Maximum Integer in a List (MAX) Input: A list of integers Ala...b] Output Ali] for some asisb such that Alil 2 Aljl for all asjsb Let M(Ala...b]) represent the output of the MAX problem on input Ala...bl. Let Max(a, b) be a simple function that returns the maximum of two elements. Let m = @tb | be the midpoint between a and b (3 points) 1. Below is a self-reduction for the MAX problem. State a recursive algorithm using pseu- docode for finding the maximum element based on this self-reduction. Alal If a = b (2 points) 2. Using the same reduction as part 1 now state a recurrence T(n) that expresses the worst case run time of the recursive algorithm. Find a similar recurrence in your notes and state the tight bound on T(n) (you do not need to prove this bound) (3 points) 3. Below is a self-reduction for the MAX problem. State a recursive algorithm using pseu- docode for finding the maximum element based on this self-reduction. if a > b If a = b if a