What is wrong with my Heapsort algorithm for building a min heap?

Question

I'm prepping for software developer interviews and have been working on algorithm problems. My book shows a Heapsort algorithm that can sort an unordered array in increasing order. I'm trying to modify it so it can sort with a min heap. But when I follow the logic in the code it doesn't get my array sorted correctly. What is wrong with my code (in pseudocode)?

The array to be sorted: 16, 14, 10, 8, 7, 9, 3, 2, 4, 1

The book's Heapsort algorithm using max-heapify:

HEAPSORT(A)
  BUILD-MAX-HEAP(A)
    for i = A.length down to 2
      swap A[1] with A[i]
      A.heapsize = A.heapsize - 1
      MAX-HEAPIFY(A, 1)

MAX-HEAPIFY(A)
  l = Left(i)
  r = Right(i)
  if l <= A.heapsize and A[l] > A[i]
    largest = l
  else
    largest = i
  if r <= A.heapsize and A[r] > A[largest]
    largest = r
  if largest != i
    swap A[i] with A[largest]
    MAX-HEAPIFY(A, largest)

My modified code using min-heapify:

HEAPSORT(A)             // where A is an array
  BUILD-MIN-HEAP(A)
    for i = A.length down to 2
      swap A[1] with A[i]
      A.heapsize = A.heapsize + 1
      MIN-HEAPIFY(A, 1)

MIN-HEAPIFY(A, i)
  l = Left(i)
  r = Right(i)
  if l <= heapsize.A and A[l] < A[i]
    smallest = l
  else
    smallest = i
  if r <= heapsize.A and A[r] < A[smallest]
    smallest = r
  if smallest != i
    swap A[i] with A[smallest]
    MIN-HEAPIFY(A, smallest)

Consider showing the original code and your modified code. Also, have you looked at similar algorithms that are suppose to achieve what you're trying to achieve? — Jonast92, Jun 30 '14 at 10:21
There are just two places where the distinction between min and max comes into play (the two comparisons involving A[] elements). You made the changes correctly. So if the second version doesn't yield a min heap, I bet the first one doesn't yield a max heap either. There's an even simpler way: change all elements' signs. — , Jun 30 '14 at 12:42
Your algorithm is pretty inefficient. See http://stackoverflow.com/questions/24434430/heap-sort-pseudo-code-algorithm/24443017 for a much better solution. — Jim Mischel, Jun 30 '14 at 16:42

Henry · Accepted Answer · 2014-06-30T11:59:47.420

3

Heap sort runs in two phases: (1) transform the unsorted array into a heap, (2) transform the heap into a sorted array.

For building up the heap, the for-loop should run from 2 to A.length; also the heap size should become larger, not smaller.

The code snippet for BUILD-MAX-HEAP(A) seems to be meant for phase 2, for building up the sorted array out of the heap.

The phase 1 would build up the heap in the beginning of the array by letting new nodes "bubble up" in the heap. As long as the new node is larger (or smaller if you generate a min-heap) than its parent, exchange it with its parent.

edited Jun 30 '14 at 11:59

answered Jun 30 '14 at 10:44

Henry

42,982
7
68
84

I just realized I made a stupid mistake in not knowing that Heapsort sorts an array into increasing order using BUILD-MAX-HEAP and MAX-HEAPIFY to do this. What do my code and your changes produce? Does it sort the array in decreasing order? I may be confused...it's way past bed time :P – MNRC Jun 30 '14 at 11:06
Your code without my changes would transform a min-heap into an array sorted in decreasing order. – Henry Jun 30 '14 at 12:01

What is wrong with my Heapsort algorithm for building a min heap?

1 Answers1