Bubble Sort Algorithm

Bubble sort, also referred to as comparison sort, is a simple sorting algorithm that repeatedly goes through the list, compares adjacent elements and swaps them if they are in the wrong order. This is the most simplest algorithm and inefficient at the same time. Yet, it is very much necessary to learn about it as it represents the basic foundations of sorting.


Application


Understand the working of Bubble sort

  • Bubble sort is mainly used in educational purposes for helping students understand the foundations of sorting.

  • This is used to identify whether the list is already sorted. When the list is already sorted (which is the best-case scenario), the complexity of bubble sort is only O(n).

  • In real life, bubble sort can be visualised when people in a queue wanting to be standing in a height wise sorted manner swap their positions among themselves until everyone is standing based on increasing order of heights.


Explanation

Algorithm: We compare adjacent elements and see if their order is wrong (i.e a[i] > a[j] for 1 <= i < j <= size of array; if array is to be in ascending order, and vice-versa). If yes, then swap them.

Explanation:

  • Let us say, we have an array of length n. To sort this array we do the above step (swapping) for n - 1 passes.

  • In simple terms, first, the largest element goes at its extreme right place then, second largest to the last by one place, and so on. In the ith pass, the ith largest element goes at its right place in the array by swappings.

  • In mathematical terms, in ith pass, at least one element from (n - i + 1) elements from start will go at its right place. That element will be the ith (for 1 <= i <= n - 1) largest element of the array. Because in the ith pass of the array, in the jth iteration (for 1 <= j <= n - i), we are checking if a[j] > a[j + 1], and a[j] will always be greater than a[j + 1] when it is the largest element in range [1, n - i + 1]. Now we will swap it. This will continue until ith largest element is at the (n - i + 1)th position of the array.


Bubble Sort Example:

Consider the following array: Arr=14, 33, 27, 35, 10. We need to sort this array using bubble sort algorithm.



First Pass:

  • We proceed with the first and second element i.e., Arr[0] and Arr[1]. Check if 14 > 33 which is false. So, no swapping happens and the array remains the same.




  • We proceed with the second and third element i.e., Arr[1] and Arr[2]. Check if 33 > 27 which is true. So, we swap Arr[1] and Arr[2].


Thus the array becomes:



  • We proceed with the third and fourth element i.e., Arr[2] and Arr[3]. Check if 33 > 35 which is false. So, no swapping happens and the array remains the same.



  • We proceed with the fourth and fifth element i.e., Arr[3] and Arr[4]. Check if 35 > 10 which is true. So, we swap Arr[3] and Arr[4].


Thus, after swapping the array becomes:



Thus, marks the end of the first pass, where the Largest element reaches its final(last) position.

Second Pass:

  • We proceed with the first and second element i.e., Arr[0] and Arr[1]. Check if 14 > 27 which is false. So, no swapping happens and the array remains the same.


We now proceed with the second and third element i.e., Arr[1] and Arr[2]. Check if 27 > 33 which is false. So, no swapping happens and the array remains the same.

  • We now proceed with the third and fourth element i.e., Arr[2] and Arr[3]. Check if 33 > 10 which is true. So, we swap Arr[2] and Arr[3].


Now, the array becomes



Thus marks the end of second pass where the second largest element in the array has occupied its correct position.


Third Pass: After the third pass, the third largest element will be at the third last position in the array.


.

i-th Pass: After the ith pass, the ith largest element will be at the ith last position in the array.

.

. n-th Pass: After the nth pass, the nth largest element(smallest element) will be at nth last position(1st position) in the array, where ‘n’ is the size of the array.


After doing all the passes, we can easily see the array will be sorted. Thus, the sorted array will look like this:


Pseudocode of Bubble Sort Algorithm

bubbleSort( Arr[], totat_elements)
   
   for i = 0 to total_elements - 1 do:
      swapped = false
		
      for j = 0 to total_elements - i - 2 do:
      
         /* compare the adjacent elements */   
         if Arr[j] > Arr[j+1] then
            /* swap them */
            swap(Arr[j], Arr[j+1])		 
            swapped = true
         end if
         
      end for
      
      /*if no number was swapped that means 
      array is sorted now, break the loop.*/
      
      if(not swapped) then
         break
      end if
      
   end for
   
end


Implementation Of Bubble Sort


1. C

 #include<stdio.h> 
 int main() { 
 int arr[] = {5, 6, 2 ,6, 9, 0, -1}, n = 7, i, j; 
 for(i = 0; i < n - 1; ++i) { 
 int swapped = 0; 
 for(j = 0; j < (n - i - 1); ++j) 
 if(arr[j] > arr[j+1]) { 
 int temp = arr[j]; 
 arr[j] = arr[j+1]; 
 arr[j+1] = temp; swapped = 1; 
 } 
 if(!swapped) break; 
 } 
 printf("\nArray after sorting: "); 
 for(i = 0; i < n; ++i) 
 printf("%d ", arr[i]); 
 return 0; 
 }

2. C++


#include <iostream>
#include <vector>
 
using namespace std;
 
void BubbleSort (vector<int> &arr, int n)
{
   for (int i = 0; i < n - 1; ++i)
   { 
      bool swapped = false;
      for (int j = 0; j < n - i - 1; ++j)
      {
         if (arr[j] > arr[j+1]) //check if adjacent element is
                      //not in order
         {
            swap(arr[j], arr[j + 1]);
            swapped = true;
         }
      }
      // Value at n-i-1 will be maximum of all the values below this index.

      if(!swapped)
         break;
   } 
} 
 
int main()
{
   vector<int> arr = {5, 6, 2, 6, 9, 0, -1};
   int n = 7;
 
   BubbleSort(arr, n);
 
   // Display the sorted data.
   cout << "\nSorted Data: ";
   for (i = 0; i < n; i++)
        Cout << arr[i] <<  ;
 
   return 0;
}

3. Java


import java.util.Scanner;
class BubbleSort {
  public static void main(String []args) {
    int n;
    Scanner in = new Scanner(System.in);
 System.out.println("Input number of integers to sort");
    n = in.nextInt();
    int array[] = new int[n];
     System.out.println("Enter " + n + " integers");
     for (int i = 0; i < n; i++)
      array[i] = in.nextInt();
   
    for (int i = 0; i < n - 1; i++) {
   Boolean swapped = false;
      for (int j = 0; j < n - i - 1; j++) {
        if (array[j] > array[j+1]) /* For descending order use < */
        {
          int temp = array[j];
          array[j]= array[j+1];
          array[j+1] = temp;

      swapped = true;
        }
      }
   if(!swapped)
      break;
   } 
System.out.println("Sorted list of numbers:");
for (int i = 0; i < n; i++)
System.out.println(array[i]);
  }
}

4. Python

def bubble_sort(arr):
    for i in range(len(arr) - 1):
        swapped = False
        for j in range(0, len(arr) - i - 1):
            if arr[j] > arr[j + 1]:
                arr[j], arr[j + 1] = arr[j + 1], arr[j]
                swapped = True
        if not swapped:
            return
 
 
arr = [int(x) for x in input(Enter numbers: ).split()]
bubble_sort(arr)
print('Sorted list: ', end='')
print(arr)


Complexity Analysis


Time Complexity of Bubble sort

  • Best case scenario: The best case scenario occurs when the array is already sorted. In this case, no swapping will happen in the first iteration (The swapped variable will be false). So, when this happens, we break from the loop after the very first iteration. Hence, time complexity in the best case scenario is O(n) because it has to traverse through all the elements once.

  • Worst case and Average case scenario: In Bubble Sort, n-1 comparisons are done in the 1st pass, n-2 in 2nd pass, n-3 in 3rd pass and so on. So, the total number of comparisons will be: Sum = (n-1) + (n-2) + (n-3) + ..... + 3 + 2 + 1 Sum = n(n-1)/2 Hence, the time complexity is of the order n2 or O(n2).


Space Complexity of Bubble sort

The space complexity for the algorithm is O(1), because only a single additional memory space is required i.e. for temporary variable used for swapping.


Resource: Interviewbit.com


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