Does Python's heapify() not play well with list comprehension and slicing?

Question

I found an interesting bug in a program that I implemented somewhat lazily, and wondered if I'm comprehending it correctly. The short version is that Python's heapq implementation doesn't actually order a list, it merely groks the list in a heap-centric way. Specifically, I was expecting heapify() to result in an ordered list that facilitated list comprehension in an ordered fashion.

Using a priority cue example, as in the Python documentation:

from heapq import heapify, heappush, heappop
from random import shuffle

class Item(object):
    def __init__(self, name):
        self.name = name

lst = []

# iterate over a pseudo-random list of unique numbers
for i in sample(range(100), 15):
    it = Item("Some name for %i" % i)
    heappush(lst, (i, it))

print([i[0] for i in lst])

Results in

>>> [2, 22, 7, 69, 32, 40, 10, 97, 89, 33, 45, 51, 94, 27, 67]

This, we note, is not the original ordering of the list, but apparently some heap-centric ordering as described here. I was lazily expecting this to be fully ordered.

As a test, running the list through heapify() results in no change (as the list is already heap-ishly ordered):

heapify(lst)

print([i[0] for i in lst])

>>> [2, 22, 7, 69, 32, 40, 10, 97, 89, 33, 45, 51, 94, 27, 67]

Whereas iterating through the list with the heappop() function results in ordering as expected:

lst2 = []
while lst: lst2.append(heappop(lst))

print([i[0] for i in lst2])

>>> [2, 7, 10, 22, 27, 32, 33, 40, 45, 51, 67, 69, 89, 94, 97]

So, it would seem that heapq does not order a list (at least in the human sense of the word), but rather the heappush() and heappop() functions are able to grok the heap-ishly ordered list.

The result: Any slicing and list comprehension operations on a heapified list will yield non-ordered results.

Is this true, and is this always true?

(BTW: Python 3.0.1 on a WinXP system)

Answer 1

A heap is not a sorted list (it's a representation of a partially sorted binary tree).

So yes, you're right, if you expect a heapified list to behave like a sorted list, you'll be disappointed. The only sorting assumption you can make about a heap is that heap[0] is always its smallest element.

(It's difficult to add much to what you've already written - your question is an excellent writeup of How Things Are. 8-)