Find Three Numbers with Given Sum

You are given an array of integers and two numbers N and X. The task is to determine whether there exists a triplet in the array such that the sum of the three numbers is exactly X.

Formally, given an array \(A\) of size \(N\) and a number \(X\), check if there exist indices \(i, j, k\) (with \(i < j < k\)) such that

\(A[i] + A[j] + A[k] = X\)

Output True if such a triplet exists, otherwise output False.

The intended solution should have a time complexity better than \(O(N^3)\), for example by sorting the array and using a two-pointer approach.

inputFormat

The input is read from standard input (stdin) and has the following format:

• The first line contains two space-separated integers \(N\) and \(X\), where \(N\) is the number of elements in the array and \(X\) is the target sum.
• The second line contains \(N\) space-separated integers representing the array elements.

outputFormat

Output a single line to standard output (stdout) which is True if there exists a triplet in the array whose sum is \(X\), otherwise output False.

6 24
12 3 4 1 6 9

True