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
console.log('N Queens problem apply for order bigger than 3');
return;
}
var nQueens = [];
var backTracking = false;
rowLoop:
for (var row=0; row
nQueens[row] = [];
}
for (var col=0; col
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
}
}
function isQueenValid(nQueens, row, col) {
for (var i=0; i
function printQueens(queens) {
for (var row=0; row
for (var col=0; col
queens[row][col] = 0;
}
rowText = rowText + queens[row][col] + ' ';
}
console.log(rowText);
}
}
var queens = getNQueens(8);
printQueens(queens);
结果