• 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: Math

Count the number of negative numbers.
1. Even negatives, we can always flip all the negatives to positives. ans = sum(abs(matrix)).
2. Odd negatives, there will be one negative left, we found the smallest abs(element) and let it become negative. ans = sum(abs(matrix))) – 2 * min(abs(matrix))

Time complexity: O(n²)
Space complexity: O(1)

// Author: Huahua
class Solution {
public:
  long long maxMatrixSum(vector<vector<int>>& matrix) {
    const int n = matrix.size();
    long long ans = 0;
    int count = 0;
    int lo = INT_MAX;
    for (int i = 0; i < n; ++i)
      for (int j = 0; j < n; ++j) {
        ans += abs(matrix[i][j]);
        lo = min(lo, abs(matrix[i][j]));
        count += matrix[i][j] < 0;          
      }    
    return ans - (count & 1) * 2 * lo;
  }
};

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