2089. Maximum Matrix Sum¶

LeetCode Problem View on GitHub

2089. Maximum Matrix Sum

Medium

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¶

class Solution {
    public long maxMatrixSum(int[][] matrix) {
        int n = matrix.length;
        int m = matrix[0].length;
        int count = 0, neg = Integer.MAX_VALUE;
        long sum = 0;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                sum += Math.abs(matrix[i][j]);
                neg = Math.min(neg, Math.abs(matrix[i][j]));
                if (matrix[i][j] < 0) count++;
            }
        }
        if (count % 2 == 1) return sum - neg * 2;
        return sum;
    }
}

Complexity Analysis¶

• Time Complexity: O(?)
• Space Complexity: O(?)

Approach¶

Detailed explanation of the approach will be added here