Suppose we know that an algorithm has 5 classes of complexity for a problem of size n. The complexities T1(n).. Ts(n) are given below. Regarding probabilities, suppose that p, is twice as likely as p2, p2 is twice as likely as p3, , p3 is twice as likely as p4 and p4 is twice as likely as p5. #2 T; for all instances: T(n) = n, T2(n) = 2n, T3(n) =3n4, T4(n) = 4n and T5(n) = 5n (a) Find all five probabilities p1, P2, P3, P4 , Ps. [Hint: the sum of all probabilities equal 1.0] (b) Find the A(n) for the algorithm.

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