The O(n logn) algorithm to compute the convex hull of a set of n points in the plane that was described in this chapter is based on the paradigm of incremental construction: add the points one by one, and update the convex hull after each addition. In this exercise we shall develop an 1.8 algorithm based on another paradigm, namely divide-and-conquer a. Let P1 and P2 be two disjoint convex polygons with n vertices in total. Give an O(n) time algorithm that computes the convex hull of P1 UP2. b. Use the algorithm from part a to develop an O(nlogn) time divide-and- conquer algorithm to compute the convex hull of a set of n points in the plane