Given the following array $\{3,14,27,31,39,42,55\}$

a$.$ Follow the textbook procedure, list all the keys of this array that will require the largest number of key

comparisons when searched for by binary search and justify your answer.

b$.$ Follow the textbook procedure, find the average number of key comparisons made by binary search in

a successful search in this array. Assume that each key is searched for with the same probability. Show

details of your reasoning.