Feature/array representation of tree swift (#649)

* refactor: encode & decode Tree * style: build warning * feat: add Swift codes for array_representation_of_tree article
2026-09-27 00:36:39 +08:00 · 2023-07-24 12:46:48 +08:00
parent c1adeb2399
commit 9ab4b0b15c
12 changed files with 200 additions and 32 deletions
@@ -35,6 +35,7 @@ let package = Package(
        .executable(name: "binary_tree", targets: ["binary_tree"]),
        .executable(name: "binary_tree_bfs", targets: ["binary_tree_bfs"]),
        .executable(name: "binary_tree_dfs", targets: ["binary_tree_dfs"]),
+        .executable(name: "array_binary_tree", targets: ["array_binary_tree"]),
        .executable(name: "binary_search_tree", targets: ["binary_search_tree"]),
        .executable(name: "avl_tree", targets: ["avl_tree"]),
        // chapter_heap
@@ -120,6 +121,7 @@ let package = Package(
        .executableTarget(name: "binary_tree", dependencies: ["utils"], path: "chapter_tree", sources: ["binary_tree.swift"]),
        .executableTarget(name: "binary_tree_bfs", dependencies: ["utils"], path: "chapter_tree", sources: ["binary_tree_bfs.swift"]),
        .executableTarget(name: "binary_tree_dfs", dependencies: ["utils"], path: "chapter_tree", sources: ["binary_tree_dfs.swift"]),
+        .executableTarget(name: "array_binary_tree", dependencies: ["utils"], path: "chapter_tree", sources: ["array_binary_tree.swift"]),
        .executableTarget(name: "binary_search_tree", dependencies: ["utils"], path: "chapter_tree", sources: ["binary_search_tree.swift"]),
        .executableTarget(name: "avl_tree", dependencies: ["utils"], path: "chapter_tree", sources: ["avl_tree.swift"]),
        // chapter_heap
@@ -25,7 +25,7 @@ func preOrder(root: TreeNode?) {
 enum PreorderTraversalICompact {
    /* Driver Code */
    static func main() {
-        let root = TreeNode.listToTree(list: [1, 7, 3, 4, 5, 6, 7])
+        let root = TreeNode.listToTree(arr: [1, 7, 3, 4, 5, 6, 7])
        print("\n初始化二叉树")
        PrintUtil.printTree(root: root)

@@ -30,7 +30,7 @@ func preOrder(root: TreeNode?) {
 enum PreorderTraversalIICompact {
    /* Driver Code */
    static func main() {
-        let root = TreeNode.listToTree(list: [1, 7, 3, 4, 5, 6, 7])
+        let root = TreeNode.listToTree(arr: [1, 7, 3, 4, 5, 6, 7])
        print("\n初始化二叉树")
        PrintUtil.printTree(root: root)

@@ -33,7 +33,7 @@ func preOrder(root: TreeNode?) {
 enum PreorderTraversalIIICompact {
    /* Driver Code */
    static func main() {
-        let root = TreeNode.listToTree(list: [1, 7, 3, 4, 5, 6, 7])
+        let root = TreeNode.listToTree(arr: [1, 7, 3, 4, 5, 6, 7])
        print("\n初始化二叉树")
        PrintUtil.printTree(root: root)

@@ -56,7 +56,7 @@ func backtrack(state: inout [TreeNode], choices: [TreeNode], res: inout [[TreeNo
 enum PreorderTraversalIIITemplate {
    /* Driver Code */
    static func main() {
-        let root = TreeNode.listToTree(list: [1, 7, 3, 4, 5, 6, 7])
+        let root = TreeNode.listToTree(arr: [1, 7, 3, 4, 5, 6, 7])
        print("\n初始化二叉树")
        PrintUtil.printTree(root: root)

@@ -0,0 +1,141 @@
+/**
+ * File: array_binary_tree.swift
+ * Created Time: 2023-07-23
+ * Author: nuomi1 (nuomi1@qq.com)
+ */
+
+import utils
+
+/* 数组表示下的二叉树类 */
+class ArrayBinaryTree {
+    private var tree: [Int?]
+
+    /* 构造方法 */
+    init(arr: [Int?]) {
+        tree = arr
+    }
+
+    /* 节点数量 */
+    func size() -> Int {
+        tree.count
+    }
+
+    /* 获取索引为 i 节点的值 */
+    func val(i: Int) -> Int? {
+        // 若索引越界，则返回 null ，代表空位
+        if i < 0 || i >= size() {
+            return nil
+        }
+        return tree[i]
+    }
+
+    /* 获取索引为 i 节点的左子节点的索引 */
+    func left(i: Int) -> Int {
+        2 * i + 1
+    }
+
+    /* 获取索引为 i 节点的右子节点的索引 */
+    func right(i: Int) -> Int {
+        2 * i + 2
+    }
+
+    /* 获取索引为 i 节点的父节点的索引 */
+    func parent(i: Int) -> Int {
+        (i - 1) / 2
+    }
+
+    /* 层序遍历 */
+    func levelOrder() -> [Int] {
+        var res: [Int] = []
+        // 直接遍历数组
+        for i in stride(from: 0, to: size(), by: 1) {
+            if let val = val(i: i) {
+                res.append(val)
+            }
+        }
+        return res
+    }
+
+    /* 深度优先遍历 */
+    private func dfs(i: Int, order: String, res: inout [Int]) {
+        // 若为空位，则返回
+        guard let val = val(i: i) else {
+            return
+        }
+        // 前序遍历
+        if order == "pre" {
+            res.append(val)
+        }
+        dfs(i: left(i: i), order: order, res: &res)
+        // 中序遍历
+        if order == "in" {
+            res.append(val)
+        }
+        dfs(i: right(i: i), order: order, res: &res)
+        // 后序遍历
+        if order == "post" {
+            res.append(val)
+        }
+    }
+
+    /* 前序遍历 */
+    func preOrder() -> [Int] {
+        var res: [Int] = []
+        dfs(i: 0, order: "pre", res: &res)
+        return res
+    }
+
+    /* 中序遍历 */
+    func inOrder() -> [Int] {
+        var res: [Int] = []
+        dfs(i: 0, order: "in", res: &res)
+        return res
+    }
+
+    /* 后序遍历 */
+    func postOrder() -> [Int] {
+        var res: [Int] = []
+        dfs(i: 0, order: "post", res: &res)
+        return res
+    }
+}
+
+@main
+enum _ArrayBinaryTree {
+    /* Driver Code */
+    static func main() {
+        // 初始化二叉树
+        // 这里借助了一个从数组直接生成二叉树的函数
+        let arr = [1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15]
+
+        let root = TreeNode.listToTree(arr: arr)
+        print("\n初始化二叉树\n")
+        print("二叉树的数组表示：")
+        print(arr)
+        print("二叉树的链表表示：")
+        PrintUtil.printTree(root: root)
+
+        // 数组表示下的二叉树类
+        let abt = ArrayBinaryTree(arr: arr)
+
+        // 访问节点
+        let i = 1
+        let l = abt.left(i: i)
+        let r = abt.right(i: i)
+        let p = abt.parent(i: i)
+        print("\n当前节点的索引为 \(i) ，值为 \(abt.val(i: i) as Any)")
+        print("其左子节点的索引为 \(l) ，值为 \(abt.val(i: l) as Any)")
+        print("其右子节点的索引为 \(r) ，值为 \(abt.val(i: r) as Any)")
+        print("其父节点的索引为 \(p) ，值为 \(abt.val(i: p) as Any)")
+
+        // 遍历树
+        var res = abt.levelOrder()
+        print("\n层序遍历为：\(res)")
+        res = abt.preOrder()
+        print("前序遍历为：\(res)")
+        res = abt.inOrder()
+        print("中序遍历为：\(res)")
+        res = abt.postOrder()
+        print("后序遍历为：\(res)")
+    }
+}
@@ -89,7 +89,6 @@ class AVLTree {
    }

    /* 插入节点 */
-    @discardableResult
    func insert(val: Int) {
        root = insertHelper(node: root, val: val)
    }
@@ -116,7 +115,6 @@ class AVLTree {
    }

    /* 删除节点 */
-    @discardableResult
    func remove(val: Int) {
        root = removeHelper(node: root, val: val)
    }
@@ -90,7 +90,6 @@ class BinarySearchTree {
    }

    /* 删除节点 */
-    @discardableResult
    func remove(num: Int) {
        // 若树为空，直接提前返回
        if root == nil {
@@ -160,7 +159,7 @@ enum _BinarySearchTree {
        PrintUtil.printTree(root: bst.getRoot())

        /* 查找节点 */
-        var node = bst.search(num: 7)
+        let node = bst.search(num: 7)
        print("\n查找到的节点对象为 \(node!)，节点值 = \(node!.val)")

        /* 插入节点 */
@@ -31,7 +31,7 @@ enum BinaryTreeBFS {
    static func main() {
        /* 初始化二叉树 */
        // 这里借助了一个从数组直接生成二叉树的函数
-        let node = TreeNode.listToTree(list: [1, 2, 3, 4, 5, 6, 7])!
+        let node = TreeNode.listToTree(arr: [1, 2, 3, 4, 5, 6, 7])!
        print("\n初始化二叉树\n")
        PrintUtil.printTree(root: node)

@@ -48,7 +48,7 @@ enum BinaryTreeDFS {
    static func main() {
        /* 初始化二叉树 */
        // 这里借助了一个从数组直接生成二叉树的函数
-        let root = TreeNode.listToTree(list: [1, 2, 3, 4, 5, 6, 7])!
+        let root = TreeNode.listToTree(arr: [1, 2, 3, 4, 5, 6, 7])!
        print("\n初始化二叉树\n")
        PrintUtil.printTree(root: root)

@@ -79,7 +79,7 @@ public enum PrintUtil {
        print("堆的数组表示：", terminator: "")
        print(queue)
        print("堆的树状表示：")
-        let root = TreeNode.listToTree(list: queue)
+        let root = TreeNode.listToTree(arr: queue)
        printTree(root: root)
    }

@@ -4,40 +4,68 @@
 * Author: nuomi1 (nuomi1@qq.com)
 */

+/* 二叉树节点类 */
 public class TreeNode {
    public var val: Int // 节点值
    public var height: Int // 节点高度
    public var left: TreeNode? // 左子节点引用
    public var right: TreeNode? // 右子节点引用

+    /* 构造方法 */
    public init(x: Int) {
        val = x
        height = 0
    }

-    public static func listToTree(list: [Int]) -> TreeNode? {
-        let size = list.count
-        if size == 0 {
+    // 序列化编码规则请参考：
+    // https://www.hello-algo.com/chapter_tree/array_representation_of_tree/
+    // 二叉树的数组表示：
+    // [1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15]
+    // 二叉树的链表表示：
+    //             /——— 15
+    //         /——— 7
+    //     /——— 3
+    //    |    \——— 6
+    //    |        \——— 12
+    // ——— 1
+    //     \——— 2
+    //        |    /——— 9
+    //         \——— 4
+    //             \——— 8
+
+    /* 将列表反序列化为二叉树：递归 */
+    private static func listToTreeDFS(arr: [Int?], i: Int) -> TreeNode? {
+        if i < 0 || i >= arr.count || arr[i] == nil {
            return nil
        }
-        let root = TreeNode(x: list[0])
-        var queue: [TreeNode] = [root]
-        var i = 0
-        while !queue.isEmpty {
-            let node = queue.removeFirst()
-            i += 1
-            if i >= size {
-                break
-            }
-            node.left = TreeNode(x: list[i])
-            queue.append(node.left!)
-            i += 1
-            if i >= size {
-                break
-            }
-            node.right = TreeNode(x: list[i])
-            queue.append(node.right!)
-        }
+        let root = TreeNode(x: arr[i]!)
+        root.left = listToTreeDFS(arr: arr, i: 2 * i + 1)
+        root.right = listToTreeDFS(arr: arr, i: 2 * i + 2)
        return root
    }
+
+    /* 将列表反序列化为二叉树 */
+    public static func listToTree(arr: [Int?]) -> TreeNode? {
+        listToTreeDFS(arr: arr, i: 0)
+    }
+
+    /* 将二叉树序列化为列表：递归 */
+    private static func treeToListDFS(root: TreeNode?, i: Int, res: inout [Int?]) {
+        if root == nil {
+            return
+        }
+        while i >= res.count {
+            res.append(nil)
+        }
+        res[i] = root?.val
+        treeToListDFS(root: root?.left, i: 2 * i + 1, res: &res)
+        treeToListDFS(root: root?.right, i: 2 * i + 2, res: &res)
+    }
+
+    /* 将二叉树序列化为列表 */
+    public static func treeToList(root: TreeNode?) -> [Int?] {
+        var res: [Int?] = []
+        treeToListDFS(root: root, i: 0, res: &res)
+        return res
+    }
 }