Comparing Heap and Quick Sorting Algorithms

Wether you’re a beginner or a greatly experienced developer, this comparison will come in handy to find the fastest of two sorting algorithms. Namely heap and quick.

Instead of a wall-of-text, we’ll get into the nitty-gritty right away!

Heap Sort

The heap sorting algorithm was invented by J. W. J. Williams in 1964, but later that same year, Robert W. Floyd imporved upon this, which made it able to sort the array in-place - meaning that this version did not require any extra memory to sort a given array.

Heap-sort has multiple proven real-world uses, one of these being in the data-compression field, as well as it being used in Dijkstra’s algorithm for finding the shortest path in a given graph.

The big-o of our heap-sort is $O(n \log n)$ .

Quick Sort

Quick sort is a powerful sorting algorithm that belongs to the divide-and-conquer family. It works by first selecting a pivot element from the unsorted list. Then, it rearranges the list by placing elements smaller than the pivot to its left and elements larger than the pivot to its right. This process is called partitioning. Finally, quicksort recursively sorts the two sub-lists on either side of the pivot, effectively sorting the entire list.

The efficiency of quicksort hinges on the choice of the pivot element. In the average case, with a randomly chosen pivot, quicksort has a time complexity of $O(n \log n)$ , making it one of the fastest sorting algorithms. This means the number of comparisons it takes to sort a list grows proportionally to the logarithm of the number of elements.

We first heard about quicksort in 1959 (published 1961) from the British computer scientist Sir Charles Antony Richard Hoare.

However, quicksort’s Achilles’ heel is its worst-case performance. If the pivot element consistently ends up being the largest or smallest element in the list, the algorithm degrades to $O(n^2)$ complexity. This can happen with already sorted or reverse-sorted data.

Comparison

We will start, with an array of 3500 random (hopefully distinct) floating-point values, to test our two sorting algorithms.

Now that we have some data to test on, we want to add the algorithm for the heap sort. This goes as follows.

And of course the quick sort as well, otherwise we won’t have anything to compare against.

Now, let’s test the two against one another.

If you want to read about something else here is a collection of some different sorting algorithms. You can also navigate directly to the implementation of heap sort VS. quick sort, this is espescially useful if you want to manipulate each of these algorithms yourself.

Running this benchmark against the heap sort and quick sort, we will notice that one is 117.15x faster than the other, which is … drum roll, please! The great quick sorting algorithm!

This means we can almost run the quick sort algorithm almost up to 118 times in the time it takes heap sort to run once!

Artificial Intelligence

We asked a well-known Artificial Intelligence (A.I. for short, AI for the lazy and ai for the lazier) to nickname our winner, the quick sort, and this shall hence on be known as ”The Quickfire Ninja“!

To be fair, of course, we also asked for one for our lesser speedy algorithm, the heap sort, which is now known as ”The Heap Hero“.

Epilogue

Does this mean you should always choose the quick sorting algorithm when you implement a new app? Well, not exactly… Please do remember that, as with everything in life, there are pros and cons as well, so choose wisely!

There are a lot of other sorting algorithms out there. Yet more to be discovered! Who knows, you might find the next one with an immersive speed increase or magnificent memory benefits!

Thanks for reading, and I truly hope this will better your understanding of the speed of heap and quick sorting algorithms.