Sum the Two Diagonals Without Double Counting
Company: Google
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: easy
Interview Round: Other
### Problem
For the square integer matrix `mat`, add every entry on either main diagonal. An entry lying on both diagonals contributes only once. Return the sum.
```cpp
class Solution {
public:
int diagonalSum(vector<vector<int>>& mat);
};
```
### Examples
**Example 1:**
```text
mat = [[2,4],[6,8]]
Output: 20
Explanation: Every cell of a 2 by 2 matrix lies on a diagonal.
```
**Example 2:**
```text
mat = [[2,1,3],[1,7,1],[5,1,4]]
Output: 21
Explanation: The five distinct diagonal entries are 2, 3, 7, 5, and 4.
```
### Constraints
- `n == mat.length == mat[i].length`.
- `1 <= n <= 100`.
- Every cell is an integer from `1` through `100`.
### Clarifying Questions
The matrix is square. The center exists as a shared diagonal entry only for odd `n`.
```hint Inspect the structure
Which cells are entitled to contribute, including a cell that belongs to both diagonals?
```
### Reasoning checkpoints
- Identify the two diagonal columns per row.
- Count the shared center once rather than twice.
### Optional extensions
How would you sum the border and both diagonals while avoiding all overlaps?
Overview: Sum the Two Diagonals Without Double Counting. For the square integer matrix mat, add every entry on either main diagonal. An entry lying on both diagonals contributes only once. Return the sum.