mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-27 17:16:28 +08:00
7ffef7e1d6
* update author information * Update index.md --------- Co-authored-by: Yudong Jin <krahets@163.com>
72 lines
2.4 KiB
Rust
72 lines
2.4 KiB
Rust
/*
|
||
* File: n_queens.rs
|
||
* Created Time: 2023-07-15
|
||
* Author: codingonion (coderonion@gmail.com)
|
||
*/
|
||
|
||
/* 回溯算法：N 皇后 */
|
||
fn backtrack(row: usize, n: usize, state: &mut Vec<Vec<String>>, res: &mut Vec<Vec<Vec<String>>>,
|
||
cols: &mut [bool], diags1: &mut [bool], diags2: &mut [bool]) {
|
||
// 当放置完所有行时，记录解
|
||
if row == n {
|
||
let mut copy_state: Vec<Vec<String>> = Vec::new();
|
||
for s_row in state.clone() {
|
||
copy_state.push(s_row);
|
||
}
|
||
res.push(copy_state);
|
||
return;
|
||
}
|
||
// 遍历所有列
|
||
for col in 0..n {
|
||
// 计算该格子对应的主对角线和次对角线
|
||
let diag1 = row + n - 1 - col;
|
||
let 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.get_mut(row).unwrap()[col] = "Q".into();
|
||
(cols[col], diags1[diag1], diags2[diag2]) = (true, true, 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.get_mut(row).unwrap()[col] = "#".into();
|
||
(cols[col], diags1[diag1], diags2[diag2]) = (false, false, false);
|
||
}
|
||
}
|
||
}
|
||
|
||
/* 求解 N 皇后 */
|
||
fn n_queens(n: usize) -> Vec<Vec<Vec<String>>> {
|
||
// 初始化 n*n 大小的棋盘，其中 'Q' 代表皇后，'#' 代表空位
|
||
let mut state: Vec<Vec<String>> = Vec::new();
|
||
for _ in 0..n {
|
||
let mut row: Vec<String> = Vec::new();
|
||
for _ in 0..n {
|
||
row.push("#".into());
|
||
}
|
||
state.push(row);
|
||
}
|
||
let mut cols = vec![false; n]; // 记录列是否有皇后
|
||
let mut diags1 = vec![false; 2 * n - 1]; // 记录主对角线上是否有皇后
|
||
let mut diags2 = vec![false; 2 * n - 1]; // 记录次对角线上是否有皇后
|
||
let mut res: Vec<Vec<Vec<String>>> = Vec::new();
|
||
|
||
backtrack(0, n, &mut state, &mut res, &mut cols, &mut diags1, &mut diags2);
|
||
|
||
res
|
||
}
|
||
|
||
/* Driver Code */
|
||
pub fn main() {
|
||
let n: usize = 4;
|
||
let res = n_queens(n);
|
||
|
||
println!("输入棋盘长宽为 {n}");
|
||
println!("皇后放置方案共有 {} 种", res.len());
|
||
for state in res.iter() {
|
||
println!("--------------------");
|
||
for row in state.iter() {
|
||
println!("{:?}", row);
|
||
}
|
||
}
|
||
}
|