Algorithms | Sorting | Question 10

What is the best time complexity of bubble sort?

(A)

N^2

(B)

NlogN

(C)

N

(D)

N(logN)^2

Answer: (C)
Explanation:

The bubble sort is at its best if the input data is sorted. i.e. If the input data is sorted in the same order as expected output. This can be achieved by using one boolean variable. The boolean variable is used to check whether the values are swapped at least once in the inner loop. Consider the following code snippet: 

int main()
{   
    int arr[] = {10, 20, 30, 40, 50}, i, j, isSwapped;
    int n = sizeof(arr) / sizeof(*arr);
    isSwapped = 1;
    for(i = 0; i < n - 1 && isSwapped; ++i)
    {
        isSwapped = 0;
        for(j = 0; j < n - i - 1; ++j)
            if (arr[j] > arr[j + 1])
            {
                swap(&arr[j], &arr[j + 1]);
                isSwapped = 1;
            }
    }
    for(i = 0; i < n; ++i)
        printf(\"%d \", arr[i]);
    return 0;
}

Please observe that in the above code, the outer loop runs only once.

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