|
|
/**
|
|
|
* File: n_queens.swift
|
|
|
* Created Time: 2023-05-14
|
|
|
* Author: nuomi1 (nuomi1@qq.com)
|
|
|
*/
|
|
|
|
|
|
/* 回溯算法：N 皇后 */
|
|
|
func backtrack(row: Int, n: Int, state: inout [[String]], res: inout [[[String]]], cols: inout [Bool], diags1: inout [Bool], diags2: inout [Bool]) {
|
|
|
// 当放置完所有行时，记录解
|
|
|
if row == n {
|
|
|
res.append(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副对角线
|
|
|
let diag1 = row - col + n - 1
|
|
|
let diag2 = row + col
|
|
|
// 剪枝：不允许该格子所在列、主对角线、副对角线存在皇后
|
|
|
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: row + 1, n: n, state: &state, res: &res, cols: &cols, diags1: &diags1, diags2: &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 */
|
|
|
func nQueens(n: Int) -> [[[String]]] {
|
|
|
// 初始化 n*n 大小的棋盘，其中 'Q' 代表皇后，'#' 代表空位
|
|
|
var state = Array(repeating: Array(repeating: "#", count: n), count: n)
|
|
|
var cols = Array(repeating: false, count: n) // 记录列是否有皇后
|
|
|
var diags1 = Array(repeating: false, count: 2 * n - 1) // 记录主对角线是否有皇后
|
|
|
var diags2 = Array(repeating: false, count: 2 * n - 1) // 记录副对角线是否有皇后
|
|
|
var res: [[[String]]] = []
|
|
|
|
|
|
backtrack(row: 0, n: n, state: &state, res: &res, cols: &cols, diags1: &diags1, diags2: &diags2)
|
|
|
|
|
|
return res
|
|
|
}
|
|
|
|
|
|
@main
|
|
|
enum NQueens {
|
|
|
/* Driver Code */
|
|
|
static func main() {
|
|
|
let n = 4
|
|
|
let res = nQueens(n: n)
|
|
|
|
|
|
print("输入棋盘长宽为 \(n)")
|
|
|
print("皇后放置方案共有 \(res.count) 种")
|
|
|
for state in res {
|
|
|
print("--------------------")
|
|
|
for row in state {
|
|
|
print(row)
|
|
|
}
|
|
|
}
|
|
|
}
|
|
|
}
|
