LeetCode #1572 — EASY

Matrix Diagonal Sum

Build confidence with an intuition-first walkthrough focused on array fundamentals.

The Problem

Problem Statement

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

Step 01

Brute Force Baseline

Problem summary: 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.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array

Example 1

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

Example 2

[[1,1,1,1],[1,1,1,1],[1,1,1,1],[1,1,1,1]]

Example 3

[[5]]

Core Insight

What unlocks the optimal approach

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.

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
Continue until all input is consumed.

Use the first example testcase as your mental trace to verify each transition.

Step 04

Edge Cases

Minimum Input

Single element / shortest valid input

Validate boundary behavior before entering the main loop or recursion.

Duplicates & Repeats

Repeated values / repeated states

Decide whether duplicates should be merged, skipped, or counted explicitly.

Extreme Constraints

Upper-end input sizes

Re-check complexity target against constraints to avoid time-limit issues.

Invalid / Corner Shape

Empty collections, zeros, or disconnected structures

Handle special-case structure before the core algorithm path.

Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #1572: Matrix Diagonal Sum
class Solution {
    public int diagonalSum(int[][] mat) {
        int ans = 0;
        int n = mat.length;
        for (int i = 0; i < n; ++i) {
            int j = n - i - 1;
            ans += mat[i][i] + (i == j ? 0 : mat[i][j]);
        }
        return ans;
    }
}

// Accepted solution for LeetCode #1572: Matrix Diagonal Sum
func diagonalSum(mat [][]int) (ans int) {
	n := len(mat)
	for i, row := range mat {
		ans += row[i]
		if j := n - i - 1; j != i {
			ans += row[j]
		}
	}
	return
}

# Accepted solution for LeetCode #1572: Matrix Diagonal Sum
class Solution:
    def diagonalSum(self, mat: List[List[int]]) -> int:
        ans = 0
        n = len(mat)
        for i, row in enumerate(mat):
            j = n - i - 1
            ans += row[i] + (0 if j == i else row[j])
        return ans

// Accepted solution for LeetCode #1572: Matrix Diagonal Sum
impl Solution {
    pub fn diagonal_sum(mat: Vec<Vec<i32>>) -> i32 {
        let n = mat.len();
        let mut ans = 0;

        for i in 0..n {
            ans += mat[i][i];
            let j = n - i - 1;
            if j != i {
                ans += mat[i][j];
            }
        }

        ans
    }
}

// Accepted solution for LeetCode #1572: Matrix Diagonal Sum
function diagonalSum(mat: number[][]): number {
    let ans = 0;
    const n = mat.length;
    for (let i = 0; i < n; ++i) {
        const j = n - i - 1;
        ans += mat[i][i] + (i === j ? 0 : mat[i][j]);
    }
    return ans;
}

Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(n)

Space

O(1)

Approach Breakdown

BRUTE FORCE

O(n²) time

O(1) space

Two nested loops check every pair or subarray. The outer loop fixes a starting point, the inner loop extends or searches. For n elements this gives up to n²/2 operations. No extra space, but the quadratic time is prohibitive for large inputs.

OPTIMIZED

O(n) time

O(1) space

Most array problems have an O(n²) brute force (nested loops) and an O(n) optimal (single pass with clever state tracking). The key is identifying what information to maintain as you scan: a running max, a prefix sum, a hash map of seen values, or two pointers.

Shortcut: If you are using nested loops on an array, there is almost always an O(n) solution. Look for the right auxiliary state.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.