算法谜题JavaScript解:N皇后问题

谜题

N皇后问题。将N个皇后放置在NxN的国际象棋棋盘上,其中没有任何两个皇后处于同一行、同一列或同一对角线上,以使得它们不能互相攻击。

策略

回溯法。

JavaScript解

以8皇后问题为例:

function getNQueens(order) {  
  if (order < 4) {
    console.log('N Queens problem apply for order bigger than 3');
    return;
  }

  var nQueens = [];
  var backTracking = false;
  rowLoop:
  for (var row=0; row<order; row++) {
    if (nQueens[row] === undefined) {
      nQueens[row] = [];
    }

    for (var col=0; col<order; col++) {
      if (nQueens[row][col] === 0) {
        continue;
      } else if (backTracking && nQueens[row][col] == 1) {
        if (col === order-1) {
          resetRow(nQueens, order, row);
          row = row - 2;
          continue rowLoop;
        }
        nQueens[row][col] = 0;
        backTracking = false;
        continue;
      }

      nQueens[row][col] = 1;
      if (isQueenValid(nQueens, row, col)) {
        continue rowLoop;
      } else if (col == order-1) {
        backTracking = true;
        resetRow(nQueens, order, row);
        row = row - 2;
        continue rowLoop;
      } else {
        nQueens[row][col] = 0;
        continue;
      };
    }
  }

  return nQueens;
}

function resetRow(nQueens, order, row) {  
  for (var col=0; col<order; col++) {
    nQueens[row][col] = undefined;
  }
}

function isQueenValid(nQueens, row, col) {  
  for (var i=0; i<col; i++) {
    if (nQueens[row][i] == 1) {
      return false;
    }
  }
  for (var j=1; j<row+1; j++) {
    if (nQueens[row-j][col]==1 || (nQueens[row-j][col-j]!=undefined && nQueens[row-j][col-j]==1) || (nQueens[row-j][col+j]!=undefined && nQueens[row-j][col+j]==1)) {
      return false;
    }
  }
  return true;
}

function printQueens(queens) {  
  for (var row=0; row<queens.length; row++) {
    var rowText = '';
    for (var col=0; col<queens.length; col++) {
      if (queens[row][col]===undefined) {
        queens[row][col] = 0;
      }
      rowText = rowText + queens[row][col] + '  ';
    }
    console.log(rowText);
  }
}

var queens = getNQueens(8);  
printQueens(queens);  

结果

1  0  0  0  0  0  0  0  
0  0  0  0  1  0  0  0  
0  0  0  0  0  0  0  1  
0  0  0  0  0  1  0  0  
0  0  1  0  0  0  0  0  
0  0  0  0  0  0  1  0  
0  1  0  0  0  0  0  0  
0  0  0  1  0  0  0  0