Exercise 7.54. You may assume that there is an O(n log n)time subroutine that solves Ex.7.53. Explain why your algorithm runs in O(n2 log n) time.

We are given an array that contains N numbers. We want to determine if there are two numbers whose sum equals a given number K. For instance, if the input is 8 4, 1, 6, and K is 10, then the answer is yes (4 and 6). A number may be used twice. Do the following a. Give an O(N2) algorithm to solve this problem. b. Give an O(Nlog N) algorithm to solve this problem. (Hint: Sort the items first. 7.53 After that is done, you can solve the problem in linear time.) C. 7.54 Repeat Exercise 7.53 for four numbers. Try to design an O(N2 log N) algorithm (Hint: Compute all possible sums of two elements. Sort these possible sums. Then proceed as in Exercise 7.53.)