2. In this exercise, you will develop a quadratic-time algorithm for the 3-sum problem. When we ask you to design an algorithm, give a crisp and concise English description of your algorithmdon't write Java code.

A. Given an integer x and a sorted array a[] of N distinct integers, design a linear-time algorithm to find if there exists two distinct indices i and j such that (a[i] + a[j] == x). (20 Points)

Hint: start by checking whether a[0] + a[N-1] is smaller than, greater than, or equal to x.

B. Given an array a[] of N distinct integers, design a quadratic-time algorithm to find if there exists three distinct indices i, j, and k such that (a[i] + a[j] + a[k] == 0). (20 Points)

Hint: Use the result from (a). You can assume the array is sorted since sorting the array can be done in quadratic (and even linearithmic) time.