diff --git a/heaps/heap_sort.py b/heaps/heap_sort.py
index 3b834a5..1f007fa 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 log n)
+        Space Complexity: O(n)
     """
-    pass
\ No newline at end of file
+
+    heap = MinHeap()
+    for element in list:
+        heap.add(element)
+
+    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 f6fe4e0..f690bb4 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
@@ -15,28 +15,52 @@ class MinHeap:
     def __init__(self):
         self.store = []
 
+    # helpers
+    def parent_index(self, index):
+        return (index - 1) // 2
+
+    def left_child_index(self, index):
+        return (2 * index) + 1
+
+    def right_child_index(self, index):
+        return (2 * index) + 2
+
 
     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
+
+        if value is None:
+            value = key
+
+        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 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):
-        """ This method lets you print the heap, when you're testing your app.
-        """
+        """ This method lets you print the heap, when you're testing your app."""
+
         if len(self.store) == 0:
             return "[]"
         return f"[{', '.join([str(element) for element in self.store])}]"
@@ -44,10 +68,10 @@ def __str__(self):
 
     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 +81,17 @@ 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
+
+        if self.store[self.parent_index(index)].key > self.store[index].key:
+            self.swap(self.parent_index(index), index)
+            self.heap_up(self.parent_index(index))
+
 
     def heap_down(self, index):
         """ This helper method takes an index and 
@@ -68,7 +99,18 @@ def heap_down(self, index):
             larger than either of its children and continues until
             the heap property is reestablished.
         """
-        pass
+        
+        if self.left_child_index(index) < len(self.store):
+            if self.right_child_index(index) < len(self.store):
+                if self.store[self.left_child_index(index)].key < self.store[self.right_child_index(index)].key:
+                    smaller_node = self.left_child_index(index)
+                else:
+                    smaller_node = self.right_child_index(index)
+            else:
+                smaller_node = self.left_child_index(index)
+            if self.store[index].key > self.store[smaller_node].key:
+                self.swap(index, smaller_node)
+                self.heap_down(smaller_node)
 
     
     def swap(self, index_1, index_2):
@@ -76,6 +118,6 @@ def swap(self, index_1, index_2):
             at index_1 and index_2
             used for heap_up & heap_down
         """
-        temp = self.store[index_1]
-        self.store[index_1] = self.store[index_2]
-        self.store[index_2] = temp
+
+        self.store[index_1], self.store[index_2] = self.store[index_2], self.store[index_1]
+