eaa630..ef9d9c3 100644
--- a/lib/min_heap.rb
+++ b/lib/min_heap.rb
@@ -14,18 +14,24 @@ def initialize
   end
 
   # This method adds a HeapNode instance to the heap
-  # Time Complexity: ?
-  # Space Complexity: ?
+  # Time Complexity: O(logn)
+  # Space Complexity: O(logn)
   def add(key, value = key)
-    raise NotImplementedError, "Method not implemented yet..."
+    node = HeapNode.new(key, value)
+    @store.push(node)
+    return 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(logn)
+  # Space Complexity: O(logn)
   def remove()
-    raise NotImplementedError, "Method not implemented yet..."
+    return if @store.empty?
+    swap(0, -1)
+    removed = @store.pop
+    heap_down(0) unless @store.empty?
+    return removed.value
   end
 
 
@@ -44,10 +50,10 @@ 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[0].nil?
   end
 
   private
@@ -55,17 +61,41 @@ 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(logn)
+  # Space complexity: O(logn)
   def heap_up(index)
-    
+    return if index == 0
+
+    parent = (index - 1)/2
+    if @store[parent].key > @store[index].key
+      swap(parent, index)
+    else
+      return
+    end
+
+    return heap_up(parent)
   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..."
+    left_child = (index * 2) + 1
+    right_child = (index * 2) + 2
+
+    # get child index
+    if @store[left_child] && @store[right_child]
+      child_index = @store[left_child].key < @store[right_child].key ? left_child : right_child
+    elsif @store[left_child]    # no case where just right and no left
+      child_index = left
+    else                        # both are null so return
+      return
+    end
+
+    if @store[index].key > @store[child_index].key
+      swap(index, child_index)
+      return heap_down(child_index)
+    end
   end
 
   # If you want a swap method... you're welcome