C15-Paper-Weishan

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(nlogn)
+        Space Complexity: O(n)
     """
-    pass
+    heap = MinHeap()
+
+    for item in list:
+        heap.add(item)
+
+    i = 0
+    while not heap.empty():
+        list[i] = heap.remove()
+        i += 1
+
+    return list

heaps/min_heap.py

@@ -21,18 +21,32 @@ 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 not value:
+            new_heapnode = HeapNode(key, key)
+        else:
+            new_heapnode = HeapNode(key, value)
+        self.store.append(new_heapnode)
+        index = len(self.store) - 1
+        self.heap_up(index)
+        return None
 
     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 self.empty():
+            return None
+
+        last_index = len(self.store) - 1
+        self.swap(0, last_index)
+        node_to_remove = self.store.pop(last_index)
+        self.heap_down(0)
+        return node_to_remove.value
 
 
 
@@ -49,7 +63,7 @@ def empty(self):
             Time complexity: ?
             Space complexity: ?
         """
-        pass
+        return len(self.store) == 0
 
 
     def heap_up(self, index):
@@ -59,19 +73,40 @@ 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(n)
         """
-        pass
+        if index == 0:
+            return index
+
+        parent_node = (index - 1) // 2
+        current_nodes = self.store
+        if current_nodes[parent_node].key > current_nodes[index].key:
+            self.swap(parent_node, index)
+            self.heap_up(parent_node)
 
     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
-
+        current_nodes = self.store
+        left_child_index = index * 2 + 1
+        right_child_index = index * 2 + 2
+
+        if left_child_index < len(self.store):
+            if right_child_index < len(current_nodes):
+                if current_nodes[left_child_index].key < current_nodes[right_child_index].key:
+                    node = left_child_index
+                else:
+                    node = right_child_index
+            else:
+                node = left_child_index
+
+            if current_nodes[index].key > current_nodes[node].key:
+                self.swap(index, node)
+                self.heap_down(node)
 
     def swap(self, index_1, index_2):
         """ Swaps two elements in self.store