Consider an algorithm for finding the maximum of an array of n numbers.
a. Write an algorithm in Pseudocode to complete the maximum of an array of n numbers.
b. Write down the loop invariant that will make your algorithm correct. First write the loop invariant informally.
c. Write the loop invariant that will make your algorithm correct formally with indices.
d. Prove correctness of the loop invariant by initialization, maintenance, and termination.