Bubble Sort

In the bubble sort, as elements are sorted they gradually "bubble" (or rise) to their proper location in the array, like bubbles rising in a glass of soda. The bubble sort repeatedly compares adjacent elements of an array. The first and second elements are compared and swapped if out of order. Then the second and third elements are compared and swapped if out of order. This sorting process continues until the last two elements of the array are compared and swapped if out of order.

When this first pass through the array is complete, the bubble sort returns to elements one and two and starts the process all over again. So, when does it stop? The bubble sort knows that it is finished when it examines the entire array and no "swaps" are needed (thus the list is in proper order). The bubble sort keeps track of occurring swaps by the use of a flag.

The table below follows an array of numbers before, during, and after a bubble sort for descending order. A "pass" is defined as one full trip through the array comparing and if necessary, swapping, adjacent elements. Several passes have to be made through the array before it is finally sorted.

Array at beginning: 84 69 76 86 94 91

After Pass #1: 84 76 86 94 91 69

After Pass #2: 84 86 94 91 76 69

After Pass #3: 86 94 91 84 76 69

After Pass #4: 94 91 86 84 76 69

After Pass #5 (done): 94 91 86 84 76 69

The bubble sort is an easy algorithm to program, but it is slower than many other sorts. With a bubble sort, it is always necessary to make one final "pass" through the array to check to see that no swaps are made to ensure that the process is finished. In actuality, the process is finished before this last pass is made.

// Bubble Sort Function for Descending Order

void BubbleSort(apvector <int> &num)

{

int i, j, flag = 1; // set flag to 1 to start first pass

int temp; // holding variable

int numLength = num.length( );

for(i = 1; (i <= numLength) && flag; i++)

{

flag = 0;

for (j=0; j < (numLength -1); j++)

{

if (num[j+1] > num[j]) // ascending order simply changes to <

{

temp = num[j]; // swap elements

num[j] = num[j+1];

num[j+1] = temp;

flag = 1; // indicates that a swap occurred.

}

}

}

return; //arrays are passed to functions by address; nothing is returned

}

Bubble sort algorithm in c/* Bubble sort code */ #include <stdio.h> int main(){ int array[100], n, c, d, swap;  printf("Enter number of elements\n"); scanf("%d", &n);  printf("Enter %d integers\n", n);  for (c = 0; c < n; c++) scanf("%d", &array[c]);  for (c = 0 ; c < ( n - 1 ); c++) { for (d = 0 ; d < n - c - 1; d++) { if (array[d] > array[d+1]) /* For decreasing order use < */ { swap = array[d]; array[d] = array[d+1]; array[d+1] = swap; } } }  printf("Sorted list in ascending order:\n");  for ( c = 0 ; c < n ; c++ ) printf("%d\n", array[c]);  return 0;}

Bubble Sort

Bubble sort is a simple and well-known sorting algorithm. It is used in practice once in a blue moon and its main application is to make an introduction to the sorting algorithms. Bubble sort belongs to O(n2) sorting algorithms, which makes it quite inefficient for sorting large data volumes. Bubble sort is stable and adaptive.

Algorithm

1. Compare each pair of adjacent elements from the beginning of an array and, if they are in reversed order, swap them.

2. If at least one swap has been done, repeat step 1.

You can imagine that on every step big bubbles float to the surface and stay there. At the step, when no bubble moves, sorting stops. Let us see an example of sorting an array to make the idea of bubble sort clearer.

Example. Sort {5, 1, 12, -5, 16} using bubble sort.

Complexity analysis

Average and worst case complexity of bubble sort is O(n2). Also, it makes O(n2) swaps in the worst case. Bubble sort is adaptive. It means that for almost sorted array it gives O(n) estimation. Avoid implementations, which don't check if the array is already sorted on every step (any swaps made). This check is  necessary, in order to preserve adaptive property.

Turtles and rabbits

One more problem of bubble sort is that its running time badly depends on the initial order of the elements. Big elements (rabbits) go up fast, while small ones (turtles) go down very slow. This problem is solved in the Cocktail sort.

Turtle example. Thought, array {2, 3, 4, 5, 1} is almost sorted, it takes O(n2) iterations to sort an array. Element {1} is a turtle.

Rabbit example. Array {6, 1, 2, 3, 4, 5} is almost sorted too, but it takes O(n) iterations to sort it. Element {6} is a rabbit. This example demonstrates adaptive property of the bubble sort.

Code snippets

There are several ways to implement the bubble sort. Notice, that "swaps" check is absolutely necessary, in order to preserve adaptive property.

Javapublic void bubbleSort(int[] arr) {

      boolean swapped = true;

      int j = 0;

      int tmp;

      while (swapped) {

            swapped = false;

            j++;

            for (int i = 0; i < arr.length - j; i++) {                                       

                  if (arr[i] > arr[i + 1]) {                          

                        tmp = arr[i];

                        arr[i] = arr[i + 1];

                        arr[i + 1] = tmp;

                        swapped = true;

                  }

            }                

      }

}

C++void bubbleSort(int arr[], int n) {

      bool swapped = true;

      int j = 0;

      int tmp;

      while (swapped) {

            swapped = false;

            j++;

            for (int i = 0; i < n - j; i++) {

                  if (arr[i] > arr[i + 1]) {

                        tmp = arr[i];

                        arr[i] = arr[i + 1];

                        arr[i + 1] = tmp;

                        swapped = true;

                  }

            }

      }

}