(20 points) 1. For this problem consider the Maximum problem stated below. Maximum Input: A sequence...

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(20 points) 1. For this problem consider the Maximum problem stated below. Maximum Input: A sequence of n integers A= (a1, a2,..., an). Output: a A such that a aj for all aj e A. (4 points) a) Using pseudocode state an algorithm that solves the Maximum problem using a loop. (4 points) b) Identify the loop invariant for the loop in your algorithm that will help you prove your algorithm is correct. That is, state the loop invariant as a proposition of the kind "After iteration i of the loop...". (8 points) c) Using induction prove that your loop invariant holds for each iteration i. (4 points) d) Using the loop invariant show that your algorithm is correct. (20 points) 1. For this problem consider the Maximum problem stated below. Maximum Input: A sequence of n integers A= (a1, a2,..., an). Output: a A such that a aj for all aj e A. (4 points) a) Using pseudocode state an algorithm that solves the Maximum problem using a loop. (4 points) b) Identify the loop invariant for the loop in your algorithm that will help you prove your algorithm is correct. That is, state the loop invariant as a proposition of the kind "After iteration i of the loop...". (8 points) c) Using induction prove that your loop invariant holds for each iteration i. (4 points) d) Using the loop invariant show that your algorithm is correct.