LeetCode 1975: Maximum Matrix Sum Solution

Master LeetCode problem 1975 (Maximum Matrix Sum), a medium challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

1975. Maximum Matrix Sum

Medium

Array Greedy Matrix

Problem Explanation

Explanation

To maximize the sum of the matrix's elements, we need to manipulate the negative values in the matrix. We can do this by multiplying adjacent elements by -1. The key insight is that multiplying a negative number by -1 will make it positive, which will increase the overall sum.

To maximize the sum, we follow these steps:

Count the number of negative numbers and the absolute sum of all numbers in the matrix.
If there are an odd number of negative numbers, we can make all but one of them positive to maximize the sum.
If there are an even number of negative numbers, we can make all of them positive to maximize the sum.
If there are zeros, we can simply make them positive as they don't affect the sum.

This algorithm ensures that we maximize the sum by making the necessary adjustments to the negative numbers in the matrix.

Time complexity: O(n^2) where n is the size of the matrix Space complexity: O(1)

Solution Code

class Solution {
    public long maxMatrixSum(int[][] matrix) {
        int n = matrix.length;
        long sum = 0;
        int minAbs = Integer.MAX_VALUE;
        int countNegatives = 0;

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                int num = matrix[i][j];
                sum += Math.abs(num);
                minAbs = Math.min(minAbs, Math.abs(num));
                if (num < 0) {
                    countNegatives++;
                }
            }
        }

        if (countNegatives % 2 == 0) {
            return sum;
        } else {
            return sum - 2 * minAbs;
        }
    }
}

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