Find a triplet in an array whose sum is closest to a given number

Given an array arr[] of N integers and an integer X, the task is to find three integers in arr[] such that the sum is closest to X.


Input: arr[] = {-1, 2, 1, -4}, X = 1
Output: 2
Sums of triplets:
(-1) + 2 + 1 = 2
(-1) + 2 + (-4) = -3
2 + 1 + (-4) = -1
2 is closest to 1.

Input: arr[] = {1, 2, 3, 4, -5}, X = 10
Output: 9
Sums of triplets:
1 + 2 + 3 = 6
2 + 3 + 4 = 9
1 + 3 + 4 = 7
9 is closest to 10.

Simple Approach: The naive approach is to explore all the subsets of size 3 and keep a track of the difference between X and the sum of this subset. Then return the subset whose difference between its sum and X is minimum.

Efficient approach: By Sorting the array the efficiency of the algorithm can be improved. This efficient approach uses the two-pointer technique. Traverse the array and fix the first element of the triplet. Now use the Two Pointers algorithm to find the closest number to x – array[i]. Update the closest sum. Two pointers algorithm take linear time so it is better than a nested loop.

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