diff --git a/heaps/heap_sort.py b/heaps/heap_sort.py
index 3b834a5..340e386 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: ?
     """
-    pass
\ No newline at end of file
+    if len(list) <= 1:  # returns list of empty or only has one node
+        return list
+
+    heap = MinHeap()
+
+    for value in list:
+        heap.add(value)
+
+    result = []  # unpacking the heap into a new result list to avoid side effects
+    while not heap.empty():
+        result.append(heap.remove())
+
+    return result
diff --git a/heaps/min_heap.py b/heaps/min_heap.py
index f6fe4e0..b26d80d 100644
--- a/heaps/min_heap.py
+++ b/heaps/min_heap.py
@@ -1,5 +1,4 @@
 class HeapNode:
-  
     def __init__(self, key, value):
         self.key = key
         self.value = value
@@ -10,71 +9,95 @@ def __str__(self):
     def __repr__(self):
         return str(self.value)
 
-class MinHeap:
 
+class MinHeap:
     def __init__(self):
         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: ?
+    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: O(logn)
+        Space Complexity: O(logn) - heap_up is recursive, stack soace being consumed
         """
-        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: ?
+        """This method removes and returns an element from the heap
+        maintaining the heap structure
+        Time Complexity: O(logn)
+        Space Complexity: O(logn) - heap_down is recursive, stack soace being consumed
         """
-        pass
+        if self.empty():
+            return None
+
+        self.swap(0, len(self.store) - 1)  # swap first w/ last
+        removed = self.store.pop()  # remove the last node
+        self.heap_down(0)  # restructure the heap
 
+        return removed.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])}]"
 
-
     def empty(self):
-        """ This method returns true if the heap is empty
-            Time complexity: ?
-            Space complexity: ?
+        """This method returns true if the heap is empty
+        Time complexity: O(1)
+        Space complexity: O(1)
         """
-        pass
-
+        return not self.store
 
     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: ?
+        """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: O(logn)
+        Space complexity: O(logn)
         """
-        pass
+        if index == 0:
+            return
+
+        check = (index - 1) // 2
+        if self.store[index].key < self.store[check].key:
+            self.swap(index, check)
+            self.heap_up(check)
 
     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.
+        """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.
         """
-        pass
+        left = index * 2 + 1
+        right = index * 2 + 2
+
+        if left < len(self.store):
+            if right < len(self.store):
+                if self.store[left].key < self.store[right].key:
+                    less = left
+                else:
+                    less = right
+            else:
+                less = left
+
+            if self.store[index].key > self.store[less].key:
+                self.swap(index, less)
+                self.heap_down(less)
 
-    
     def swap(self, index_1, index_2):
-        """ Swaps two elements in self.store
-            at index_1 and index_2
-            used for heap_up & heap_down
+        """Swaps two elements in self.store
+        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]