Matrix Diagonal Sum

LeetCode 1677 | Difficulty: Easy

Easy

Problem Description

Given a square matrix mat, return the sum of the matrix diagonals.

Only include the sum of all the elements on the primary diagonal and all the elements on the secondary diagonal that are not part of the primary diagonal.

Example 1:

Input: mat = [[1,2,3],
              [4,5,6],
              [7,8,9]]
Output: 25
Explanation: Diagonals sum: 1 + 5 + 9 + 3 + 7 = 25
Notice that element mat[1][1] = 5 is counted only once.

Example 2:

Input: mat = [[1,1,1,1],
              [1,1,1,1],
              [1,1,1,1],
              [1,1,1,1]]
Output: 8

Example 3:

Input: mat = [[5]]
Output: 5

Constraints:

- `n == mat.length == mat[i].length`

- `1 <= n <= 100`

- `1 <= mat[i][j] <= 100`

Topics: Array, Matrix

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Approach

Matrix

Treat the matrix as a 2D grid. Common techniques: directional arrays (dx, dy) for movement, BFS/DFS for connected regions, in-place marking for visited cells, boundary traversal for spiral patterns.

When to use

Grid traversal, island problems, path finding, rotating/transforming matrices.

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Solutions

Solution 1: C# (Best: 104 ms)

Metric	Value
Runtime	104 ms
Memory	27.7 MB
Date	2020-09-23

Solution

public class Solution {
    public int DiagonalSum(int[][] mat) {
        int m = mat.GetLength(0);
    int n = mat[0].GetLength(0);
    List<int> nums = new List<int>();
    
    for (int i = 0,j=0; i <m && j<n; i++,j++)
    {
        nums.Add(mat[i][j]);
    }
    for (int i = 0, j = n-1; i < m && j >= 0; i++, j--)
    {
        if(i!=j)
        nums.Add(mat[i][j]);
    }
    
    return nums.Sum();
    }
}

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Complexity Analysis

Approach	Time	Space
Solution	$O(n)$	$O(1) to O(n)$

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Interview Tips

Key Points

• Start by clarifying edge cases: empty input, single element, all duplicates.
• LeetCode provides 1 hint(s) for this problem — try solving without them first.

💡 Hints

Hint 1: There will be overlap of elements in the primary and secondary diagonals if and only if the length of the matrix is odd, which is at the center.