Given a positive integer n, find the pivot integer x such that:

• The sum of all elements between 1 and x inclusively equals the sum of all elements between x and n inclusively.

Return the pivot integer x. If no such integer exists, return -1. It is guaranteed that there will be at most one pivot index for the given input.

Solution

class Solution {
    public int pivotInteger(int n) {
        if(n==1) return 1;
        for (int i = n - 1; i > 0; i--) {
            if (((n * (n + 1)) / 2) - ((i * (i - 1)) / 2) == (i * (i + 1)) / 2)
                return i;
        }

        return -1;
    }
}

reference:
https://leetcode.com/problems/find-the-pivot-integer/
https://math.stackexchange.com/a/2713667/1053103