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：
复制代码 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<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

复制代码 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