Leetcode #1975: Maximum Matrix Sum
In this guide, we solve Leetcode #1975 Maximum Matrix 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
You are given an n x n integer matrix. You can do the following operation any number of times: Choose any two adjacent elements of matrix and multiply each of them by -1.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Greedy, Array, Matrix
Intuition
A locally optimal choice leads to a globally optimal result for this structure.
That means we can commit to decisions as we scan without backtracking.
Approach
Sort or preprocess if needed, then repeatedly take the best available local choice.
Maintain the minimal state necessary to validate the greedy decision.
Steps:
- Sort or preprocess as needed.
- Iterate and pick the best local option.
- Track the current solution.
Example
Input: matrix = [[1,-1],[-1,1]]
Output: 4
Explanation: We can follow the following steps to reach sum equals 4:
- Multiply the 2 elements in the first row by -1.
- Multiply the 2 elements in the first column by -1.
Python Solution
class Solution:
def maxMatrixSum(self, matrix: List[List[int]]) -> int:
mi = inf
s = cnt = 0
for row in matrix:
for x in row:
cnt += x < 0
y = abs(x)
mi = min(mi, y)
s += y
return s if cnt % 2 == 0 else s - mi * 2
Complexity
The time complexity is , where and are the number of rows and columns of the matrix, respectively. 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.