The processing time of an algorithm is described by the following recurrence equation (c is a positive constant): T(n) = 3T(n/3) + 2cn; T(1) = 0 What is the running time complexity of this algorithm?

Justify using the Master Theorem:

Let a >= 1, b > 1, d >= 0, and T(N) be a monotonically increasing function of the form: T(N) = aT(N/b) + O(N^d);

a is the number of subproblems, N/b is the size of each subproblem, N^d is the work done to prepare the subproblems and assemble/combine the subresults

T(N) is O(N^d); if a < b^d

T(N) is O(N^d logN); if a = b^d

T(N) is O(N logb a); if a > b^d