diff --git a/heaps/heap_sort.py b/heaps/heap_sort.py
index 3b834a5..2963506 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:  On
+        Space Complexity: On
     """
-    pass
\ No newline at end of file
+    result = []
+    heap = MinHeap()
+
+    for item in list:
+        heap.add(item)
+
+    while len(heap.store) > 0:
+        result.append(heap.remove())
+
+    return result
diff --git a/heaps/min_heap.py b/heaps/min_heap.py
index f6fe4e0..d2bef1f 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
@@ -10,30 +10,43 @@ def __str__(self):
     def __repr__(self):
         return str(self.value)
 
+
 class MinHeap:
 
     def __init__(self):
         self.store = []
 
-
-    def add(self, key, value = None):
+    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: Ologn
+            Space Complexity: On
         """
-        pass
+        if value is None:
+            value = key
+
+        node = HeapNode(key, value)
+
+        self.store.append(node)
+        index = len(self.store) - 1
+
+        self.heap_up(index)
 
     def remove(self):
         """ This method removes and returns an element from the heap
             maintaining the heap structure
-            Time Complexity: ?
-            Space Complexity: ?
+            Time Complexity: Ologn
+            Space Complexity: O1
         """
-        pass
+        if self.empty():
+            return None
+
+        self.swap(0, len(self.store)-1)
+        result = self.store.pop()
+        self.heap_down(0)
 
+        return result.value
 
-    
     def __str__(self):
         """ This method lets you print the heap, when you're testing your app.
         """
@@ -41,36 +54,61 @@ 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: O1
+            Space complexity: 01
         """
-        pass
-
+        return len(self.store) == 0
 
     def heap_up(self, index):
         """ This helper method takes an index and
             moves the corresponding element up the heap, if 
             it is less than it's parent node until the Heap
             property is reestablished.
-            
+
             This could be **very** helpful for the add method.
-            Time complexity: ?
-            Space complexity: ?
+            Time complexity: Ologn
+            Space complexity: O1
         """
-        pass
+        if index == 0:
+            return None
+
+        # left = index * 2 +
+        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 
             moves the corresponding element down the heap if it's 
             larger than either of its children and continues until
             the heap property is reestablished.
+            Time Complexity: Ologn
+            Space Complexity: O1
+            [2, 5, 3, 6 ]
+             0  1  2  3
         """
-        pass
+        left = index * 2 + 1
+        right = index * 2 + 2
+
+        if left < len(self.store):  # check if left node is valid
+            if right < len(self.store):  # determine if left or right is smaller
+                if self.store[left].key < self.store[right].key:
+                    smaller_child = left
+                    self.swap(index, smaller_child)
+                    self.heap_down(smaller_child)
+                else:
+                    smaller_child = right
+                    self.swap(index, smaller_child)
+                    self.heap_down(smaller_child)
+            elif self.store[index].key > self.store[left].key:
+                smaller_child = left
+                self.swap(index, smaller_child)
+                self.heap_down(smaller_child)
 
-    
     def swap(self, index_1, index_2):
         """ Swaps two elements in self.store
             at index_1 and index_2