Comparing Heap and Merge 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 merge.

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 $O(n \log n)$ .

Merge Sort

The merge sorting (also commonly seen in one word mergesort) algorithm was invented in 1945 by John von Neumann. This is based on the divide-and-conquer strategy.

The worst-case time complexity of this is $O(n\log n)$ .

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 merge 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. merge sort, this is espescially useful if you want to manipulate each of these algorithms yourself.

Running this benchmark against the heap sort and merge sort, we will notice that one is 236.78x faster than the other, which is … drum roll, please! The great heap sorting algorithm!

This means we can almost run the heap sort algorithm almost up to 237 times in the time it takes merge 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 heap sort, and this shall hence on be known as ”The Heap Hero“!

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

Epilogue

Does this mean you should always choose the heap 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 merge sorting algorithms.