Suppose you have an array of n items (the "member items") and a separate list of k items (the "test items"). The member items are not stored in any particular order. You want to know which of the k test items belong to the set of member items. Here are two different ways to solve the problem: .

Algorithm 1: Look up each test item in the array of member items, using sequential search. .
Algorithm 2: Sort the array of member items, using an optimal comparison- based sorting algorithm, and then look up each test item in the array of member items using binary search Answer the following questions, and briefly justify your answer to each part.

(a) What is the worst-case running time of Algorithm 1 (asymptotically, in terms
(b) What is the worst-case running time of Algorithm 2 (asymptotically, in terms
(c) For a given value of n, for what values of k is Algorithm 2 at least as efficient as of n and k)? of n and k)? Algorithm 1?