Search code examples
pythonheapmin-heapmax-heap

Python built-in heap (heapq): Odd behavior if inverted (max-heap)


I'm trying to use the Python (2.0) built-in min-heap data structure from the heapq module (https://docs.python.org/3/library/heapq.html) to build a max-heap. To do that I simply use the negative of the numbers I need to push into my heap.

Using this (max-heap version):

import heapq
h=[]
for i in xrange(10):
    heapq.heappush(h,-i)
    print h

I get something which doesn't look correct:

[0]
[-1, 0]
[-2, 0, -1]
[-3, -2, -1, 0]
[-4, -3, -1, 0, -2]
[-5, -3, -4, 0, -2, -1]
[-6, -3, -5, 0, -2, -1, -4]
[-7, -6, -5, -3, -2, -1, -4, 0]
[-8, -7, -5, -6, -2, -1, -4, 0, -3]
[-9, -8, -5, -6, -7, -1, -4, 0, -3, -2]

The min-heap version instead looks fine:

import heapq
h=[]
for i in xrange(10):
    heapq.heappush(h,i)
    print h

As you can see:

[0]
[0, 1]
[0, 1, 2]
[0, 1, 2, 3]
[0, 1, 2, 3, 4]
[0, 1, 2, 3, 4, 5]
[0, 1, 2, 3, 4, 5, 6]
[0, 1, 2, 3, 4, 5, 6, 7]
[0, 1, 2, 3, 4, 5, 6, 7, 8]
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

What am I missing?

I've checked other SE questions/answers (e.g., python topN max heap, use heapq or self implement?, What do I use for a max-heap implementation in Python?, etc.) but they don't mention this issue.


Solution

  • As @user2357112 already mentioned, it is a min-heap. There is nothing wrong with the output. The difference between the 2 inputs is that, in the first scenario you enter the data in sorted fashion and in the second scenario, you input the data in reverse sorted fashion.

    the min-heap property: the value of each node is greater than or equal to the value of its parent, with the minimum-value element at the root.

    Case 1 : Reverse Sorted Input = 10,9,8,7,6

             10
            [10]
    
             9
            /
          10
          [9,10]
    
    
            8
           / \
         10   9
         [8,10,9]
    
    
            7
           / \
          8   9
         /
        10
        [7, 8,9,10]
    
            6
           / \
          7   9
         / \
        10  8
        [6,7,9,10,8]
    

    Case 2 : Sorted Input = 1,2,3,4,5

             1
            [1]
    
             1
            /
           2
          [1,2]
    
    
            1
           / \
          2   3
         [1,2,3]
    
    
            1
           / \
          2   3
         /
        4
        [1,2,3,4]
    
            1
           / \
          2   3
         / \
        4   5
        [1,2,3,4,5]
    

    If you are interested in how the heap is built and how it balances after every input, go to the following url. You can insert one element at a time and see it in action. https://www.cs.usfca.edu/~galles/JavascriptVisual/Heap.html