Leetcode #1572: Matrix Diagonal Sum
In this guide, we solve Leetcode #1572 Matrix Diagonal Sum in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
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.
Quick Facts
- Difficulty: Easy
- Premium: No
- Tags: Array, Matrix
Intuition
Grid problems are easiest when you define clear row/column boundaries.
A consistent traversal order prevents off-by-one errors.
Approach
Iterate by rows, columns, or layers depending on the requirement.
Keep bounds updated as the traversal progresses.
Steps:
- Define bounds or directions.
- Visit cells in order.
- Update result and move bounds.
Example
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.
Python Solution
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
Complexity
The time complexity is , where is the number of rows in the matrix. The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.