a) Given a sorted array of distinct integers A[1, ..., n], you want to find out whether there is an index i for which, A[i] = i. Give a divide and conqure algorithm in pseudocode that runs in O(log n).

b) Given a sorted array B, suppose that p and q are two elements of B. Design a divide and conqure algorithm to compute the number of elements between p and q (let p q). what is the running time of your algorithm?