diff --git a/heaps/heap_sort.py b/heaps/heap_sort.py
index 3b834a5..918bf08 100644
--- a/heaps/heap_sort.py
+++ b/heaps/heap_sort.py
@@ -1,8 +1,16 @@
-
+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 log n)
+        Space Complexity: O(n)
     """
-    pass
\ No newline at end of file
+    heap = MinHeap()
+
+    for item in list:
+        heap = heap.add(item)
+    
+    for i in range(len(list)):
+        list[i] = heap.remove()
+
+    return list
\ No newline at end of file
diff --git a/heaps/min_heap.py b/heaps/min_heap.py
index f6fe4e0..16d8cc3 100644
--- a/heaps/min_heap.py
+++ b/heaps/min_heap.py
@@ -1,5 +1,4 @@
 class HeapNode:
-  
     def __init__(self, key, value):
         self.key = key
         self.value = value
@@ -11,29 +10,35 @@ def __repr__(self):
         return str(self.value)
 
 class MinHeap:
-
     def __init__(self):
         self.store = []
 
-
     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(1)
         """
-        pass
+        value = key if value == None else value
+        new_node = HeapNode(key, value)
+        self.store.append(new_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(1)
         """
-        pass
+        if self.empty():
+            return None
 
+        self.swap(0, len(self.store) - 1)
+        removed = self.store.pop()
+
+        self.heap_down(0)
+        return removed.value
 
-    
     def __str__(self):
         """ This method lets you print the heap, when you're testing your app.
         """
@@ -41,13 +46,12 @@ def __str__(self):
             return "[]"
         return f"[{', '.join([str(element) for element in self.store])}]"
 
-
     def empty(self):
         """ This method returns true if the heap is empty
-            Time complexity: ?
-            Space complexity: ?
+            Time complexity: O(1)
+            Space complexity: O(1)
         """
-        pass
+        return len(self.store) == 0
 
 
     def heap_up(self, index):
@@ -57,10 +61,17 @@ def heap_up(self, index):
             property is reestablished.
             
             This could be **very** helpful for the add method.
-            Time complexity: ?
-            Space complexity: ?
+            Time complexity: O(log n)
+            Space complexity: O(1)
         """
-        pass
+        if index == 0:
+            return
+        
+        parent = (index-1)//2
+        store = self.store
+        if store[parent].key > store[index].key:
+            self.swap(parent, index)
+            self.heap_up(parent)
 
     def heap_down(self, index):
         """ This helper method takes an index and 
@@ -68,7 +79,21 @@ 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):
+            return
+        elif right_child >= len(self.store):
+            smaller_child_index = left_child
+        else:
+            smaller_child_index = left_child if self.store[left_child].key < self.store[right_child].key else right_child
+        
+        if self.store[index].key < self.store[smaller_child_index].key:
+            return
+        self.swap(index, smaller_child_index)
+        
+        return self.heap_down(smaller_child_index)
 
     
     def swap(self, index_1, index_2):