Question

19.5 (Enhanced Bubble Sort) Explain why bubble sort is an O(n^2) algorithm.

Answer 1

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]) {
                temp = arr[j];
                arr[j] = arr[j + 1];
                arr[j + 1] = temp;
            }
        }
    }
}


This bubble sort code has a nested for loop

First for loop running for i values from 0 to n-1
So, Number of values for i = n-1

Inner for loop running for j values from 0 to n-i-1
So, in worst case inner for loop running for n-1 times 

Total time complexity
= O((n-1)(n-1))
= O(n^2)