Hi, I am stuck with this problem. Please provide me a descriptive answer. Appreciate your help!!

Consider the problem of determining the maximum in an array S containing n real numbers.

Divide-and-conquer algorithm

a. Write the problem, inputs, outputs, and algorithm in pseudo-code.

b. Let T(n) denote the number of pair-wise comparisons of elements in S required by your algorithm. Write a recurrence relation for T(n) for your algorithm and solve it to determine T(n).

c. Draw a decision tree (comparison tree) for your algorithm when S is (a, b, c, d).

i) How many comparisons does your algorithm do in the best case?

ii) How many comparisons does your algorithm do in the worst case?

d. Is your algorithm optimal? Justify your answer.