mirror of
https://github.com/krahets/hello-algo.git
synced 2025-10-31 18:37:48 +08:00
f6976978dd
* Update the book with the thrid revised edition * Fix a typo * Update the contributors' information * Update the mindmap * Update the version number
76 lines
2.1 KiB
Dart
76 lines
2.1 KiB
Dart
/**
|
||
* File: n_queens.dart
|
||
* Created Time: 2023-08-10
|
||
* Author: liuyuxin (gvenusleo@gmail.com)
|
||
*/
|
||
|
||
/* 回溯算法：n 皇后 */
|
||
void backtrack(
|
||
int row,
|
||
int n,
|
||
List<List<String>> state,
|
||
List<List<List<String>>> res,
|
||
List<bool> cols,
|
||
List<bool> diags1,
|
||
List<bool> diags2,
|
||
) {
|
||
// 当放置完所有行时，记录解
|
||
if (row == n) {
|
||
List<List<String>> copyState = [];
|
||
for (List<String> sRow in state) {
|
||
copyState.add(List.from(sRow));
|
||
}
|
||
res.add(copyState);
|
||
return;
|
||
}
|
||
// 遍历所有列
|
||
for (int col = 0; col < n; col++) {
|
||
// 计算该格子对应的主对角线和次对角线
|
||
int diag1 = row - col + n - 1;
|
||
int diag2 = row + col;
|
||
// 剪枝：不允许该格子所在列、主对角线、次对角线上存在皇后
|
||
if (!cols[col] && !diags1[diag1] && !diags2[diag2]) {
|
||
// 尝试：将皇后放置在该格子
|
||
state[row][col] = "Q";
|
||
cols[col] = true;
|
||
diags1[diag1] = true;
|
||
diags2[diag2] = true;
|
||
// 放置下一行
|
||
backtrack(row + 1, n, state, res, cols, diags1, diags2);
|
||
// 回退：将该格子恢复为空位
|
||
state[row][col] = "#";
|
||
cols[col] = false;
|
||
diags1[diag1] = false;
|
||
diags2[diag2] = false;
|
||
}
|
||
}
|
||
}
|
||
|
||
/* 求解 n 皇后 */
|
||
List<List<List<String>>> nQueens(int n) {
|
||
// 初始化 n*n 大小的棋盘，其中 'Q' 代表皇后，'#' 代表空位
|
||
List<List<String>> state = List.generate(n, (index) => List.filled(n, "#"));
|
||
List<bool> cols = List.filled(n, false); // 记录列是否有皇后
|
||
List<bool> diags1 = List.filled(2 * n - 1, false); // 记录主对角线上是否有皇后
|
||
List<bool> diags2 = List.filled(2 * n - 1, false); // 记录次对角线上是否有皇后
|
||
List<List<List<String>>> res = [];
|
||
|
||
backtrack(0, n, state, res, cols, diags1, diags2);
|
||
|
||
return res;
|
||
}
|
||
|
||
/* Driver Code */
|
||
void main() {
|
||
int n = 4;
|
||
List<List<List<String>>> res = nQueens(n);
|
||
print("输入棋盘长宽为 $n");
|
||
print("皇后放置方案共有 ${res.length} 种");
|
||
for (List<List<String>> state in res) {
|
||
print("--------------------");
|
||
for (List<String> row in state) {
|
||
print(row);
|
||
}
|
||
}
|
||
}
|