2. Consider the following algorithm that operates on a list of n integers: Divide the n values into n 2 pairss. Find the max of each pair. Repeat until you have the max value of the list

(a) (2 pts) Show the steps of the above algorithm for the list (25, 19, 9, 8, 2, 26, 21, 26, 31, 26, 3, 14).

(b) (3 pts) Derive and prove a tight bound on the asymptotic runtime of this algorithm

(c) (3 pts) Assuming you just ran the above algorithm, show that you can use the result and all intermediate steps to find the 2nd largest number in at most log2 n additional steps.

(d) (2 pts) Show the steps for the algorithm in part c for the input in part a.