Question: 2. (20 points) We will soon study an algorithm called merge sort. Merge sort may be generalized to break the sorting task into any fixed

2. (20 points) We will soon study an algorithm called merge

2. (20 points) We will soon study an algorithm called merge sort. Merge sort may be generalized to break the sorting task into any fixed number of subproblems per recursive call; in this problem, we will consider 3-way merge sort, which solves 3 subproblems per recursive call. The runtime of 3-way merge sort may be expressed as T(n) = 3T(n/3) + n with base case T(1) 1. (3 points) Sketch a recursion tree representing the recurrence above. Please sketch at least 3 levels of the recursion tree plus the base level. You may assume n is a power of 3 a. (7 points) Based on your recursion tree, what is the closed form solution of the recurrence T(n) 3T(n/3)+n? b. (3 points) Given your solution, what is the strongest statement we can make about the asymptotic complexity of 3-way merge sort? c. T(n) = d. (7 points) Suppose a parallel implementation of 3-way merge sort can reduce the runtime of the algorithm to T(n) = T(n/3) + c with base-case time still T(1)1. What is the strongest statement we can make about the asymptotic complexity of this

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