Add implementation of array binary tree.

Rewrite the tree serialization and deserialization methods.
Add applications of array and linked list.

codes/cpp/chapter_backtracking/preorder_traversal_i_compact.cpp

@@ -23,7 +23,7 @@ static void preOrder(TreeNode *root) {
 
 /* Driver Code */
 int main() {
-    TreeNode *root = vecToTree(vector<int>{1, 7, 3, 4, 5, 6, 7});
+    TreeNode *root = vectorToTree(vector<int>{1, 7, 3, 4, 5, 6, 7});
     cout << "\n初始化二叉树" << endl;
     printTree(root);
 

codes/cpp/chapter_backtracking/preorder_traversal_ii_compact.cpp

@@ -28,7 +28,7 @@ static void preOrder(TreeNode *root) {
 
 /* Driver Code */
 int main() {
-    TreeNode *root = vecToTree(vector<int>{1, 7, 3, 4, 5, 6, 7});
+    TreeNode *root = vectorToTree(vector<int>{1, 7, 3, 4, 5, 6, 7});
     cout << "\n初始化二叉树" << endl;
     printTree(root);
 

codes/cpp/chapter_backtracking/preorder_traversal_iii_compact.cpp

@@ -29,7 +29,7 @@ static void preOrder(TreeNode *root) {
 
 /* Driver Code */
 int main() {
-    TreeNode *root = vecToTree(vector<int>{1, 7, 3, 4, 5, 6, 7});
+    TreeNode *root = vectorToTree(vector<int>{1, 7, 3, 4, 5, 6, 7});
     cout << "\n初始化二叉树" << endl;
     printTree(root);
 

codes/cpp/chapter_backtracking/preorder_traversal_iii_template.cpp

@@ -56,7 +56,7 @@ void backtrack(vector<TreeNode *> &state, vector<TreeNode *> &choices, vector<ve
 
 /* Driver Code */
 int main() {
-    TreeNode *root = vecToTree(vector<int>{1, 7, 3, 4, 5, 6, 7});
+    TreeNode *root = vectorToTree(vector<int>{1, 7, 3, 4, 5, 6, 7});
     cout << "\n初始化二叉树" << endl;
     printTree(root);
 

codes/cpp/chapter_heap/my_heap.cpp

@@ -114,7 +114,7 @@ class MaxHeap {
         cout << "堆的数组表示：";
         printVector(maxHeap);
         cout << "堆的树状表示：" << endl;
-        TreeNode *root = vecToTree(maxHeap);
+        TreeNode *root = vectorToTree(maxHeap);
         printTree(root);
         freeMemoryTree(root);
     }

codes/cpp/chapter_tree/CMakeLists.txt

@@ -3,3 +3,4 @@ add_executable(binary_search_tree binary_search_tree.cpp)
 add_executable(binary_tree binary_tree.cpp)
 add_executable(binary_tree_bfs binary_tree_bfs.cpp)
 add_executable(binary_tree_dfs binary_tree_dfs.cpp)
+add_executable(array_binary_tree array_binary_tree.cpp)

codes/cpp/chapter_tree/array_binary_tree.cpp

@@ -0,0 +1,137 @@
+/**
+ * File: array_binary_tree.cpp
+ * Created Time: 2023-07-19
+ * Author: Krahets (krahets@163.com)
+ */
+
+#include "../utils/common.hpp"
+
+/* 数组表示下的二叉树类 */
+class ArrayBinaryTree {
+  public:
+    /* 构造方法 */
+    ArrayBinaryTree(vector<int> arr) {
+        tree = arr;
+    }
+
+    /* 节点数量 */
+    int size() {
+        return tree.size();
+    }
+
+    /* 获取索引为 i 节点的值 */
+    int val(int i) {
+        // 若索引越界，则返回 INT_MAX ，代表空位
+        if (i < 0 || i >= size())
+            return INT_MAX;
+        return tree[i];
+    }
+
+    /* 获取索引为 i 节点的左子节点的索引 */
+    int left(int i) {
+        return 2 * i + 1;
+    }
+
+    /* 获取索引为 i 节点的右子节点的索引 */
+    int right(int i) {
+        return 2 * i + 2;
+    }
+
+    /* 获取索引为 i 节点的父节点的索引 */
+    int parent(int i) {
+        return (i - 1) / 2;
+    }
+
+    /* 层序遍历 */
+    vector<int> levelOrder() {
+        vector<int> res;
+        // 直接遍历数组
+        for (int i = 0; i < size(); i++) {
+            if (val(i) != INT_MAX)
+                res.push_back(val(i));
+        }
+        return res;
+    }
+
+    /* 前序遍历 */
+    vector<int> preOrder() {
+        vector<int> res;
+        dfs(0, "pre", res);
+        return res;
+    }
+
+    /* 中序遍历 */
+    vector<int> inOrder() {
+        vector<int> res;
+        dfs(0, "in", res);
+        return res;
+    }
+
+    /* 后序遍历 */
+    vector<int> postOrder() {
+        vector<int> res;
+        dfs(0, "post", res);
+        return res;
+    }
+
+  private:
+    vector<int> tree;
+
+    /* 深度优先遍历 */
+    void dfs(int i, string order, vector<int> &res) {
+        // 若为空位，则返回
+        if (val(i) == INT_MAX)
+            return;
+        // 前序遍历
+        if (order == "pre")
+            res.push_back(val(i));
+        dfs(left(i), order, res);
+        // 中序遍历
+        if (order == "in")
+            res.push_back(val(i));
+        dfs(right(i), order, res);
+        // 后序遍历
+        if (order == "post")
+            res.push_back(val(i));
+    }
+};
+
+/* Driver Code */
+int main() {
+    // 初始化二叉树
+    // 使用 INT_MAX 代表空位 nullptr
+    vector<int> arr = {1, 2, 3, 4, INT_MAX, 6, 7, 8, 9, INT_MAX, INT_MAX, 12, INT_MAX, INT_MAX, 15};
+    TreeNode *root = vectorToTree(arr);
+    cout << "\n初始化二叉树\n";
+    cout << "二叉树的数组表示：\n";
+    printVector(arr);
+    cout << "二叉树的链表表示：\n";
+    printTree(root);
+
+    // 数组表示下的二叉树类
+    ArrayBinaryTree abt(arr);
+
+    // 访问节点
+    int i = 1;
+    int l = abt.left(i), r = abt.right(i), p = abt.parent(i);
+    cout << "\n当前节点的索引为 " << i << "，值为 " << abt.val(i) << "\n";
+    cout << "其左子节点的索引为 " << l << "，值为 " << (l != INT_MAX ? to_string(abt.val(l)) : "None") << "\n";
+    cout << "其右子节点的索引为 " << r << "，值为 " << (r != INT_MAX ? to_string(abt.val(r)) : "None") << "\n";
+    cout << "其父节点的索引为 " << p << "，值为 " << (p != INT_MAX ? to_string(abt.val(p)) : "None") << "\n";
+
+    // 遍历树
+    vector<int> res = abt.levelOrder();
+    cout << "\n层序遍历为： ";
+    printVector(res);
+    res = abt.preOrder();
+    cout << "前序遍历为： ";
+    printVector(res);
+    res = abt.inOrder();
+    cout << "中序遍历为： ";
+    printVector(res);
+    res = abt.postOrder();
+    cout << "后序遍历为： ";
+    printVector(res);
+
+    return 0;
+}

codes/cpp/chapter_tree/binary_tree_bfs.cpp

@@ -29,7 +29,7 @@ vector<int> levelOrder(TreeNode *root) {
 int 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
-    TreeNode *root = vecToTree(vector<int>{1, 2, 3, 4, 5, 6, 7});
+    TreeNode *root = vectorToTree(vector<int>{1, 2, 3, 4, 5, 6, 7});
     cout << endl << "初始化二叉树\n" << endl;
     printTree(root);
 

codes/cpp/chapter_tree/binary_tree_dfs.cpp

@@ -43,7 +43,7 @@ void postOrder(TreeNode *root) {
 int 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
-    TreeNode *root = vecToTree(vector<int>{1, 2, 3, 4, 5, 6, 7});
+    TreeNode *root = vectorToTree(vector<int>{1, 2, 3, 4, 5, 6, 7});
     cout << endl << "初始化二叉树\n" << endl;
     printTree(root);
 

codes/cpp/utils/list_node.hpp

@@ -7,6 +7,8 @@
 #pragma once
 
 #include <iostream>
+#include <vector>
+
 using namespace std;
 
 /* Definition for a singly-linked list node */

codes/cpp/utils/print_utils.hpp

@@ -223,7 +223,7 @@ template <typename T, typename S, typename C> void printHeap(priority_queue<T, S
     cout << "堆的数组表示：";
     printVector(vec);
     cout << "堆的树状表示：" << endl;
-    TreeNode *root = vecToTree(vec);
+    TreeNode *root = vectorToTree(vec);
     printTree(root);
     freeMemoryTree(root);
 }

codes/cpp/utils/tree_node.hpp

@@ -7,8 +7,11 @@
 #pragma once
 
 #include <limits.h>
+#include <vector>
 
-/* Definition for a binary tree node */
+using namespace std;
+
+/* 二叉树节点结构体 */
 struct TreeNode {
     int val{};
     int height = 0;
@@ -20,45 +23,55 @@ struct TreeNode {
     }
 };
 
-/* Generate a binary tree with a vector */
-TreeNode *vecToTree(vector<int> list) {
-    if (list.empty())
+// 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, None, 6, 7, 8, 9, None, None, 12, None, None, 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 */
+TreeNode *vectorToTreeDFS(vector<int> &arr, int i) {
+    if (i < 0 || i >= arr.size() || arr[i] == INT_MAX) {
         return nullptr;
-
-    auto *root = new TreeNode(list[0]);
-    queue<TreeNode *> que;
-    que.emplace(root);
-    size_t n = list.size(), i = 0;
-    while (!que.empty()) {
-        auto node = que.front();
-        que.pop();
-        if (++i >= n)
-            break;
-        // INT_MAX represent null
-        if (list[i] != INT_MAX) {
-            node->left = new TreeNode(list[i]);
-            que.emplace(node->left);
-        }
-        if (++i >= n)
-            break;
-        if (list[i] != INT_MAX) {
-            node->right = new TreeNode(list[i]);
-            que.emplace(node->right);
-        }
     }
-
+    TreeNode *root = new TreeNode(arr[i]);
+    root->left = vectorToTreeDFS(arr, 2 * i + 1);
+    root->right = vectorToTreeDFS(arr, 2 * i + 2);
     return root;
 }
 
-/* Get a tree node with specific value in a binary tree */
-TreeNode *getTreeNode(TreeNode *root, int val) {
+/* 将列表反序列化为二叉树 */
+TreeNode *vectorToTree(vector<int> arr) {
+    return vectorToTreeDFS(arr, 0);
+}
+
+/* 将二叉树序列化为列表：递归 */
+void treeToVecorDFS(TreeNode *root, int i, vector<int> &res) {
     if (root == nullptr)
-        return nullptr;
-    if (root->val == val)
-        return root;
-    TreeNode *left = getTreeNode(root->left, val);
-    TreeNode *right = getTreeNode(root->right, val);
-    return left != nullptr ? left : right;
+        return;
+    while (i >= res.size()) {
+        res.push_back(INT_MAX);
+    }
+    res[i] = root->val;
+    treeToVecorDFS(root->left, 2 * i + 1, res);
+    treeToVecorDFS(root->right, 2 * i + 2, res);
+}
+
+/* 将二叉树序列化为列表 */
+vector<int> treeToVecor(TreeNode *root) {
+    vector<int> res;
+    treeToVecorDFS(root, 0, res);
+    return res;
 }
 
 /* Free the memory allocated to a tree */

codes/cpp/utils/vertex.hpp

@@ -7,6 +7,7 @@
 #pragma once
 
 #include <vector>
+
 using namespace std;
 
 /* 顶点类 */

codes/csharp/utils/TreeNode.cs

@@ -59,15 +59,4 @@ public class TreeNode {
         }
         return list;
     }
-
-    /* Get a tree node with specific value in a binary tree */
-    public static TreeNode? GetTreeNode(TreeNode? root, int val) {
-        if (root == null)
-            return null;
-        if (root.val == val)
-            return root;
-        TreeNode? left = GetTreeNode(root.left, val);
-        TreeNode? right = GetTreeNode(root.right, val);
-        return left ?? right;
-    }
 }

codes/java/chapter_tree/array_binary_tree.java

@@ -0,0 +1,136 @@
+/**
+ * File: array_binary_tree.java
+ * Created Time: 2023-07-19
+ * Author: Krahets (krahets@163.com)
+ */
+
+package chapter_tree;
+
+import utils.*;
+import java.util.*;
+
+/* 数组表示下的二叉树类 */
+class ArrayBinaryTree {
+    private List<Integer> tree;
+
+    /* 构造方法 */
+    public ArrayBinaryTree(List<Integer> arr) {
+        tree = new ArrayList<>(arr);
+    }
+
+    /* 节点数量 */
+    public int size() {
+        return tree.size();
+    }
+
+    /* 获取索引为 i 节点的值 */
+    public Integer val(int i) {
+        // 若索引越界，则返回 null ，代表空位
+        if (i < 0 || i >= size())
+            return null;
+        return tree.get(i);
+    }
+
+    /* 获取索引为 i 节点的左子节点的索引 */
+    public Integer left(int i) {
+        return 2 * i + 1;
+    }
+
+    /* 获取索引为 i 节点的右子节点的索引 */
+    public Integer right(int i) {
+        return 2 * i + 2;
+    }
+
+    /* 获取索引为 i 节点的父节点的索引 */
+    public Integer parent(int i) {
+        return (i - 1) / 2;
+    }
+
+    /* 层序遍历 */
+    public List<Integer> levelOrder() {
+        List<Integer> res = new ArrayList<>();
+        // 直接遍历数组
+        for (int i = 0; i < size(); i++) {
+            if (val(i) != null)
+                res.add(val(i));
+        }
+        return res;
+    }
+
+    /* 深度优先遍历 */
+    private void dfs(Integer i, String order, List<Integer> res) {
+        // 若为空位，则返回
+        if (val(i) == null)
+            return;
+        // 前序遍历
+        if (order == "pre")
+            res.add(val(i));
+        dfs(left(i), order, res);
+        // 中序遍历
+        if (order == "in")
+            res.add(val(i));
+        dfs(right(i), order, res);
+        // 后序遍历
+        if (order == "post")
+            res.add(val(i));
+    }
+
+    /* 前序遍历 */
+    public List<Integer> preOrder() {
+        List<Integer> res = new ArrayList<>();
+        dfs(0, "pre", res);
+        return res;
+    }
+
+    /* 中序遍历 */
+    public List<Integer> inOrder() {
+        List<Integer> res = new ArrayList<>();
+        dfs(0, "in", res);
+        return res;
+    }
+
+    /* 后序遍历 */
+    public List<Integer> postOrder() {
+        List<Integer> res = new ArrayList<>();
+        dfs(0, "post", res);
+        return res;
+    }
+}
+
+public class array_binary_tree {
+    public static void main(String[] args) {
+        // 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
+        List<Integer> arr = Arrays.asList(1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15);
+
+        TreeNode root = TreeNode.listToTree(arr);
+        System.out.println("\n初始化二叉树\n");
+        System.out.println("二叉树的数组表示：");
+        System.out.println(arr);
+        System.out.println("二叉树的链表表示：");
+        PrintUtil.printTree(root);
+
+        // 数组表示下的二叉树类
+        ArrayBinaryTree abt = new ArrayBinaryTree(arr);
+
+        // 访问节点
+        int i = 1;
+        Integer l = abt.left(i);
+        Integer r = abt.right(i);
+        Integer p = abt.parent(i);
+        System.out.println("\n当前节点的索引为 " + i + " ，值为 " + abt.val(i));
+        System.out.println("其左子节点的索引为 " + l + " ，值为 " + (l == null ? "null" : abt.val(l)));
+        System.out.println("其右子节点的索引为 " + r + " ，值为 " + (r == null ? "null" : abt.val(r)));
+        System.out.println("其父节点的索引为 " + p + " ，值为 " + (p == null ? "null" : abt.val(p)));
+
+        // 遍历树
+        List<Integer> res = abt.levelOrder();
+        System.out.println("\n层序遍历为：" + res);
+        res = abt.preOrder();
+        System.out.println("前序遍历为：" + res);
+        res = abt.inOrder();
+        System.out.println("中序遍历为：" + res);
+        res = abt.postOrder();
+        System.out.println("后序遍历为：" + res);
+    }
+}

codes/java/utils/TreeNode.java

@@ -8,61 +8,66 @@ package utils;
 
 import java.util.*;
 
-/* Definition for a binary tree node. */
+/* 二叉树节点类 */
 public class TreeNode {
     public int val; // 节点值
     public int height; // 节点高度
     public TreeNode left; // 左子节点引用
     public TreeNode right; // 右子节点引用
 
+    /* 构造方法 */
     public TreeNode(int x) {
         val = x;
     }
 
-    /* Generate a binary tree given an array */
-    public static TreeNode listToTree(List<Integer> list) {
-        int size = list.size();
-        if (size == 0)
-            return null;
+    // 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, None, 6, 7, 8, 9, None, None, 12, None, None, 15]
+    // 二叉树的链表表示：
+    //             /——— 15
+    //         /——— 7
+    //     /——— 3
+    //    |    \——— 6
+    //    |        \——— 12
+    // ——— 1
+    //     \——— 2
+    //        |    /——— 9
+    //         \——— 4
+    //             \——— 8
 
-        TreeNode root = new TreeNode(list.get(0));
-        Queue<TreeNode> queue = new LinkedList<>();
-        queue.add(root);
-        int i = 0;
-        while (!queue.isEmpty()) {
-            TreeNode node = queue.poll();
-            if (++i >= size)
-                break;
-            if (list.get(i) != null) {
-                node.left = new TreeNode(list.get(i));
-                queue.add(node.left);
-            }
-            if (++i >= size)
-                break;
-            if (list.get(i) != null) {
-                node.right = new TreeNode(list.get(i));
-                queue.add(node.right);
-            }
+    /* 将列表反序列化为二叉树：递归 */
+    private static TreeNode listToTreeDFS(List<Integer> arr, int i) {
+        if (i < 0 || i >= arr.size() || arr.get(i) == null) {
+            return null;
         }
+        TreeNode root = new TreeNode(arr.get(i));
+        root.left = listToTreeDFS(arr, 2 * i + 1);
+        root.right = listToTreeDFS(arr, 2 * i + 2);
         return root;
     }
 
-    /* Serialize a binary tree to a list */
-    public static List<Integer> treeToList(TreeNode root) {
-        List<Integer> list = new ArrayList<>();
+    /* 将列表反序列化为二叉树 */
+    public static TreeNode listToTree(List<Integer> arr) {
+        return listToTreeDFS(arr, 0);
+    }
+
+    /* 将二叉树序列化为列表：递归 */
+    private static void treeToListDFS(TreeNode root, int i, List<Integer> res) {
         if (root == null)
-            return list;
-        Queue<TreeNode> queue = new LinkedList<TreeNode>() {{ add(root); }};
-        while (!queue.isEmpty()) {
-            TreeNode node = queue.poll();
-            if (node != null) {
-                list.add(node.val);
-                queue.add(node.left);
-                queue.add(node.right);
-            } else {
-                list.add(null);
-            }
+            return;
+        while (i >= res.size()) {
+            res.add(null);
         }
-        return list;
+        res.set(i, root.val);
+        treeToListDFS(root.left, 2 * i + 1, res);
+        treeToListDFS(root.right, 2 * i + 2, res);
+    }
+
+    /* 将二叉树序列化为列表 */
+    public static List<Integer> treeToList(TreeNode root) {
+        List<Integer> res = new ArrayList<>();
+        treeToListDFS(root, 0, res);
+        return res;
     }
 }

codes/python/chapter_tree/array_binary_tree.py

@@ -0,0 +1,118 @@
+"""
+File: array_binary_tree.py
+Created Time: 2023-07-19
+Author: Krahets (krahets@163.com)
+"""
+
+import sys, os.path as osp
+
+sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
+from modules import *
+
+
+class ArrayBinaryTree:
+    """数组表示下的二叉树类"""
+
+    def __init__(self, arr: list[int | None]):
+        """构造方法"""
+        self.__tree = list(arr)
+
+    def size(self):
+        """节点数量"""
+        return len(self.__tree)
+
+    def val(self, i: int) -> int:
+        """获取索引为 i 节点的值"""
+        # 若索引越界，则返回 None ，代表空位
+        if i < 0 or i >= self.size():
+            return None
+        return self.__tree[i]
+
+    def left(self, i: int) -> int | None:
+        """获取索引为 i 节点的左子节点的索引"""
+        return 2 * i + 1
+
+    def right(self, i: int) -> int | None:
+        """获取索引为 i 节点的右子节点的索引"""
+        return 2 * i + 2
+
+    def parent(self, i: int) -> int | None:
+        """获取索引为 i 节点的父节点的索引"""
+        return (i - 1) // 2
+
+    def level_order(self) -> list[int]:
+        """层序遍历"""
+        self.res = []
+        # 直接遍历数组
+        for i in range(self.size()):
+            if self.val(i) is not None:
+                self.res.append(self.val(i))
+        return self.res
+
+    def __dfs(self, i: int, order: str):
+        """深度优先遍历"""
+        if self.val(i) is None:
+            return
+        # 前序遍历
+        if order == "pre":
+            self.res.append(self.val(i))
+        self.__dfs(self.left(i), order)
+        # 中序遍历
+        if order == "in":
+            self.res.append(self.val(i))
+        self.__dfs(self.right(i), order)
+        # 后序遍历
+        if order == "post":
+            self.res.append(self.val(i))
+
+    def pre_order(self) -> list[int]:
+        """前序遍历"""
+        self.res = []
+        self.__dfs(0, order="pre")
+        return self.res
+
+    def in_order(self) -> list[int]:
+        """中序遍历"""
+        self.res = []
+        self.__dfs(0, order="in")
+        return self.res
+
+    def post_order(self) -> list[int]:
+        """后序遍历"""
+        self.res = []
+        self.__dfs(0, order="post")
+        return self.res
+
+
+"""Driver Code"""
+if __name__ == "__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
+    arr = [1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, None, None, 15]
+    root = list_to_tree(arr)
+    print("\n初始化二叉树\n")
+    print(f"二叉树的数组表示：")
+    print(arr)
+    print(f"二叉树的链表表示：")
+    print_tree(root)
+
+    # 数组表示下的二叉树类
+    abt = ArrayBinaryTree(arr)
+
+    # 访问节点
+    i = 1
+    l, r, p = abt.left(i), abt.right(i), abt.parent(i)
+    print(f"\n当前节点的索引为 {i} ，值为 {abt.val(i)}")
+    print(f"其左子节点的索引为 {l} ，值为 {abt.val(l)}")
+    print(f"其右子节点的索引为 {r} ，值为 {abt.val(r)}")
+    print(f"其父节点的索引为 {p} ，值为 {abt.val(p)}")
+
+    # 遍历树
+    res = abt.level_order()
+    print("\n层序遍历为：", res)
+    res = abt.pre_order()
+    print("前序遍历为：", res)
+    res = abt.in_order()
+    print("中序遍历为：", res)
+    res = abt.post_order()
+    print("后序遍历为：", res)

codes/python/modules/__init__.py

@@ -3,13 +3,13 @@
 from __future__ import annotations
 
 # Import common libs here to simplify the codes by `from module import *`
-from .linked_list import (
+from .list_node import (
     ListNode,
     list_to_linked_list,
     linked_list_to_list,
     get_list_node,
 )
-from .binary_tree import TreeNode, list_to_tree, tree_to_list, get_tree_node
+from .tree_node import TreeNode, list_to_tree, tree_to_list, get_tree_node
 from .vertex import Vertex, vals_to_vets, vets_to_vals
 from .print_util import (
     print_matrix,

codes/python/modules/binary_tree.py

@@ -1,72 +0,0 @@
-"""
-File: binary_tree.py
-Created Time: 2021-12-11
-Author: Krahets (krahets@163.com)
-"""
-
-from collections import deque
-
-
-class TreeNode:
-    """Definition for a binary tree node"""
-
-    def __init__(self, val: int = 0):
-        self.val: int = val  # 节点值
-        self.height: int = 0  # 节点高度
-        self.left: TreeNode | None = None  # 左子节点引用
-        self.right: TreeNode | None = None  # 右子节点引用
-
-
-def list_to_tree(arr: list[int]) -> TreeNode | None:
-    """Generate a binary tree with a list"""
-    if not arr:
-        return None
-
-    i = 0
-    root = TreeNode(arr[0])
-    queue: deque[TreeNode] = deque([root])
-    while queue:
-        node: TreeNode = queue.popleft()
-        i += 1
-        if i >= len(arr):
-            break
-        if arr[i] != None:
-            node.left = TreeNode(arr[i])
-            queue.append(node.left)
-        i += 1
-        if i >= len(arr):
-            break
-        if arr[i] != None:
-            node.right = TreeNode(arr[i])
-            queue.append(node.right)
-
-    return root
-
-
-def tree_to_list(root: TreeNode | None) -> list[int]:
-    """Serialize a tree into an array"""
-    if not root:
-        return []
-    queue: deque[TreeNode] = deque()
-    queue.append(root)
-    res: list[int] = []
-    while queue:
-        node: TreeNode | None = queue.popleft()
-        if node:
-            res.append(node.val)
-            queue.append(node.left)
-            queue.append(node.right)
-        else:
-            res.append(None)
-    return res
-
-
-def get_tree_node(root: TreeNode | None, val: int) -> TreeNode | None:
-    """Get a tree node with specific value in a binary tree"""
-    if not root:
-        return
-    if root.val == val:
-        return root
-    left: TreeNode | None = get_tree_node(root.left, val)
-    right: TreeNode | None = get_tree_node(root.right, val)
-    return left if left else right

codes/python/modules/list_node.py

@@ -1,5 +1,5 @@
 """
-File: linked_list.py
+File: list_node.py
 Created Time: 2021-12-11
 Author: Krahets (krahets@163.com)
 """

codes/python/modules/print_util.py

@@ -4,8 +4,8 @@ Created Time: 2021-12-11
 Author: Krahets (krahets@163.com), msk397 (machangxinq@gmail.com)
 """
 
-from .binary_tree import TreeNode, list_to_tree
-from .linked_list import ListNode, linked_list_to_list
+from .tree_node import TreeNode, list_to_tree
+from .list_node import ListNode, linked_list_to_list
 
 
 def print_matrix(mat: list[list[int]]) -> None:

codes/python/modules/tree_node.py

@@ -0,0 +1,80 @@
+"""
+File: tree_node.py
+Created Time: 2021-12-11
+Author: Krahets (krahets@163.com)
+"""
+
+from collections import deque
+
+
+class TreeNode:
+    """二叉树节点类"""
+
+    def __init__(self, val: int = 0):
+        self.val: int = val  # 节点值
+        self.height: int = 0  # 节点高度
+        self.left: TreeNode | None = None  # 左子节点引用
+        self.right: TreeNode | None = None  # 右子节点引用
+
+    # 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, None, 6, 7, 8, 9, None, None, 12, None, None, 15]
+    # 二叉树的链表表示：
+    #             /——— 15
+    #         /——— 7
+    #     /——— 3
+    #    |    \——— 6
+    #    |        \——— 12
+    # ——— 1
+    #     \——— 2
+    #        |    /——— 9
+    #         \——— 4
+    #             \——— 8
+
+
+def list_to_tree_dfs(arr: list[int], i: int) -> TreeNode | None:
+    """将列表反序列化为二叉树：递归"""
+    # 如果索引超出数组长度，或者对应的元素为 None，返回 None
+    if i < 0 or i >= len(arr) or arr[i] is None:
+        return None
+    # 构建当前节点
+    root = TreeNode(arr[i])
+    # 递归构建左右子树
+    root.left = list_to_tree_dfs(arr, 2 * i + 1)
+    root.right = list_to_tree_dfs(arr, 2 * i + 2)
+    return root
+
+
+def list_to_tree(arr: list[int]) -> TreeNode | None:
+    """将列表反序列化为二叉树"""
+    return list_to_tree_dfs(arr, 0)
+
+
+def tree_to_list_dfs(root: TreeNode, i: int, res: list[int]) -> list[int]:
+    """将二叉树序列化为列表：递归"""
+    if root is None:
+        return
+    if i >= len(res):
+        res += [None] * (i - len(res) + 1)
+    res[i] = root.val
+    tree_to_list_dfs(root.left, 2 * i + 1, res)
+    tree_to_list_dfs(root.right, 2 * i + 2, res)
+
+
+def tree_to_list(root: TreeNode | None) -> list[int]:
+    """将二叉树序列化为列表"""
+    res = []
+    tree_to_list_dfs(root, 0, res)
+    return res
+
+
+def get_tree_node(root: TreeNode | None, val: int) -> TreeNode | None:
+    """Get a tree node with specific value in a binary tree"""
+    if not root:
+        return
+    if root.val == val:
+        return root
+    left: TreeNode | None = get_tree_node(root.left, val)
+    right: TreeNode | None = get_tree_node(root.right, val)
+    return left if left else right