Score After Flipping Matrix in C++

Suppose we have a two dimensional matrix A where each value is 0 or 1. Here 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. Now 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. So our task is to find the highest possible score. If the input is like −

The output will be 39 as after toggling, the matrix will be −

So the numbers are 15 + 9 + 15 = 39

To solve this, we will follow these steps −

• n := row count and m := column count

• ret := n x (2^(m – 1))

• for j in range 1 to m – 1

  • cnt : = 0

  • for i in range 0 to n – 1

    • cnt := cnt + A[i, j] = A[i, 0]

  • temp := 2^(m – j – 1) * maximum of cnt and n – cnt

  • ret := ret + temp

• return ret

Let us see the following implementation to get better understanding −

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
class Solution {
   public:
   int matrixScore(vector<vector<int>>& A) {
      int n = A.size();
      int m = A[0].size();
      int ret = (1 << (m - 1)) * n;
      for(int j = 1; j < m; j++){
         int cnt = 0;
         for(int i = 0; i < n; i++){
            cnt += (A[i][j] == A[i][0]);
         }
         int temp = ((1 << (m - (j + 1))) * max(cnt, n - cnt));
         ret += temp;
      }
      return ret;
   }
};
main(){
   vector<vector<int>> v = {{0,0,1,1},{1,0,1,0},{1,1,0,0}};
   Solution ob;
   cout << (ob.matrixScore(v));
}

Input

[[0,0,1,1],[1,0,1,0],[1,1,0,0]]

Output

39