4. Consider the problem of counting, in a given text, the number of substrings that start with an A and end with a B. For example, in the given text CABAAXBYA, there are four such substrings: CABAAXBYA CABAAXBYA CABAAXBYA CABAAXBYA (a) Design a brute-force algorithm to solve this problem. (b) What is the worst-case run time efficiency of your algorithm? 5. Consider the convex hull problem. Is there a way to identify some of the extreme points of the convex hull in linear runtime? Describe how you can identify some of these extreme points, and devise an O(n) algorithm for finding at least 2 of them from a given set S of (n > 1) points. 1. Design an algorithm for computing the floor of vn (the largest integer