Bubble sort is a simple sorting algorithm that processes the elements of an array on multiple

runs. At each run, the algorithm compares adjacent elements and swaps them if they are

not in order. Its name suggests that the larger elements bubble to the end of the array.

Take an array of numbers $"51428",$ 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;

First Pass

$(51428)->(15428),$ Here, algorithm compares the first two elements, and swaps since $5>1.$

$(15428)->(14528),$ Swap since $5>4$

$(14528)->(14258),$ Swap since $5>2$

$(14258)->(14258),$ Now, since these elements are already in order $(8>5),$ algorithm does not swap them.

Second Pass

$(14258)->(14258)$

$(14258)->(12458),$ Swap since $4>2$

$(12458)->(12458)$

$(12458)->(12458)$

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

Third Pass

$(12458)->(12458)$

$(12458)->(12458)$

$(12458)->(12458)$

$(12458)->(12458)$

Implement in c$0$ the function for sorting the array using BubbleSort algorithm in a file bubblesort.c$0$ with same interface of selsort.c$0,$ and put all contracts related to preconditions, postconditions and loop invariants.

Implement a testing program in c$0$ by using sort$-$test.c$0,$ and try to use the algorithm on arrays of various size to understand the complexity.