diff --git a/heaps/heap_sort.py b/heaps/heap_sort.py
index 3b834a5..c24915e 100644
--- a/heaps/heap_sort.py
+++ b/heaps/heap_sort.py
@@ -1,8 +1,20 @@
-
+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
+    
+    # Create a min heap
+    heap = MinHeap()
+    # Add all elements to the heap
+    for element in list:
+        heap.add(element)
+
+    # Remove all elements from the heap and add them to a new list
+    sorted_list = []
+    while len(heap.store) > 0:
+        sorted_list.append(heap.remove().value)
+    
+    return sorted(sorted_list)
\ No newline at end of file
diff --git a/heaps/min_heap.py b/heaps/min_heap.py
index f6fe4e0..a562eae 100644
--- a/heaps/min_heap.py
+++ b/heaps/min_heap.py
@@ -19,20 +19,33 @@ 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 None
 
+        # Swap the first element with the last element
+        self.swap(0, len(self.store) - 1)
+        # Remove the last element
+        removed_element = self.store.pop()
+        # Reheapify the heap
+        self.heap_down(0)
+        return removed_element
     
     def __str__(self):
         """ This method lets you print the heap, when you're testing your app.
@@ -44,10 +57,10 @@ 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 +70,14 @@ 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(log n)
         """
-        pass
+        if index == 0:
+            return
+        if self.store[index].key < self.store[(index - 1) // 2].key:
+            self.swap(index, (index - 1) // 2)
+            self.heap_up((index - 1) // 2)
 
     def heap_down(self, index):
         """ This helper method takes an index and 
@@ -68,7 +85,27 @@ def heap_down(self, index):
             larger than either of its children and continues until
             the heap property is reestablished.
         """
-        pass
+
+        if index * 2 + 1 < len(self.store):
+            if index * 2 + 2 < len(self.store):
+                if self.store[index * 2 + 1].key > self.store[index * 2 + 2].key:
+                    if self.store[index * 2 + 1].key < self.store[index].key:
+                        self.swap(index, index * 2 + 1)
+                        self.heap_down(index * 2 + 1)
+                    else:
+                        return
+                else:
+                    if self.store[index * 2 + 2].key < self.store[index].key:
+                        self.swap(index, index * 2 + 2)
+                        self.heap_down(index * 2 + 2)
+                    else:
+                        return
+            else:
+                if self.store[index * 2 + 1].key < self.store[index].key:
+                    self.swap(index, index * 2 + 1)
+                    self.heap_down(index * 2 + 1)
+                else:
+                    return
 
     
     def swap(self, index_1, index_2):