feat: add Swift codes for n_queens_problem article (#495)

* refactor: rename PreorderTraversalIIITemplate

* feat: add Swift codes for n_queens_problem article

codes/swift/Package.swift

@@ -61,6 +61,7 @@ let package = Package(
         .executable(name: "preorder_traversal_iii_template", targets: ["preorder_traversal_iii_template"]),
         .executable(name: "permutations_i", targets: ["permutations_i"]),
         .executable(name: "permutations_ii", targets: ["permutations_ii"]),
+        .executable(name: "n_queens", targets: ["n_queens"]),
     ],
     targets: [
         // helper
@@ -122,5 +123,6 @@ let package = Package(
         .executableTarget(name: "preorder_traversal_iii_template", dependencies: ["utils"], path: "chapter_backtracking", sources: ["preorder_traversal_iii_template.swift"]),
         .executableTarget(name: "permutations_i", path: "chapter_backtracking", sources: ["permutations_i.swift"]),
         .executableTarget(name: "permutations_ii", path: "chapter_backtracking", sources: ["permutations_ii.swift"]),
+        .executableTarget(name: "n_queens", path: "chapter_backtracking", sources: ["n_queens.swift"]),
     ]
 )

codes/swift/chapter_backtracking/n_queens.swift

@@ -0,0 +1,67 @@
+/**
+ * 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 或 主对角线 或 副对角线) 包含皇后
+        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)
+            }
+        }
+    }
+}

codes/swift/chapter_backtracking/preorder_traversal_iii_template.swift

@@ -53,7 +53,7 @@ func backtrack(state: inout [TreeNode], choices: [TreeNode], res: inout [[TreeNo
 }
 
 @main
-enum preorder_traversal_iii_template {
+enum PreorderTraversalIIITemplate {
     /* Driver Code */
     static func main() {
         let root = TreeNode.listToTree(list: [1, 7, 3, 4, 5, 6, 7])