Question

1975. Maximum Matrix Sum

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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

Solutions

Solution 1

class Solution:
  def maxMatrixSum(self, matrix: List[List[int]]) -> int:
    s = cnt = 0
    mi = inf
    for row in matrix:
      for v in row:
        s += abs(v)
        mi = min(mi, abs(v))
        if v < 0:
          cnt += 1
    if cnt % 2 == 0 or mi == 0:
      return s
    return s - mi * 2

class Solution {
  public long maxMatrixSum(int[][] matrix) {
    long s = 0;
    int cnt = 0;
    int mi = Integer.MAX_VALUE;
    for (var row : matrix) {
      for (var v : row) {
        s += Math.abs(v);
        mi = Math.min(mi, Math.abs(v));
        if (v < 0) {
          ++cnt;
        }
      }
    }
    if (cnt % 2 == 0 || mi == 0) {
      return s;
    }
    return s - mi * 2;
  }
}

class Solution {
public:
  long long maxMatrixSum(vector<vector<int>>& matrix) {
    long long s = 0;
    int cnt = 0, mi = INT_MAX;
    for (auto& row : matrix) {
      for (int& v : row) {
        s += abs(v);
        mi = min(mi, abs(v));
        cnt += v < 0;
      }
    }
    if (cnt % 2 == 0 || mi == 0) return s;
    return s - mi * 2;
  }
};

func maxMatrixSum(matrix [][]int) int64 {
  s := 0
  cnt, mi := 0, math.MaxInt32
  for _, row := range matrix {
    for _, v := range row {
      s += abs(v)
      mi = min(mi, abs(v))
      if v < 0 {
        cnt++
      }
    }
  }
  if cnt%2 == 1 {
    s -= mi * 2
  }
  return int64(s)
}

func abs(x int) int {
  if x < 0 {
    return -x
  }
  return x
}

/**
 * @param {number[][]} matrix
 * @return {number}
 */
var maxMatrixSum = function (matrix) {
  let cnt = 0;
  let s = 0;
  let mi = Infinity;
  for (const row of matrix) {
    for (const v of row) {
      s += Math.abs(v);
      mi = Math.min(mi, Math.abs(v));
      cnt += v < 0;
    }
  }
  if (cnt % 2 == 0) {
    return s;
  }
  return s - mi * 2;
};