diff --git a/heaps/heap_sort.py b/heaps/heap_sort.py
index 3b834a5..36b744a 100644
--- a/heaps/heap_sort.py
+++ b/heaps/heap_sort.py
@@ -1,8 +1,18 @@
-
+from heaps.min_heap import MinHeap
 
 def heap_sort(list):
     """ This method uses a heap to sort an array.
-        Time Complexity:  ?
-        Space Complexity: ?
+        Time Complexity:  O(n)
+        Space Complexity: O(1)
     """
-    pass
\ No newline at end of file
+    heap = MinHeap()
+
+    for num in list:
+        heap.add(num)
+
+    index = 0
+
+    while not heap.empty():
+        list[index] = heap.remove()
+        index += 1
+    return list
\ No newline at end of file
diff --git a/heaps/min_heap.py b/heaps/min_heap.py
index 0095872..efe1d05 100644
--- a/heaps/min_heap.py
+++ b/heaps/min_heap.py
@@ -1,5 +1,5 @@
 class HeapNode:
-  
+
     def __init__(self, key, value):
         self.key = key
         self.value = value
@@ -21,19 +21,29 @@ def __init__(self):
     def add(self, key, value = None):
         """ This method adds a HeapNode instance to the heap
             If value == None the new node's value should be set to key
-            Time Complexity: ?
-            Space Complexity: ?
+            Time Complexity: O(log n)
+            Space Complexity: O(log n)
         """
-        pass
+        if value == None:
+            value = key
+
+        node = HeapNode(key, value)
+        self.store.append(node)
+        self.heap_up(len(self.store) -1)
 
     def remove(self):
         """ 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)
         """
-        pass
+        if len(self.store) == 0:
+            return
+        self.swap(0, len(self.store) - 1)
+        min = self.store.pop()
+        self.heap_down(0)
 
+        return min.value
 
     
     def __str__(self):
@@ -49,7 +59,7 @@ def empty(self):
             Time complexity: ?
             Space complexity: ?
         """
-        pass
+        return len(self.store) == 0
 
 
     def heap_up(self, index):
@@ -62,7 +72,14 @@ def heap_up(self, index):
             Time complexity: ?
             Space complexity: ?
         """
-        pass
+        if index == 0:
+            return
+
+        parent = (index -1) // 2
+        if self.store[index].key < self.store[parent].key:
+            self.swap(index, parent)
+            self.heap_up(parent)
+            
 
     def heap_down(self, index):
         """ This helper method takes an index and 
@@ -70,8 +87,20 @@ def heap_down(self, index):
             larger than either of its children and continues until
             the heap property is reestablished.
         """
-        pass
-
+        left_child = (2 * index) + 1
+        right_child = (2 * index) + 2
+
+        if left_child < len(self.store):
+            if right_child < len(self.store):
+                if self.store[left_child.key] < self.store[right_child].key:
+                    min_child = left_child
+                else:
+                    min_child = right_child
+            else: min_child = left_child
+
+            if self.store[index].key > self.store[min_child.key]:
+                self.swap(index, min_child)
+                self.heap_down(min_child)
     
     def swap(self, index_1, index_2):
         """ Swaps two elements in self.store