861. Score After Flipping Matrix

We have a two dimensional matrix A where each value is 0 or 1.

A move consists of choosing any row or column, and toggling each value in that row or column: changing all 0s to 1s, and all 1s to 0s.

After making any number of moves, every row of this matrix is interpreted as a binary number, and the score of the matrix is the sum of these numbers.

Return the highest possible score.

Example 1:

Input: [[0,0,1,1],[1,0,1,0],[1,1,0,0]]
Output: 39
Explanation:
Toggled to [[1,1,1,1],[1,0,0,1],[1,1,1,1]].
0b1111 + 0b1001 + 0b1111 = 15 + 9 + 15 = 39

Note:

1. 1 <= A.length <= 20

2. 1 <= A[0].length <= 20

3. A[i][j] is 0 or 1.

// Greedy Method
int matrixScore(vector<vector<int>>& A) { // time: O(m * n); space: O(1)
    int m = A.size(), n = A[0].size(), res = m * (1 << (n - 1));
    for (int j = 1; j < n; ++j) {
        int cnt = 0;
        for (int i = 0; i < m; ++i)  cnt += A[i][j] == A[i][0];
        res += max(cnt, m - cnt) * (1 << (n - 1 - j));
    }
    return res;
}