Python etc / heapq


A priority queue is a data structure that supports two operations: add element and extract the minimum of all elements among previously added.

One of the most common implementations of a priority queue is a binary heap. It's a complete binary tree with the following property: the key stored in each node is equal to or less than (≤) the keys in the node's children. The minimum of all elements is a root of such tree.


      3               7

  5       4       9       8

15 16   17 18   19

In a binary heap, both inserting and extraction operations' complexity is O(log n).

The common way of storing a complete binary tree in memory is an array, where children of x[i] are x[2*i+1] and x[2*i+2]:

[1, 3, 7, 5, 4, 9, 8, 15, 16, 17, 18, 19]

Python doesn't provide a binary heap as a class, but it does provide a number of functions that treat list like a binary heap. They are placed in the heapq module.

In [1]: from heapq import *
In [2]: heap = [3,2,1]
In [3]: heapify(heap)
In [4]: heap
Out[4]: [1, 2, 3]
In [5]: heappush(heap, 0)
In [6]: heap
Out[6]: [0, 1, 3, 2]
In [7]: heappop(heap)
Out[7]: 0
In [8]: heap
Out[8]: [1, 2, 3]
More advanced example live

heapq — extra

heapq also contains general purpose functions: merge, nlargest and nsmallest. Guido van Rossum used the first one in his 10-year-old article, which one of the readers sent me today.

Feel free to do the same — @pushtaev.