Heap Sort in Python

Author: OmkarPathak

Heap/P01_HeapSort.py

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+# Author: OMKAR PATHAK
+
+#  Approach:
+#  Heap sort happens in two phases. In the first phase, the array
+#  is transformed into a heap. A heap is a binary tree where
+#  1) each node is greater than each of its children
+#  2) the tree is perfectly balanced
+#  3) all leaves are in the leftmost position available.
+#  In phase two the heap is continuously reduced to a sorted array:
+#  1) while the heap is not empty
+#  - remove the top of the head into an array
+#  - fix the heap.
+
+#  Time Complexity of Solution:
+#  Best O(nlog(n)); Average O(nlog(n)); Worst O(nlog(n)).
+
+def HeapSort(alist):
+    heapify(alist)              # create the heap
+    end = len(alist) - 1
+    while end > 0:
+        alist[end], alist[0] = alist[0], alist[end]
+        shiftDown(alist, 0, end - 1)
+        end -= 1
+
+def heapify(alist):
+    ''' This function helps to maintain the heap property '''
+    # start = (len(alist) - 2) // 2         (faster execution)
+    start = len(alist) // 2
+    while start >= 0:
+        shiftDown(alist, start, len(alist) - 1)
+        start -= 1
+
+def shiftDown(alist, start, end):
+    root = start
+    while root * 2 + 1 <= end:
+        child = root * 2 + 1
+        # right child exists and is greater than left child
+        if child + 1 <= end and alist[child] < alist[child + 1]:
+            child += 1
+        # if child is greater than root(parent), then swap their positions
+        if child <= end and alist[root] < alist[child]:
+            alist[root], alist[child] = alist[child], alist[root]
+            root = child
+        else:
+            return
+
+if __name__ == '__main__':
+    alist = [12, 2, 4, 5, 2, 3]
+    HeapSort(alist)
+    print('Sorted Array:',alist)