Here is a statement of the Master Theorem. Master Theorem: Let a > 1 and b > 1 be constants, let f(n) be a function, and let T(n) be defined on the nonnegative integers by the recurrence T(n) = aT(n/b) + f(n), where we interpret n/b to mean either [n/b] or [n/b]. Then T(n) can be bounded asymptotically as follows: 1. If f(n) = O(nlogs 2-6) for some constant e > 0, then T(n) (nlogna). 2. If f(n) = (nog), then T(n) = (nloggn). 3. If f(n) = 2(nlog, a+) for some e > 0, and if af(n/b) 0 Igr-Igy, 2, Y > 0 Igr rlgr, > 0 1. a) Suppose that you have a choice of two algorithms A and B that both apply to n pieces of data, where n is a big number. Suppose that A and B perform equally well with the exception that A has a run-time of R(n), where R(n) = O(n1-5), and B has a run-time of S(n), where S(n) = O(n lg n). Which algorithm should you choose? Why? b) If T(n) = O(n?) and T(n) = 2(n?), then is T(n) = O(n?)? Yes or No? (No justification is needed for this part of the question.)