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/**
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* File: n_queens.swift
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* Created Time: 2023-05-14
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* Author: nuomi1 (nuomi1@qq.com)
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*/
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/* 回溯演算法：n 皇后 */
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func backtrack(row: Int, n: Int, state: inout [[String]], res: inout [[[String]]], cols: inout [Bool], diags1: inout [Bool], diags2: inout [Bool]) {
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// 當放置完所有行時，記錄解
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if row == n {
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res.append(state)
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return
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}
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// 走訪所有列
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for col in 0 ..< n {
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// 計算該格子對應的主對角線和次對角線
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let diag1 = row - col + n - 1
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let diag2 = row + col
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// 剪枝：不允許該格子所在列、主對角線、次對角線上存在皇后
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if !cols[col] && !diags1[diag1] && !diags2[diag2] {
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// 嘗試：將皇后放置在該格子
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state[row][col] = "Q"
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cols[col] = true
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diags1[diag1] = true
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diags2[diag2] = true
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// 放置下一行
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backtrack(row: row + 1, n: n, state: &state, res: &res, cols: &cols, diags1: &diags1, diags2: &diags2)
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// 回退：將該格子恢復為空位
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state[row][col] = "#"
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cols[col] = false
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diags1[diag1] = false
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diags2[diag2] = false
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}
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}
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}
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/* 求解 n 皇后 */
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func nQueens(n: Int) -> [[[String]]] {
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// 初始化 n*n 大小的棋盤，其中 'Q' 代表皇后，'#' 代表空位
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var state = Array(repeating: Array(repeating: "#", count: n), count: n)
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var cols = Array(repeating: false, count: n) // 記錄列是否有皇后
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var diags1 = Array(repeating: false, count: 2 * n - 1) // 記錄主對角線上是否有皇后
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var diags2 = Array(repeating: false, count: 2 * n - 1) // 記錄次對角線上是否有皇后
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var res: [[[String]]] = []
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backtrack(row: 0, n: n, state: &state, res: &res, cols: &cols, diags1: &diags1, diags2: &diags2)
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return res
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}
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@main
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enum NQueens {
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/* Driver Code */
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static func main() {
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let n = 4
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let res = nQueens(n: n)
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print("輸入棋盤長寬為 \(n)")
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print("皇后放置方案共有 \(res.count) 種")
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for state in res {
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print("--------------------")
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for row in state {
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print(row)
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}
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}
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}
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}
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