Find the Integer Shared by Two Equal Inclusive Range Sums
Company: Google
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: easy
Interview Round: Other
### Problem
Find an integer `x` in `[1, n]` such that the sum from 1 through `x` equals the sum from `x` through `n`, including `x` in both sums. Return `x`, or `-1` if none exists. There is at most one answer.
```cpp
class Solution {
public:
int pivotInteger(int n);
};
```
### Examples
**Example 1:**
```text
Input: n = 49
Output: 35
Explanation: Both sums, from 1 through 35 and from 35 through 49, equal 630.
```
**Example 2:**
```text
Input: n = 3
Output: -1
Explanation: The total triangular sum 6 is not a square, so no pivot exists.
```
### Constraints
- `1 <= n <= 1000`.
### Clarifying Questions
- Is `x` included on both sides? Yes.
- Is this an array index? No; return an integer value in 1 through n.
- Can `n = 1` have an answer? Yes; both sums then contain 1.
```hint Check the boundary
Check that both inclusive sums contain the candidate pivot.
```
Overview: Find an integer where the inclusive sums from 1 to the pivot and from the pivot to n are equal, or return -1.