Given an input parameter n, Alice has an unsorted array A of nn items, and she needs to perform O(log n) search operations on A. She has two algorithms in mind to achieve this:

Algorithm 1: Sort A using MERGE SORT and then perform all of O(log n) search operations using binary search.

Algorithm 2: Perform all of O(log n) search operations directly on A using linear search. Present the running times of each of the two algorithms separately, and select the algorithm you would suggest to Alice by determining which one is asymptotically faster.