|
|
|
|
|
/**
|
|
|
|
|
|
* File: n_queens.js
|
|
|
|
|
|
* Created Time: 2023-05-13
|
|
|
|
|
|
* Author: Justin (xiefahit@gmail.com)
|
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
|
|
/* 回溯演算法：n 皇后 */
|
|
|
|
|
|
function backtrack(row, n, state, res, cols, diags1, diags2) {
|
|
|
|
|
|
// 當放置完所有行時，記錄解
|
|
|
|
|
|
if (row === n) {
|
|
|
|
|
|
res.push(state.map((row) => row.slice()));
|
|
|
|
|
|
return;
|
|
|
|
|
|
}
|
|
|
|
|
|
// 走訪所有列
|
|
|
|
|
|
for (let col = 0; col < n; col++) {
|
|
|
|
|
|
// 計算該格子對應的主對角線和次對角線
|
|
|
|
|
|
const diag1 = row - col + n - 1;
|
|
|
|
|
|
const diag2 = row + col;
|
|
|
|
|
|
// 剪枝：不允許該格子所在列、主對角線、次對角線上存在皇后
|
|
|
|
|
|
if (!cols[col] && !diags1[diag1] && !diags2[diag2]) {
|
|
|
|
|
|
// 嘗試：將皇后放置在該格子
|
|
|
|
|
|
state[row][col] = 'Q';
|
|
|
|
|
|
cols[col] = diags1[diag1] = diags2[diag2] = true;
|
|
|
|
|
|
// 放置下一行
|
|
|
|
|
|
backtrack(row + 1, n, state, res, cols, diags1, diags2);
|
|
|
|
|
|
// 回退：將該格子恢復為空位
|
|
|
|
|
|
state[row][col] = '#';
|
|
|
|
|
|
cols[col] = diags1[diag1] = diags2[diag2] = false;
|
|
|
|
|
|
}
|
|
|
|
|
|
}
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
/* 求解 n 皇后 */
|
|
|
|
|
|
function nQueens(n) {
|
|
|
|
|
|
// 初始化 n*n 大小的棋盤，其中 'Q' 代表皇后，'#' 代表空位
|
|
|
|
|
|
const state = Array.from({ length: n }, () => Array(n).fill('#'));
|
|
|
|
|
|
const cols = Array(n).fill(false); // 記錄列是否有皇后
|
|
|
|
|
|
const diags1 = Array(2 * n - 1).fill(false); // 記錄主對角線上是否有皇后
|
|
|
|
|
|
const diags2 = Array(2 * n - 1).fill(false); // 記錄次對角線上是否有皇后
|
|
|
|
|
|
const res = [];
|
|
|
|
|
|
|
|
|
|
|
|
backtrack(0, n, state, res, cols, diags1, diags2);
|
|
|
|
|
|
return res;
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
// Driver Code
|
|
|
|
|
|
const n = 4;
|
|
|
|
|
|
const res = nQueens(n);
|
|
|
|
|
|
|
|
|
|
|
|
console.log(`輸入棋盤長寬為 ${n}`);
|
|
|
|
|
|
console.log(`皇后放置方案共有 ${res.length} 種`);
|
|
|
|
|
|
res.forEach((state) => {
|
|
|
|
|
|
console.log('--------------------');
|
|
|
|
|
|
state.forEach((row) => console.log(row));
|
|
|
|
|
|
});
|
