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Python's heapq module: Implementing heap queue algorithm

  • May 04, 2023
  • 6 Minute Read
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  • By Kusum Jain
Python's heapq module: Implementing heap queue algorithm

Python has many applications outside of the web and computer science. One reason for this is that its standard library contains numerous pre-built modules that simplify common programming tasks. In this article, we will guide you to one such module called Heapq in Python which permits users to create and modify heap data structures.

What is Heapq in Python?

Priority Queues as well as Heaps are surprisingly useful data structures despite being quite unpopular. Locating the best element in a dataset, for example, is made simple and highly effective with the help of these data structures.

The Python heapq module is part of its Standard Library and is used to implement the heap queue algorithm, also referred to as the priority queue algorithm. This offers functions for building and modifying heap data structures. Heapq makes it easy to find the minimum and maximum value element from a collection of elements.

But before we can get to that, we must review Heap concepts. If you're searching for a Python data structure that meets the heap property, look no further than the heap. The children of each parent node must have a value greater than or less than the parent node, depending on whether the heap property specifies a min heap or a max heap. 

Python's heapq module is an excellent illustration of a heap data structure implementation. It module contains multiple heaps, including the min heap and the max heap.

If you use a min heap, the smallest item will always be at the root node, whereas a max heap will place the largest item at the root node. The algorithms Dijkstra's shortest path algorithm, Prim's minimum spanning tree algorithm, and heap sort frequently utilize the heap data structure.

Is Heapq a min or max heap?

By default, the heapq module employs a min heap, which places smaller items at the top of the heap. But the module provides functions for both minimum and maximum heaps. There is also a max heap that can be constructed by negating the element values that will be stored in the heap.

The code below creates a minimum heap:

import heapq

heap = []

heapq.heappush(heap, 3)

heapq.heappush(heap, 1)

heapq.heappush(heap, 2)




[1, 3, 2]


In contrast, a max heap can be made with the following code:

import heapq

heap = []

heapq.heappush(heap, -3)

heapq.heappush(heap, -8)

heapq.heappush(heap, -1)

print([-x for x in heap])



[8, 3, 1]


Difference between sorted and heapq in Python

Sorting the data is a common application of the built-in heapq module and sorted function in Python. There are, however, several key differences between the two.

The sorted function rearranges the elements of a collection into a new sorted list. This indicates that the original set is not modified, while the sorted list is kept in memory.  In contrast, using the heapq module, a collection is sorted without rearranging the original data.

The 'sorted' also preserves the order of elements that are of equal value, but you can't say that for heapq. Time complexity distinguishes one from the other as well. The sorted's worst-case time complexity is O(n log n), whereas heapq's is O(n log k), where k is the size of the heap. As a result, heapq works better with large datasets.

Time Complexity of heapq in Python

The time complexity of each individual Heapq Python operation varies. The following table lists the time complexity of some of heapq's most popular functions.

  • Depending on the heap size, heapify can take up to O(n) time to complete.
  • heappush is complex O(log n), where n is the number of elements in the heap.
  • heappop takes O(log n), where n is the total number of elements in the heap.
  • heappushpop has a complexity of O(log n), where n is the number of elements in the heap.
  • heapreplace takes O(log n) time, where n is the number of elements in the heap.
  • nlargest has a time complexity of O(n log k), where n is the total number of elements in the iterable and k is the maximum size desired for the returned set.
  • nsmallest has an O(1) time complexity, where n is the total number of elements in the iterable and k is the minimum number of elements to return.(n log k).

Clearly, the majority of heapq functions are quite efficient, with a time complexity of O(log n) or O(n log k). Therefore, heapq is a viable option when working with Python's heap data structure and larger datasets.

Is heapq faster than sort?

Depending on the size and structure of the data to be sorted, the efficiency of Python's sorting options, heapq, and sort, varies. Sort is typically more efficient than heapq for processing small arrays and lists. This is due to the fact that sort makes use of the cache memory available on modern CPUs and employs a highly optimized algorithm designed specifically for working with small lists.

However, heapq outperforms sort as the list or array size increases. This is because heapq uses a heap data structure, and operations such as adding and removing items from a heap have a logarithmic time complexity. This indicates that heapq is preferable to sort when dealing with large datasets, particularly when the data is only partially sorted.

It is essential to keep in mind that heapq and sort's performance can vary based on the data being sorted and the scenario in which they are used. To determine which algorithm is more effective for your specific application, it is advised that you conduct benchmarks on both.


In conclusion, the heapq module in Python is a dependable and effective instrument for working with heap data structures. Its adaptability makes it useful in a variety of contexts, and it can be used to sort massive datasets efficiently. Happy Learning :)

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About The Author
Kusum Jain
I am an avid coder on CodeChef, I partake in hackathons regularly. I am an independent and self-motivated student with a love for coding and experiencing new things.