scissors laurel O

.github/PULL_REQUEST_TEMPLATE

@@ -6,9 +6,9 @@ Congratulations! You're submitting your assignment!
 
 Question | Answer
 :------------- | :-------------
-How is a Heap different from a Binary Search Tree? | 
-Could you build a heap with linked nodes? | 
-Why is adding a node to a heap an O(log n) operation? |
-Were the `heap_up` & `heap_down` methods useful?  Why? |
+How is a Heap different from a Binary Search Tree? | A BST is ordered; A Heap is not entirely ordered. And heaps allow duplicates, unlike BSTs
+Could you build a heap with linked nodes? | uh, I guess you *could* but it would not be very efficient to search compared to a normal array 
+Why is adding a node to a heap an O(log n) operation? | Because it has to figure out where it truly belongs 
+Were the `heap_up` & `heap_down` methods useful?  Why? | Because after big changes, they help every node and child find where to go. They restore balance to the heap.
 
 

heaps/heap_sort.py

@@ -1,8 +1,19 @@
-
+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 Complexitty: O(n)?
     """
-    pass
+    listless = MinHeap()
+    sorts= []
+
+    for node in list:
+      listless.add(node)
+
+    for i in range(len(list)):
+      nod = listless.remove()
+      sorts.append(nod)
+
+    return sorts
+

heaps/min_heap.py

@@ -1,9 +1,14 @@
 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)
+
+    def __repr__(self):
+        return str(self.value)
 
 class MinHeap:
 
@@ -14,19 +19,31 @@ 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(1)? O(log n)?
         """
-        pass
+        if value == 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)
         """
-        pass
+        if len(self.store) == 0:
+            return None
 
+        caboose = len(self.store) - 1
+        self.swap(0, caboose)
+        smol = self.store.pop()
+
+        self.heap_down(0)
+        return smol.value
 
 
     def __str__(self):
@@ -39,27 +56,50 @@ 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):
+
         """ 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(log n)
         """
-        pass
+        if index == 0:
+            return
+
+        parent = (index - 1) // 2
+        store = self.store
+        if store[parent].key > store[index].key:
+            self.swap(parent, index)
+            self.heap_up(parent)
+
 
     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
+        children = index * 2 + 1
+        lefty = children
+        poncho = children + 1
+        if lefty < len(self.store):
+            if poncho < len(self.store):
+                if self.store[lefty].key < self.store[poncho].key:
+                    smol = lefty
+                else:
+                    smol = poncho
+            else:
+                smol = lefty
+
+            if self.store[index].key > self.store[smol].key:
+                self.swap(index, smol)
+                self.heap_down(smol)
 
 
     def swap(self, index_1, index_2):