Bubble Sort in Python, Java, C, and C++: A Step-by-Step Guide

Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the input list element by element, comparing the current element with the one after it, swapping their values if needed. These passes through the list are repeated until no swaps had to be performed during a pass, meaning that the list has become fully sorted. The algorithm, which is a comparison sort, is named for the way the larger elements "bubble" up to the top of the list.

This simple algorithm performs poorly in real world use and is used primarily as an educational tool. More efficient algorithms such as quicksort, timsort, or merge sort are used by the sorting libraries built into popular programming languages such as Python and Java. However, if parallel processing is allowed, bubble sort sorts in O(n) time, making it considerably faster than parallel implementations of insertion sort or selection sort which do not parallelize as effectively. [2][3]

bubble sort

The earliest description of the Bubble sort algorithm was in a 1956 paper by mathematician and actuary Edward Harry Friend,[4] Sorting on electronic computer systems,[5] published in the third issue of the third volume of the Journal of the Association of Computing Machinery (ACM) , as a "Sorting exchange algorithm". Friend described the fundamentals of the algorithm, and, although initially his paper went unnoticed, some years later, it was rediscovered by many computer scientists, including Kenneth E. Iverson who coined its current name.

While any sorting algorithm can be made O ( n ) \displaystyle O(n) on a presorted list simply by checking the list before the algorithm runs, improved performance on almost-sorted lists is harder to replicate.

Various efforts have been made to eliminate turtles to improve upon the speed of bubble sort. Cocktail sort is a bi-directional bubble sort that goes from beginning to end, and then reverses itself, going end to beginning. It can move turtles fairly well, but it retains O ( n 2 ) \displaystyle O(n^2) worst-case complexity. Comb sort compares elements separated by large gaps, and can move turtles extremely quickly before proceeding to smaller and smaller gaps to smooth out the list. Its average speed is comparable to faster algorithms like quicksort.

Take an array of numbers "5 1 4 2 8", and sort the array from lowest number to greatest number using bubble sort. In each step, elements written in bold are being compared. Three passes will be required;

More generally, it can happen that more than one element is placed in their final position on a single pass. In particular, after every pass, all elements after the last swap are sorted, and do not need to be checked again. This allows to skip over many elements, resulting in about a worst case 50% improvement in comparison count (though no improvement in swap counts), and adds very little complexity because the new code subsumes the "swapped" variable:

Although bubble sort is one of the simplest sorting algorithms to understand and implement, its O(n2) complexity means that its efficiency decreases dramatically on lists of more than a small number of elements. Even among simple O(n2) sorting algorithms, algorithms like insertion sort are usually considerably more efficient.

Due to its simplicity, bubble sort is often used to introduce the concept of an algorithm, or a sorting algorithm, to introductory computer science students. However, some researchers such as Owen Astrachan have gone to great lengths to disparage bubble sort and its continued popularity in computer science education, recommending that it no longer even be taught.[6]

The Jargon File, which famously calls bogosort "the archetypical [sic] perversely awful algorithm", also calls bubble sort "the generic bad algorithm".[7] Donald Knuth, in The Art of Computer Programming, concluded that "the bubble sort seems to have nothing to recommend it, except a catchy name and the fact that it leads to some interesting theoretical problems", some of which he then discusses.[8]

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Bubble sort is asymptotically equivalent in running time to insertion sort in the worst case, but the two algorithms differ greatly in the number of swaps necessary. Experimental results such as those of Astrachan have also shown that insertion sort performs considerably better even on random lists. For these reasons many modern algorithm textbooks avoid using the bubble sort algorithm in favor of insertion sort.

Bubble sort also interacts poorly with modern CPU hardware. It produces at least twice as many writes as insertion sort, twice as many cache misses, and asymptotically more branch mispredictions.[citation needed] Experiments by Astrachan sorting strings in Java show bubble sort to be roughly one-fifth as fast as an insertion sort and 70% as fast as a selection sort.[6]

In computer graphics bubble sort is popular for its capability to detect a very small error (like swap of just two elements) in almost-sorted arrays and fix it with just linear complexity (2n). For example, it is used in a polygon filling algorithm, where bounding lines are sorted by their x coordinate at a specific scan line (a line parallel to the x axis) and with incrementing y their order changes (two elements are swapped) only at intersections of two lines. Bubble sort is a stable sort algorithm, like insertion sort.

For example, Donald Knuth describes the insertion of values at or towards their desired location as letting "[the value] settle to its proper level", and that "this method of sorting has sometimes been called the sifting or sinking technique.[10]

In 2007, former Google CEO Eric Schmidt asked then-presidential candidate Barack Obama during an interview about the best way to sort one million integers; Obama paused for a moment and replied: "I think the bubble sort would be the wrong way to go."[11][12]

Bubble sort is a simple sorting algorithm. This sorting algorithm is comparison-based algorithm in which each pair of adjacent elements is compared and the elements are swapped if they are not in order. This algorithm is not suitable for large data sets as its average and worst case complexity are of Ο(n2) where n is the number of items.

We observe in algorithm that Bubble Sort compares each pair of array element unless the whole array is completely sorted in an ascending order. This may cause a few complexity issues like what if the array needs no more swapping as all the elements are already ascending.

To ease-out the issue, we use one flag variable swapped which will help us see if any swap has happened or not. If no swap has occurred, i.e. the array requires no more processing to be sorted, it will come out of the loop.

One more issue we did not address in our original algorithm and its improvised pseudocode, is that, after every iteration the highest values settles down at the end of the array. Hence, the next iteration need not include already sorted elements. For this purpose, in our implementation, we restrict the inner loop to avoid already sorted values.

In computer science, Data structure is a paradigm of how we can organize data, manage data, store data so, we can use it efficiently. It supports special formatting for storing data for a particular purpose. And Sorting is one of the important aspects of Data Structure. It makes it easier to search through it quickly. Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in the wrong order. In this video, we will see how to Visualize Bubble Sort in GUI Python. To visualize the bubble sort we will use matplotlib libraries. Matplotlib is not a built-in tool so before starting we need to install this package into our system. It is a visualization library in Python for 2D plots of arrays. While writing these scripts we will learn about the bubbles sorts algorithm and how we can visualize in a bar plot with animation using animation.funcanimation() method which is comes with matplotlib library to use in a barplot.

Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in the wrong order. This algorithm is not suitable for large data sets as its average and worst case time complexity is quite high.

Bubble sort starts with very first two elements, comparing them to check which one is greater.( 5 1 4 2 8 ) \u2013> ( 1 5 4 2 8 ), Here, algorithm compares the first two elements, and swaps since 5 > 1. ( 1 5 4 2 8 ) \u2013> ( 1 4 5 2 8 ), Swap since 5 > 4 ( 1 4 5 2 8 ) \u2013> ( 1 4 2 5 8 ), Swap since 5 > 2 ( 1 4 2 5 8 ) \u2013> ( 1 4 2 5 8 ), Now, since these elements are already in order (8 > 5), algorithm does not swap them.

What you've pasted there isn't a bubble sort. It's a sort of "brute force" sort but it's not bubble sort. Here's an example of a generic bubble sort. It uses an arbitrary comparer, but lets you omit it in which case the default comparer is used for the relevant type. It will sort any (non-readonly) implementation of IList, which includes arrays. Read the above link (to Wikipedia) to get more of an idea of how bubble sort is meant to work. Note how on each loop we go through from start to finish, but only compare each item with its neighbour. It's still an O(n2) sort algorithm, but in many cases it will be quicker than the version you've given.

Bubble sort has many of the same properties as insertion sort, but has slightly higher overhead. In the case of nearly sorted data, bubble sort takes O(n) time, but requires at least 2 passes through the data (whereas insertion sort requires something more like 1 pass).

Without loss of generality, we assume that we will sort only Integers, not necessarily distinct, in non-decreasing order in this visualization. Try clicking Bubble Sort for a sample animation of sorting the list of 5 jumbled integers (with duplicate) above.