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：

代码如下:

/**

* Created by cshao on 12/28/14.

*/

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

if (nQueens[row] === undefined) {

nQueens[row] = [];

}

for (var col=0; 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

nQueens[row][col] = undefined;

}

}

function isQueenValid(nQueens, row, col) {

for (var i=0; i

if (nQueens[row][i] == 1) {

return false;

}

}

for (var j=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

var rowText = '';

for (var col=0; 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

代码如下:

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