Bubble Sort
Video Lecture
Bubble Sort Operation
Bubble Sort – Iteration/Passes
Algorithm
BubbleSort(arr[0]..arr[n-1])
Input: Array arr contains n elements in unsorted order.
Output: Array arr contains n elements in sorted order.
Step 1: Initialize i = 0.
Step 2: The for loop variable i varies from 0 to n-2.
Step 3: The for loop variable j varies from 0 to n-2-i.
Step 4: If arr[j] > arr[j+1], then swap arr[j] and arr[j+1].
Step 5: Increment j and go to Step 3.
Step 6: Increment i and go to Step 2.
Step 7: Output the sorted array.
Working of Bubble Sort algorithm - Example
Bubble Sort Code
#include <stdio.h>
#include
// A function to implement Bubble Sort
void bubbleSort(int arr[], int n) {
int i, j, temp;
for (i = 0; i < n - 1; i++) {
// Last i elements are already sorted
for (j = 0; j < n - i - 1; j++) {
// Swap if the element found is greater than the next element
if (arr[j] > arr[j + 1]) {
temp = arr[j];
arr[j] = arr[j + 1];
arr[j + 1] = temp;
}
}
}
}
// Function to print an array
void printArray(int arr[], int size) {
for (int i = 0; i < size; i++)
printf("%d ", arr[i]);
printf("\n");
}
// Driver code
int main() {
int n;
// Get the size of the array from the user
printf("Enter the number of elements: ");
scanf("%d", &n);
// Declare an array with a size based on user input
int arr[n];
// Get the elements of the array from the user
printf("Enter the elements of the array:\n");
for (int i = 0; i < n; i++) {
scanf("%d", &arr[i]);
}
// Sort the array using Bubble Sort
bubbleSort(arr, n);
// Print the sorted array
printf("Sorted array: ");
printArray(arr, n);
return 0;
}
#include <iostream>
using namespace std;
void bubbleSort(int arr[], int n) {
int i, j, temp;
for (i = 0; i < n-1; i++) {
for (j = 0; j < n-i-1; j++) {
if (arr[j] > arr[j+1]) {
// Swap arr[j] and arr[j+1]
temp = arr[j];
arr[j] = arr[j+1];
arr[j+1] = temp;
}
}
}
}
void printArray(int arr[], int size) {
for (int i = 0; i < size; i++)
cout << arr[i] << " ";
cout << endl;
}
int main() {
int arr[] = {64, 34, 25, 12, 22, 11, 90};
int n = sizeof(arr)/sizeof(arr[0]);
bubbleSort(arr, n);
cout << "Sorted array: " << endl;
printArray(arr, n);
return 0;
}
public class BubbleSort {
static void bubbleSort(int[] arr) {
int n = arr.length;
int temp;
for (int i = 0; i < n-1; i++) {
for (int j = 0; j < n-i-1; j++) {
if (arr[j] > arr[j+1]) {
// Swap arr[j] and arr[j+1]
temp = arr[j];
arr[j] = arr[j+1];
arr[j+1] = temp;
}
}
}
}
static void printArray(int[] arr) {
for (int i : arr)
System.out.print(i + " ");
System.out.println();
}
public static void main(String[] args) {
int[] arr = {64, 34, 25, 12, 22, 11, 90};
bubbleSort(arr);
System.out.println("Sorted array:");
printArray(arr);
}
}
def bubble_sort(arr):
n = len(arr)
for i in range(n-1):
for j in range(0, n-i-1):
if arr[j] > arr[j+1]:
# Swap arr[j] and arr[j+1]
arr[j], arr[j+1] = arr[j+1], arr[j]
def print_array(arr):
for i in arr:
print(i, end=' ')
print()
if __name__ == "__main__":
arr = [64, 34, 25, 12, 22, 11, 90]
bubble_sort(arr)
print("Sorted array:")
print_array(arr)
Analysis of Bubble Sort
Time Complexity
Best Case: In the best case, the input array is already in sorted order, and the algorithm performs a minimum of n-1 comparisons. The best case complexity is O(n).
Worst Case: In the worst case, the input array is in descending order, and the algorithm performs a maximum of n(n-1) comparisons. The algorithm performs n-1 iterations, and each iteration involves a maximum of n-1 comparisons. The worst-case and average-case complexity is O(n²).
Space Complexity
No additional space is required. The space complexity of insertion sort is O(1).
Comparison of Insertion Sort and Bubble Sort
