> ## Documentation Index
> Fetch the complete documentation index at: https://leetcode-py.wisl.dev/llms.txt
> Use this file to discover all available pages before exploring further.

> ## Agent Instructions
> leetcode-py is a Python LeetCode practice environment generator with one CLI: lcpy. It is not a service or platform.
> Each problem is a directory under leetcode/ with README.md, solution.py, test_solution.py, helpers.py, and playground.ipynb. lcpy gen creates them from JSON templates bundled with the package.
> Examples are backed by tests; copy them verbatim.

# Maximum Matrix Sum Python Solution with Tests

> Tested Python solution for LeetCode 1975 with 20 pytest cases. Generate a practice environment with lcpy.

LeetCode 1975, [Medium](/catalog/medium). Topics: [Array](/catalog/topics/array), [Greedy](/catalog/topics/greedy), [Matrix](/catalog/topics/matrix). [View on LeetCode](https://leetcode.com/problems/maximum-matrix-sum/description/).

Generate this problem as a practice environment: tested reference solution, 20 [parametrized pytest cases](/practice/testing), and a playground notebook:

```bash theme={"theme":{"light":"github-light","dark":"github-dark"}}
lcpy gen -n 1975   # by problem number
lcpy gen -s maximum_matrix_sum   # by problem name
```

## Problem

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`.

Two elements are considered **adjacent** if and only if they share a **border**.

Your goal is to **maximize** the summation of the matrix's elements. Return *the **maximum** sum of the matrix's elements using the operation mentioned above.*

### Examples

![Example 1](https://assets.leetcode.com/uploads/2021/07/16/pc79-q2ex1.png)

```
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.
```

![Example 2](https://assets.leetcode.com/uploads/2021/07/16/pc79-q2ex2.png)

```
Input: matrix = [[1,2,3],[-1,-2,-3],[1,2,3]]
Output: 16
Explanation: We can follow the following step to reach sum equals 16:
- Multiply the 2 last elements in the second row by -1.
```

### Constraints

* `n == matrix.length == matrix[i].length`
* `2 <= n <= 250`
* `-10^5 <= matrix[i][j] <= 10^5`

## Solution

Reference implementation from [solution.py on GitHub](https://github.com/wislertt/leetcode-py/blob/main/leetcode/maximum_matrix_sum/solution.py), full suite in [test\_solution.py](https://github.com/wislertt/leetcode-py/blob/main/leetcode/maximum_matrix_sum/test_solution.py):

```python theme={"theme":{"light":"github-light","dark":"github-dark"}}
class Solution:
    # Time: O(n^2)
    # Space: O(1)
    def max_matrix_sum(self, matrix: list[list[int]]) -> int:
        total = 0
        neg_count = 0
        min_abs = 10**9
        for row in matrix:
            for value in row:
                total += abs(value)
                neg_count += value < 0
                min_abs = min(min_abs, abs(value))
        if neg_count % 2:
            total -= 2 * min_abs
        return total
```

## Complexity

| Time | Space |
| - | - |
| O(n^2) | O(1) |

## Tags

[NeetCode All](/catalog/neetcode).


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