Find the big-O runtime for each of the following algorithm:

a. Suppose an algorithm solves a problem of size n by dividing the input into 5 subproblems, each subproblem is of 1/3 the size of the original input. Then the non-recursive part of the algorithm takes O(n 2 ) time.

b. Suppose an algorithm solves a problem of size n by dividing the input into 3 subproblems, each of subproblem is of 1/3 the size of the original input. Then the non-recursive part of the algorithm takes O(n) time.

c. Suppose an algorithm solves a problem of size n by dividing the input into 8 subproblems, each of subproblem is of 1/2 the size of the original input. Then the non-recursive part of the algorithm takes O(n 1/2 ) time.

d. Suppose an algorithm solves a problem of size n by dividing the input into 2 subproblems, each of size n − 1. Then the non-recursive part of the algorithm takes O(1) time.