(1) We want to design a better algorithm using divide and conquer. Let (X, Y) refer to the given problem. Let T(n) be the complexity of your algorithm when each of X, Y has n elements. Consider each of X, Y divided into two equal halves as shown below If such a pair p, q of numbers existed, then p has to be in one of X1, X2, and q has to be in one of Yi, Y2. Thus, we can determine the answer to problem (X, Y) from answers to the following four smaller problems of half the size