diff --git a/heaps/heap_sort.py b/heaps/heap_sort.py
index 3b834a5..e64e08c 100644
--- a/heaps/heap_sort.py
+++ b/heaps/heap_sort.py
@@ -1,8 +1,13 @@
-
+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) where n is the number of items in the list
+        Space Complexity: O(n) where n is the number of items in the list
     """
-    pass
\ No newline at end of file
+    heap = MinHeap()
+    for item in list:
+        heap.add(item)
+    for i in range(len(list)):
+        list[i] = heap.remove()
+    return list
diff --git a/heaps/min_heap.py b/heaps/min_heap.py
index f6fe4e0..1a351a1 100644
--- a/heaps/min_heap.py
+++ b/heaps/min_heap.py
@@ -19,18 +19,29 @@ 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) due to recursive stack calls
         """
-        pass
+        if value is None:
+            value = key
+        self.store.append(HeapNode(key, value))
+        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) due to recursive stack calls
         """
-        pass
+        if self.empty():
+            return None
+        last_index = len(self.store) - 1
+        root_index = 0
+        self.swap(last_index, root_index)
+        removed = self.store.pop()
+        self.heap_down(root_index)
+        return removed.value
+
 
 
     
@@ -44,10 +55,10 @@ 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 +68,13 @@ def heap_up(self, index):
             property is reestablished.
             
             This could be **very** helpful for the add method.
-            Time complexity: ?
-            Space complexity: ?
+            Time complexity: O(1)
+            Space complexity: O(1)
         """
-        pass
+        parent_index = (index - 1) // 2
+        if parent_index >= 0 and self.store[parent_index].key > self.store[index].key:
+            self.swap(parent_index, index)
+            self.heap_up(parent_index)
 
     def heap_down(self, index):
         """ This helper method takes an index and 
@@ -68,7 +82,18 @@ def heap_down(self, index):
             larger than either of its children and continues until
             the heap property is reestablished.
         """
-        pass
+        left_index = (index * 2) + 1
+        right_index = (index * 2) + 2
+        if left_index < len(self.store) and right_index < len(self.store):
+            smallest = left_index
+            if self.store[left_index].key > self.store[right_index].key:
+                smallest = right_index
+            if self.store[smallest].key < self.store[index].key:
+                self.swap(smallest, index)
+                self.heap_down(smallest)
+        elif left_index < len(self.store) and self.store[left_index].key < self.store[index].key:
+            self.swap(left_index, index)
+            self.heap_down(left_index)
 
     
     def swap(self, index_1, index_2):