#782 - Transform to Chessboard

Hard • View on LeetCode • View on GitHub

Problem Description

You are given an n x n binary grid board. In each move, you can swap any two rows with each other, or any two columns with each other.

Return the minimum number of moves to transform the board into a chessboard board. If the task is impossible, return -1.

A chessboard board is a board where no 0's and no 1's are 4-directionally adjacent.

Solution

/**
 * @param {number[][]} board
 * @return {number}
 */
var movesToChessboard = function(board) {
  const n = board.length;

  for (let i = 0; i < n; i++) {
    for (let j = 0; j < n; j++) {
      if ((board[0][0] ^ board[i][0] ^ board[0][j] ^ board[i][j]) === 1) {
        return -1;
      }
    }
  }

  let rowSum = 0;
  let colSum = 0;
  let rowSwaps = 0;
  let colSwaps = 0;

  for (let i = 0; i < n; i++) {
    rowSum += board[0][i];
    colSum += board[i][0];

    if (board[i][0] === i % 2) rowSwaps++;
    if (board[0][i] === i % 2) colSwaps++;
  }

  if (rowSum !== Math.floor(n / 2) && rowSum !== Math.ceil(n / 2)) return -1;
  if (colSum !== Math.floor(n / 2) && colSum !== Math.ceil(n / 2)) return -1;

  if (n % 2 === 1) {
    if (rowSwaps % 2 === 1) rowSwaps = n - rowSwaps;
    if (colSwaps % 2 === 1) colSwaps = n - colSwaps;
  } else {
    rowSwaps = Math.min(rowSwaps, n - rowSwaps);
    colSwaps = Math.min(colSwaps, n - colSwaps);
  }

  return Math.floor((rowSwaps + colSwaps) / 2);
};