Bubble Sort

Bubble Sort

Bubble sort, sometimes incorrectly referred to as sinking sort, is a simple sorting algorithm that works by repeatedly stepping through the list to be sorted, comparing each pair of adjacent items and swapping t    hem if they are in the wrong order. The pass through the list is repeated until no swaps are needed, which indicates that the list is sorted. The algorithm gets its name from the way smaller elements "bubble" to the top of the list. Because it only uses comparisons to operate on elements, it is a comparison sort. Although the algorithm is simple, most of the other sorting algorithms are more efficient for large lists.

Example

First Pass:
( 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:
( 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 )
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.
Third Pass:
( 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 )

Algorithm

for i = 1:n,

    swapped = false

 for j = n:i+1,

     if a[j] < a[j-1],

            swap a[j,j-1]

            swapped = true

    ? invariant: a[1..i] in final position

break if not swapped

end