You are given an array A, which stores n non-negative integers. Design an efficient divide-and-conquer algorithm that accepts A and n as inputs and returns the index of the maximum value in the array A.

(1) Pseudocode:

(2) Analysis: derive a recurrence for the runing time of your algorithm. Justify your answer by listing the cost for executing each line of code and the number of executions for each line. You may mark the cost with your algorithm.