Bubble Sort

Algorithm AnalysisThe bubble sort is the oldest and simplest sort in use. Unfortunately, it's also the slowest.
The bubble sort works by comparing each item in the list with the item next to it, and swapping them if required. The algorithm repeats this process until it makes a pass all the way through the list without swapping any items (in other words, all items are in the correct order). This causes larger values to "bubble" to the end of the list while smaller values "sink" towards the beginning of the list.
The bubble sort is generally considered to be the most inefficient sorting algorithm in common usage. Under best-case conditions (the list is already sorted), the bubble sort can approach a constant O(n) level of complexity. General-case is an abysmal O(n2).
While the insertion, selection, and shell sorts also have O(n2) complexities, they are significantly more efficient than the bubble sort.
Pros: Simplicity and ease of implementation.Cons: Horribly inefficient.
Source CodeBelow is the basic bubble sort algorithm.
void bubbleSort(int numbers[], int array_size)
{
int i, j, temp;
for (i = (array_size - 1); i >= 0; i--)
{
for (j = 1; j <= i; j++)
{
if (numbers[j-1] > numbers[j])
{
temp = numbers[j-1];
numbers[j-1] = numbers[j];
numbers[j] = temp;
}
}
}
}