heaps

heaps/heap_sort.py

@@ -1,8 +1,18 @@
+from heapq import heappush, heappop
 
 
 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(1)
     """
-    pass
+    heap = []
+    for element in list:
+        heappush(heap, element)
+
+    sorted_elements = []
+
+    while len(heap) != 0:
+        sorted_elements.append(heappop(heap))
+
+    return sorted_elements

heaps/min_heap.py

@@ -1,3 +1,6 @@
+from heapq import heappop
+
+
 class HeapNode:
 
     def __init__(self, key, value):
@@ -19,20 +22,41 @@ 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) if extra space is available
         """
-        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(1)
         """
-        pass
-
+        # if len(self.store) == 0:
+        #     return None
+        # if value == None: 
+        #     value = key
 
+        # node = HeapNode(key, value)
+        # self.store.append(node)
+        # self.heap_up(len(self.store) - 1)
+        # heap_list = list(self.store)
+        # for i in range(len(heap_list)):
+        #     while heap_list[i] > heap_list[0]:
+        #         up = (i + 1) / 2 - 1
+        #         heap_list[i] = heap_list[up]
+        #         i = up
+        #     return i
+        for value in self.store:
+            self.store[value] = next(iter(self.store[value:value+1]), "error")
+            while len(self.store) and self.store[0] in self.store and self.store[self.store[0]]:
+                heappop(self.store)
 
     def __str__(self):
         """ This method lets you print the heap, when you're testing your app.
@@ -44,11 +68,10 @@ 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 not self.store
 
     def heap_up(self, index):
         """ This helper method takes an index and
@@ -57,20 +80,37 @@ 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(1)
         """
-        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 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
+        store = self.store
+        if left < len(self.store):
+            if right < len(self.store):
+                if store[left].key < store[right].key:
+                    smaller_value = left
+                else:
+                    smaller_value = right
+                if store[index].key > store[smaller_value].key:
+                    self.swap(index, smaller_value)
+                    self.heap_down(smaller_value)
 
-
     def swap(self, index_1, index_2):
         """ Swaps two elements in self.store
             at index_1 and index_2