Problem 1 For each of the following functions f find specific values k, p and a such that f(n)- (n log" n) or f(n) 6(ann*) (each of the paramieters k.p.a may be 0). (a) f(n) 6n+5 log n (b) (n) (n log n2 +2(n +3 logn) (c) f(n)- Vn.4 m Explain all simplifications you use. Problem 2 (a) Find asymptotic solutions in big- notation) to the following recurrence relations: T(n) T(n/3) n2 (b) The recurrence T(n) TT(n/2)n2 describes the ning time of an algorithm A. A competing algorithrn A, has a running time of T"(n)-aT'(n/4) + na what is the largest integer value for a such that A' is asymptotically faster than A? Problem 3. You are given an array of n numbers, and you notice that some of the numbers are duplicates; tha is, tey appear more than once in the array. Show how to remove all duplicates from the array in time O(nlog