1975. Maximum Matrix Sum

Description

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.

Example 1:

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:

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
-10⁵ <= matrix[i][j] <= 10⁵

Solution

maximum-matrix-sum.py

class Solution:
    def maxMatrixSum(self, matrix: List[List[int]]) -> int:
        rows, cols = len(matrix), len(matrix[0])
        total = count = 0
        mmin = float('inf')

        for i in range(rows):
            for j in range(cols):
                total += abs(matrix[i][j])

                if matrix[i][j] < 0: count += 1
                mmin = min(mmin, abs(matrix[i][j]))

        if count % 2 == 0:
            return total
        else:
            return total - 2 * mmin