1975. Maximum Matrix Sum

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題目敘述

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.

解題思路

Complexity

• Time complexity: $O(n^2)$

• Space complexity: $O(1)$

Solution

class Solution {
    public long maxMatrixSum(int[][] matrix) {
        long result = 0;
        long isOdd = 0;
        int min = Integer.MAX_VALUE;

        for(int matrixRow[] : matrix) {
            for(int num : matrixRow) {
                int abs = Math.abs(num);
                result += abs;
                min = Math.min(min, abs);
                isOdd ^= (num >>> 31);
            }
        }

        return result - ((min << 1) & -isOdd);
    }
}