Question

Code:

            int c = 0;
            for (int i = 0; i < n; i++)
            {
                for (int j = 0; j < n; j++)
                {
                    c = i * j;
                }
            }

Time Complexity: O(n²)

Now what will be the complexity of following code:

            for (int i = 0; i < n; i++)
            {
                for (int j = 0; j < n; j++)
                {
                    //c = i * j;
                    // nothing is happening inside the loop
                }
            }

whether complexity will be same as above( O(n²) ) or something else??

Answer 1

Theoretically – yes because there is still the issue of increasing the i and j which still needs to happen, and comparing them to the end value in each iteration.

However – compilers might optimize it to be done in constant time, and just set the post values of i and j.