2. (60%) The convex hull of a set of S is the smallest convex set containing S. (Please find more about the convex hull problem, especially the definition of extreme point, on pages 109-113 in the textbook.) It is assumed that not all the points in S are on a straight line. 2.1 Design a brute force algorithm to solve the convex-hull problem and analyze its efficiency. 2.2 Design a recursive divide-and-conquer algorithm of On log n) to solve the convex-hull problem, set up a recurrence to analyze the number of executions of the basic operation of the best case, and determine the efficiency class. Use the Master Theorem to verify the efficiency class in your analysis result. 2. (60%) The convex hull of a set of S is the smallest convex set containing S. (Please find more about the convex hull problem, especially the definition of extreme point, on pages 109-113 in the textbook.) It is assumed that not all the points in S are on a straight line. 2.1 Design a brute force algorithm to solve the convex-hull problem and analyze its efficiency. 2.2 Design a recursive divide-and-conquer algorithm of On log n) to solve the convex-hull problem, set up a recurrence to analyze the number of executions of the basic operation of the best case, and determine the efficiency class. Use the Master Theorem to verify the efficiency class in your analysis result