AMcGinley C15 Heaps

heaps/heap_sort.py

@@ -1,8 +1,18 @@
-
+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
+    heap = MinHeap()
+
+    for num in list:
+        heap.add(num)
+
+    i = 0
+    while not heap.empty():
+        list[i]  = heap.remove()
+        i+= 1
+
+    return list

heaps/min_heap.py

@@ -21,19 +21,31 @@ 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(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 self.empty():
+            return None
+
+        self.swap(0, len(self.store) -1)
+        min = self.store.pop()
+        self.heap_down(0)
 
+        return min.value
 
 
     def __str__(self):
@@ -46,10 +58,10 @@ 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):
@@ -59,18 +71,40 @@ 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 index
+
+        parentIndex = (index-1) // 2
+
+        if self.store[parentIndex].key > self.store[index].key:
+            self.swap(parentIndex, index)
+            self.heap_up(parentIndex)
+
 
     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
+        leftIndex = (2 * index) + 1
+        rightIndex =  (2 * index) + 2
+
+        if leftIndex < len(self.store):
+            if rightIndex < len(self.store):
+                if self.store[leftIndex].key < self.store[rightIndex].key:
+                    minIndex = leftIndex
+                else:
+                    minIndex = rightIndex
+            else:
+                minIndex = leftIndex
+
+            if self.store[index].key > self.store[minIndex].key:
+                self.swap(index, minIndex)
+                self.heap_down(minIndex)
 
 
     def swap(self, index_1, index_2):