Beginning Python - From Novice to Professional

224 CHAPTER 10 ■ BATTERIES INCLUDED
>>> from heapq import *
>>> from random import shuffle
>>> data = range(10)
>>> shuffle(data)
>>> heap = []
>>> for n in data:
... heappush(heap, n)
>>> heap
[0, 1, 3, 6, 2, 8, 4, 7, 9, 5]
>>> heappush(heap, 0.5)
>>> heap
[0, 0.5, 3, 6, 1, 8, 4, 7, 9, 5, 2]
■Note The order of the elements isn’t as arbitrary as it seems. They aren’t in strictly sorted order, but there
is one guarantee made: the element at position i is always greater than the one in position i // 2 (or,
conversely, it’s smaller than the elements at positions 2*i and 2*i + 1). This is the basis for the underlying
heap algorithm. This is called the heap property.
The heappop function pops off the smallest element, which is always found at index 0, and
makes sure that the smallest of the remaining element takes over this position (while preserving
the heap property mentioned in the previous note). Even though popping the first element of a
list isn’t efficient in general, it’s not a problem here, because heappop does some nifty shuffling
behind the scenes:
>>> heappop(heap)
0
>>> heappop(heap)
0.5
>>> heappop(heap)
1
>>> heap
[2, 5, 3, 6, 9, 8, 4, 7]
The heapify function takes an arbitrary list and makes it a legal heap (that is, it imposes the
heap property mentioned in the previous note) through the least possible amount of shuffling.
If you don’t build your heap from scratch with heappush, this is the function to use before starting
to use heappush and heappop:
>>> heap = [5, 8, 0, 3, 6, 7, 9, 1, 4, 2]
>>> heapify(heap)
>>> heap
[0, 1, 5, 3, 2, 7, 9, 8, 4, 6]