Cover Data Structures and Algorithms with Object-Oriented Design Patterns in Java
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Bubble Sort

The simplest and, perhaps, the best known of the exchange sorts is the bubble sort .gif Figure gif shows the operation of bubble sort.

   figure34868
Figure: Bubble sorting.

To sort the sequence tex2html_wrap_inline68753, bubble sort makes n-1 passes through the data. In each pass, adjacent elements are compared and swapped if necessary. First, tex2html_wrap_inline61610 and tex2html_wrap_inline61612 are compared; next, tex2html_wrap_inline61612 and tex2html_wrap_inline68763; and so on.

Notice that after the first pass through the data, the largest element in the sequence has bubbled up into the last array position. In general, after k passes through the data, the last k elements of the array are correct and need not be considered any longer. In this regard the bubble sort differs from the insertion sort algorithms--the sorted subsequence of k elements is never modified (by an insertion).

Figure gif also shows that while n-1 passes through the data are required to guarantee that the list is sorted in the end, it is possible for the list to become sorted much earlier! When no exchanges at all are made in a given pass, then the array is sorted and no additional passes are required. A minor algorithmic modification would be to count the exchanges made in a pass, and to terminate the sort when none are made.

Program gif defines the BubbleSorter class. The BubbleSorter class extends the AbstractSorter class defined in Program gif. It simply provides an implementation for the no-arg sort method.

   program36051
Program: BubbleSorter class sort method.

The outer loop (lines 6-9) is done for tex2html_wrap_inline68773. That makes n-1 iterations in total. During the tex2html_wrap_inline57340 iteration of the outer loop, exactly i-1 iterations of the inner loop are done (lines 7-9). Therefore, the number of iterations of the inner loop, summed over all the passes of the outer loop is

displaymath68733

Consequently, the running time of bubble sort is tex2html_wrap_inline68781.

The body of the inner loop compares adjacent array elements and swaps them if necessary (lines 8-9). This takes at most a constant amount of time. Of course, the algorithm will run slightly faster when no swapping is needed. For example, this occurs if the array is already sorted to begin with. In the worst case, it is necessary to swap in every iteration of the inner loop. This occurs when the array is sorted initially in reverse order. Since only adjacent elements are swapped, bubble sort removes inversions one at time. Therefore, the average number of swaps required is tex2html_wrap_inline58122. Nevertheless, the running time of bubble sort is always tex2html_wrap_inline68781.


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Bruno Copyright © 1998 by Bruno R. Preiss, P.Eng. All rights reserved.