# Transform to Chessboard in C++

Suppose we have one N x N board contains only 0s and 1s. Now in each move, we can swap any 2 rows, or any 2 columns. We have to find the minimum number of moves to transform the board into a "chessboard". If the solution does not exist, then return -1.

So if the input is like −

Then the output will be 2, as first two columns in the first move, then board will be like −

Then swap second and 3rd rows −

This is the chessboard

To solve this, we will follow these steps −

• n := size of b
• for initialize i := 0, when i < n, update (increase i by 1), do −
• for initialize j := 0, when j < n, update (increase j by 1), do −
• if b[0, 0] XOR b[0, j] XOR b[i, 0] XOR b[i, j] is non-zero, then −
• return -1
• rowSum := 0, colSum := 0, rowSwap := 0, colSwap := 0
• for initialize i := 0, when i < n, update (increase i by 1), do −
• rowSum := rowSum + b[i, 0], colSum := colSum + b[0, i]
• rowSwap := true when rowSwap + b[i, 0] is same as i mod 2,
• colSwap := true when colSwap + b[0, i] is same as i mod 2
• if rowSum is not equal to n / 2 and rowSum is not equal to (n + 1) / 2, then −
• return -1
• if colSum is not equal to n / 2 and colSum is not equal to (n + 1) / 2, then −
• return -1
• if n mod 2 is same as 1, then −
• if colSwap mod 2 is non-zero, then −
• colSwap := n - colSwap
• if rowSwap mod 2 is non-zero, then −
• rowSwap := n - rowSwap
• Otherwise
• colSwap := minimum of colSwap and n - colSwap
• rowSwap := minimum of rowSwap and n - rowSwap
• return (rowSwap + colSwap) / 2

Let us see the following implementation to get better understanding −

## Example

Live Demo

#include <bits/stdc++.h>
using namespace std;
class Solution {
public:
int movesToChessboard(vector<vector<int>>& b) {
int n = b.size();
for(int i = 0; i < n; i++){
for(int j = 0; j < n; j++){
if(b[0][0] ^ b[0][j] ^ b[i][0] ^ b[i][j]) return -1;
}
}
int rowSum = 0;
int colSum = 0;
int rowSwap = 0;
int colSwap = 0;
for(int i = 0; i < n; i++){
rowSum += b[i][0];
colSum += b[0][i];
rowSwap += b[i][0] == i % 2;
colSwap += b[0][i] == i % 2;
}
if(rowSum != n/2 && rowSum != (n + 1)/2)return -1;
if(colSum != n/2 && colSum != (n + 1)/2)return -1;
if(n % 2 == 1){
if(colSwap % 2) colSwap = n - colSwap;
if(rowSwap % 2) rowSwap = n - rowSwap;
}else{
colSwap = min(colSwap, n - colSwap);
rowSwap = min(rowSwap, n - rowSwap);
}
return (rowSwap + colSwap)/2;
}
};
main(){
Solution ob;
vector<vector<int>> v = {{0,1,1,0},{0,1,1,0},{1,0,0,1},{1,0,0,1}};
cout << (ob.movesToChessboard(v));
}

## Input

{{0,1,1,0},{0,1,1,0},{1,0,0,1},{1,0,0,1}};

## Output

2