Bubble Sort Algorithm in C

Bubble 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 them 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. Bubble 
sort is not a stable sort which means that if two same elements are
there in the list, they may not get their same order with respect to 
each other.

Step-by-step example

Let us take the 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.

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

Step 1: Repeat Steps 2 and 3 for i=1 to 10

Step 2: Set j=1

Step 3: Repeat while j<=n

         (A) if  a[i] < a[j]

             Then interchange a[i] and a[j]

             [End of if]

         (B) Set j = j+1


        [End of Inner Loop]

    [End of Step 1 Outer Loop]

Step 4: Exit

Optimized Pseudo-code

procedure bubbleSort( A : list of sortable items )

    n = length(A)
    repeat
       swapped = false
       for i = 1 to n-1 inclusive do
          if A[i-1] > A[i] then
             swap(A[i-1], A[i])
             swapped = true
          end if
       end for
       n = n - 1
    until not swapped
end procedure