Scissors - Araceli

heaps/heap_sort.py

@@ -1,8 +1,42 @@
+from heaps.min_heap import MinHeap
 
-
-def heap_sort(list):
+def heap_sort(arr):
     """ This method uses a heap to sort an array.
-        Time Complexity:  ?
-        Space Complexity: ?
+        Time Complexity:  O (log n)
+        Space Complexity: O(1)
     """
-    pass
+    n = len(arr)
+
+    # Build a maxheap.
+    # Since last parent will be at ((n//2)-1) we can start at that location.
+    for i in range(n // 2 - 1, -1, -1):
+        heapify(arr, n, i)
+
+    # One by one extract elements
+    for i in range(n-1, 0, -1):
+        arr[i], arr[0] = arr[0], arr[i]   # swap
+        heapify(arr, i, 0)
+
+    return arr 
+
+def heapify(arr, n, i):
+    largest = i  # Initialize largest as root
+    left = 2 * i + 1     # left = 2*i + 1
+    right = 2 * i + 2     # right = 2*i + 2
+
+    # See if left child of root exists and is
+    # greater than root
+    if left < n and arr[i] < arr[left]:
+        largest = left
+
+    # See if right child of root exists and is
+    # greater than root
+    if right < n and arr[largest] < arr[right]:
+        largest = right
+
+    # Change root, if needed
+    if largest != i:
+        arr[i],arr[largest] = arr[largest],arr[i]  # swap
+
+        # Heapify the root.
+        heapify(arr, n, largest)

heaps/min_heap.py

@@ -10,8 +10,6 @@ def __str__(self):
     def __repr__(self):
         return str(self.value)
 
-
-
 class MinHeap:
 
     def __init__(self):
@@ -21,21 +19,35 @@ 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)
         """
-        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
 
+        self.swap(0, len(self.store) - 1)
+        min = self.store.pop()
+        self.heap_down(0)
+
+        return min.value
 
-
     def __str__(self):
         """ This method lets you print the heap, when you're testing your app.
         """
@@ -46,11 +58,12 @@ def __str__(self):
 
     def empty(self):
         """ This method returns true if the heap is empty
-            Time complexity: ?
-            Space complexity: ?
+            Time complexity: O(log n)
+            Space complexity: O(log n)
         """
-        pass
+        self.store = []
 
+        return self.store
 
     def heap_up(self, index):
         """ This helper method takes an index and
@@ -59,18 +72,41 @@ def heap_up(self, index):
             property is reestablished.
 
             This could be **very** helpful for the add method.
-            Time complexity: ?
-            Space complexity: ?
+            Time complexity: O(1)
+            Space complexity: O(1)
         """
-        pass
+
+        if index == 0:
+            return index
+
+        parent_index = (index - 1) // 2
+
+        if self.store[parent_index].key > self.store[index].key:
+            self.swap(parent_index, index)
+            self.heap_up(parent_index)
 
     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
+        arr = self.store
+        left_child = index * 2 + 1
+        right_child = index * 2 + 2
+
+        if left_child < len(arr):
+            if right_child < len(arr):
+                if arr[left_child].key < arr[right_child].key:
+                    less = left_child
+                else:
+                    less = right_child
+            else:
+                less = left_child
+
+            if arr[index].key > arr[less].key:
+                self.swap(index, less)
+                self.heap_down(less)
 
 
     def swap(self, index_1, index_2):