diff --git a/heaps/heap_sort.py b/heaps/heap_sort.py
index 3b834a5..e7f377f 100644
--- a/heaps/heap_sort.py
+++ b/heaps/heap_sort.py
@@ -1,8 +1,17 @@
-
+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(nlogn)
+        Space Complexity O(n): 
     """
-    pass
\ No newline at end of file
+    list1 = MinHeap()
+    list2 = []
+    for j in list:
+        list1.add(j)
+    for _ in range(len(list1.store)):
+        element = list1.remove()
+        list2.append(element)
+    return list2
+
+
diff --git a/heaps/min_heap.py b/heaps/min_heap.py
index a1340e3..efbc1a7 100644
--- a/heaps/min_heap.py
+++ b/heaps/min_heap.py
@@ -1,32 +1,48 @@
 class HeapNode:
   
-    def initialize(self, key, value):
+    def __init__(self, key, value):
         self.key = key
         self.value = value
+    
+    def __str__(self):
+        return str(self.value)
 
 
 class MinHeap:
 
     def __init__(self):
         self.store = []
+    
+    def __len__(self):
+        return len(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
+        if value == None:
+            value = key
+        newNode = HeapNode(key, value)
+        self.store.append(newNode)
+        last = len(self.store) - 1
+        self.heap_up(last)
+        
 
     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)
+        min = self.store.pop()
+        self.heap_down(0)
+        return min.value
 
     
     def __str__(self):
@@ -34,33 +50,63 @@ def __str__(self):
         """
         if len(self.store) == 0:
             return "[]"
-        return f"[{', '.join([str(element) for element in self.store])}]"
+        return f"[{', '.join([str(element.value) 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
+        if len(self.store) == 0:
+            return True
+        return False
 
 
     def heap_up(self, index):
         """ 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(log n)
+            Space complexity: O(1)
         """
-        pass
+        if index == 0:
+            return
+        
+        parentIndex = (index -1)//2
+        if self.store[index].key < self.store[parentIndex].key:
+            self.swap(index, parentIndex)
+            self.heap_up(parentIndex)
+
+
 
     def heap_down(self, index):
         """ This helper method takes an index and 
             moves it up the heap if it's smaller
             than it's parent node.
         """
-        pass
-
+        size = len(self.store)
+        while True:
+            l, r = index * 2 + 1, index * 2 + 2 
+            if max(l, r) < size:
+                if self.store[index].key < self.store[l].key and  self.store[index].key < self.store[r].key: break
+                elif self.store[l].key > self.store[r].key:
+                    self.swap(index, r)
+                    index = r
+                else:
+                    self.swap(index, l)
+                    index = l 
+            elif l < size:
+                if self.store[l].key < self.store[index].key:
+                    self.swap(index, l)
+                    index = l
+                else: break
+            elif r < size:
+                if self.store[r].key < self.store[index].key:
+                    self.swap(index, r)
+                    index = r
+                else: break
+            else: break
     
     def swap(self, index_1, index_2):
         """ Swaps two elements in self.store
@@ -70,3 +116,6 @@ def swap(self, index_1, index_2):
         temp = self.store[index_1]
         self.store[index_1] = self.store[index_2]
         self.store[index_2] = temp
+
+
+
diff --git a/tests/test_min_heap.py b/tests/test_min_heap.py
index 74867dc..4280d77 100644
--- a/tests/test_min_heap.py
+++ b/tests/test_min_heap.py
@@ -57,7 +57,6 @@ def test_it_can_remove_nodes_in_proper_order(heap):
     heap.add(0, "Donuts")
     heap.add(16, "Cookies")
 
-
     # Act
     returned_items = ["Donuts", "Pizza", "Pasta", "Soup", "Cookies", "Cake"]