THIS IS THE QUESTION ABOUT THE D&L OF ALGORITHMS

Recurrence Relations for Complexity Analysis

QUESTION 4: A very natural question to ask related to MergeSort is whether we can do better by dividing the list into more than two parts. It turns out we can't do any better, at least in the worst case. In this exercise you will verify this fact mathematically. TriMergeSort, given below, is a variant of MergeSort, where the list is split into three equal parts instead of two. For convenience, assume that n= 3^k , for some nonnegative integer k.

(a) Give a recurrence relation for the worst-case complexity W(n) of TriMergeSort for an input list of size n.

(b) Solve the recurrence formula you have given in (a) to obtain an explicit formula for the worst-case complexity W(n) of TriMergeSort.

(c) Which is more efficient in the worst case, MergeSort or TriMergeSort? Discuss.