Implement the following in c++, by adding a clock to show how the runtime increases a. sum = 0; for (int i = 0; i < n; i++) sum++; O(n) b. sum = 0; for (int i = 0; i < n; i++) for (int j = 0; j < n; j++) sum++; O(n^2) c. sum = 0; for (int i = 0; i < n; i++) for (int j = 0; j < n * n; j++) sum++; O(n^3)

d. sum = 0; for (int i = 0; i < n; i++) for (int j = 0; j < i; j++) sum++; O(n^2) e. sum 0; for (int i = 0; i < n; i++) for (int j = 0; j < i * i; j++) for (int k = 0; k < j; k++) sum++; O(n^5) f. sum = 0; for (int i = 1; i < n; i++) for (int j = 1; j < i * i; j++) if (j % i == 0) for (k = 0; k < j; k++) sum++; O(n^4)