(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 Xi, X2, and q has to be in one of Y , Y . Thus, we can determine the answer to problem (X, Y) from answers to the following four smaller problems of half the size: (a) (5 pts) Suppose we solve all the four smaller problems (recursively, until we find a p and q such that p+q is zero or we are left with problems of size one). Do you think this approach will give an algorithm with better complexity than O(n*)? Justify your answer. There is no need to provide any algorithm Next, we want to consider the "middle" elements of X and Y and try to infer about the four smaller subproblems. Let m-L12nj, i.e., the index of the "usual" middle element when the first index of interest is 1 and the last index of interest in n