Bubble sort

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.

Working of Bubble Sort algorithm:

Lets consider the following array as an example: arr[]  = {5, 1, 4, 2, 8}

First Pass:

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

Second Pass:

Now, during second iteration it should look like this:

( 1 4 2 5 8 ) –> ( 1 4 2 5 8 ) 
( 1 4 2 5 8 ) –> ( 1 2 4 5 8 ), Swap since 4 > 2 
( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) 
( 1 2 4 5 8 ) –>  ( 1 2 4 5 8
Third Pass:

Now, the array is already sorted, but our algorithm does not know if it is completed.
The algorithm needs one whole pass without any swap to know it is sorted.

( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) 
( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) 
( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) 
( 1 2 4 5 8 ) –> ( 1 2 4 5 8

Illustration:

Illustration of Bubble Sort

Introduction to Sorting Techniques – Data Structure and Algorithm Tutorials

Sorting refers to rearrangement of a given array or list of elements according to a comparison operator on the elements. The comparison operator is used to decide the new order of elements in the respective data structure.

When we have a large amount of data, it can be difficult to deal with it, especially when it is arranged randomly. When this happens, sorting that data becomes crucial. It is necessary to sort data in order to make searching easier.

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1. Selection sort

Selection sort is another sorting technique in which we find the minimum element in every iteration and place it in the array beginning from the first index. Thus, a selection sort also gets divided into a sorted and unsorted subarray....

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Comparison of Complexity Analysis Between Sorting Algorithms:

NameBest Case  Average Case  Worst Case MemoryStable   Method UsedQuick Sort[Tex]n log n[/Tex][Tex]n log n[/Tex][Tex]n^{2}[/Tex][Tex]log n[/Tex]NoPartitioningMerge Sort[Tex]n log n[/Tex][Tex]n log n[/Tex][Tex]n log n[/Tex]nYesMergingHeap Sort[Tex]n log n[/Tex][Tex]n log n[/Tex][Tex]n log n[/Tex]1NoSelectionInsertion Sortn[Tex]n^{2}[/Tex][Tex]n^{2}[/Tex]1YesInsertionTim Sortn[Tex]n log n[/Tex][Tex]n log n[/Tex]nYesInsertion & MergingSelection Sort[Tex]n^{2}[/Tex][Tex]n^{2}[/Tex][Tex]n^{2}[/Tex]1NoSelectionShell Sort[Tex]n log n[/Tex][Tex]n^{4/3}[/Tex][Tex]n^{3/2}[/Tex]1NoInsertionBubble Sortn[Tex]n^{2}[/Tex][Tex]n^{2}[/Tex]1YesExchangingTree Sort[Tex]n log n[/Tex][Tex]n log n[/Tex][Tex]n log n[/Tex]nYesInsertionCycle Sort[Tex]n^{2}[/Tex][Tex]n^{2}[/Tex][Tex]n^{2}[/Tex]1NoSelectionStrand Sortn[Tex]n^{2}[/Tex][Tex]n^{2}[/Tex]nYesSelectionCocktail Shaker Sortn[Tex]n^{2}[/Tex][Tex]n^{2}[/Tex]1YesExchangingComb Sort[Tex]n log n[/Tex][Tex]n^{2}[/Tex][Tex]n^{2}[/Tex]1NoExchangingGnome Sortn[Tex]n^{2}[/Tex][Tex]n^{2}[/Tex]1YesExchangingOdd–even Sortn[Tex]n^{2}[/Tex][Tex]n^{2}[/Tex]1YesExchanging...

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