EXPLANATION FILE OF BUBBLE SORTING

 
 Suppose we declare:

   static int a[] = {7, 3, 66, 3, -5, 22, -77, 2};
  
 The following table shows the elemnts of a[] after
 each pass of the i loop:

   unordered data:   7   3   66    3   -5   22   -77    2
   first pass:	   -77   7    3   66    3   -5    22    2	
   second pass:    -77  -5    7    3   66    3     2   22
   third pass:     -77  -5    2    7    3   66     3   22
   fourth pass:    -77  -5    2    3    7    3    66   22
   fifth pass      -77  -5    2    3    3    7    22   66
   sixth pass:     -77  -5    2    3    3    7    22   66
   seventh pass:   -77  -5    2    3    3    7    22   66
   
 At the start of the first pass a[6] is compared to a[7].
 Since the values are in order they are not exchanged. Then
 a[5] is compared with a[6], and since these values are out
 of order they are exchanged. Then a[4] is compared with 
 a[5], etc. Adjacent out-of-order values are exchanged. The
 effect of the first pass is to "bubble" the samllest value
 in the array into the elemnt a[0]. In the second pass a[0]
 is left unchanged and a[6] is compared with a[7], etc. 
 After the second pass, the next to the smallest value is in
 a[1]. Since each pass bubbles the next smallest element to
 its appropriate array position, the algorithm will, after
 n - 1 passes, have all the elements ordered. Notice in this
 example that after the fifth pass all the elements have been
 ordered. It is possible to modify the algorithm to terminate
 earlier by adding a variable that detects if no exchanges
 are made in a given pass. We leave this as an exercise.
 
 A bubble sort is very inefficient. If the size of the array
 is n, then the number of comparisons performed is proportio-
 nal to nē.
 
 [From BIBLI 09].