# Explanation for Triplets with Smaller Sum provided solution

``````Input: [-1, 4, 2, 1, 1, 3], target=5
Expected Output: 4
Explanation:
There are four triplets whose sum is less than the target:    [-1, 1, 4], [-1, 1, 3], [-1, 1, 2], [-1, 2, 3]
``````

The provided solution actual output is 9.
Does it mean that the provided solution is incorrect?

``````import java.util.*;

class TripletWithSmallerSum {

public static int searchTriplets(int[] arr, int target) {
Arrays.sort(arr);
int count = 0;
for (int i = 0; i < arr.length - 2; i++) {
count += searchPair(arr, target - arr[i], i);
}
return count;
}

private static int searchPair(int[] arr, int targetSum, int first) {
int count = 0;
int left = first + 1, right = arr.length - 1;
while (left < right) {
if (arr[left] + arr[right] < targetSum) { // found the triplet
// since arr[right] >= arr[left], therefore, we can replace arr[right] by any number between
// left and right to get a sum less than the target sum
count += right - left;
left++;
} else {
right--; // we need a pair with a smaller sum
}
}
return count;
}

public static void main(String[] args) {
System.out.println(TripletWithSmallerSum.searchTriplets(new int[] { -1, 0, 2, 3 }, 3));
System.out.println(TripletWithSmallerSum.searchTriplets(new int[] { -1, 4, 2, 1, 3 }, 5));
System.out.println(TripletWithSmallerSum.searchTriplets(new int[] { -1, 4, 2, 1, 1, 3 }, 5));
}
}
``````