Matrix Diagonal Sum

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Leetcode

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Arrays

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Math

Matrix Diagonal Sum

Compute the sum of the primary and secondary diagonals of a square matrix, counting the center element only once.

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Problem Statement

Given an $n \times n$ square matrix of integers, return the sum of all values on the primary diagonal and secondary diagonal.

The primary diagonal contains cells where row index equals column index.
The secondary diagonal contains cells where row index plus column index equals $n - 1$ .

If the matrix has an odd size, the center cell belongs to both diagonals, so count it only once.

Input Format

A square matrix mat of size n x n.

Output Format

Return a single integer: the diagonal sum.

Constraints

The matrix is square: n == mat.length == mat[i].length
$1 \le n$
Values may be positive, negative, or zero.

Hints

Traverse one row at a time and add the two diagonal positions for that row.
Be careful not to double count the middle element when n is odd.

Input Format

mat: an n x n integer matrix

Output Format

Integer sum of both diagonals with the center counted once

Constraints

Square matrix only
Count overlapping center cell once
Integer values may be negative or zero

Examples

Sample cases returned by the problem API.

Example 1

Input

mat = [[1,2,3],[4,5,6],[7,8,9]]

Output

Explanation

Primary diagonal = 1 + 5 + 9 = 15. Secondary diagonal = 3 + 5 + 7 = 15. The center 5 is counted once, so total = 15 + 15 - 5 = 25.

Example 2

Input

mat = [[5]]

Output

Explanation

There is only one cell, which lies on both diagonals. Count it once.

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