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https://github.com/krahets/hello-algo.git
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Add implementation of array binary tree.
Rewrite the tree serialization and deserialization methods. Add applications of array and linked list.
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krahets
136
codes/java/chapter_tree/array_binary_tree.java
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136
codes/java/chapter_tree/array_binary_tree.java
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/**
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* File: array_binary_tree.java
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* Created Time: 2023-07-19
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* Author: Krahets (krahets@163.com)
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*/
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package chapter_tree;
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import utils.*;
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import java.util.*;
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/* 数组表示下的二叉树类 */
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class ArrayBinaryTree {
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private List<Integer> tree;
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/* 构造方法 */
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public ArrayBinaryTree(List<Integer> arr) {
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tree = new ArrayList<>(arr);
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}
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/* 节点数量 */
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public int size() {
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return tree.size();
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}
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/* 获取索引为 i 节点的值 */
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public Integer val(int i) {
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// 若索引越界，则返回 null ，代表空位
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if (i < 0 || i >= size())
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return null;
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return tree.get(i);
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}
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/* 获取索引为 i 节点的左子节点的索引 */
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public Integer left(int i) {
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return 2 * i + 1;
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}
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/* 获取索引为 i 节点的右子节点的索引 */
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public Integer right(int i) {
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return 2 * i + 2;
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}
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/* 获取索引为 i 节点的父节点的索引 */
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public Integer parent(int i) {
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return (i - 1) / 2;
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}
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/* 层序遍历 */
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public List<Integer> levelOrder() {
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List<Integer> res = new ArrayList<>();
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// 直接遍历数组
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for (int i = 0; i < size(); i++) {
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if (val(i) != null)
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res.add(val(i));
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}
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return res;
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}
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/* 深度优先遍历 */
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private void dfs(Integer i, String order, List<Integer> res) {
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// 若为空位，则返回
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if (val(i) == null)
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return;
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// 前序遍历
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if (order == "pre")
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res.add(val(i));
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dfs(left(i), order, res);
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// 中序遍历
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if (order == "in")
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res.add(val(i));
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dfs(right(i), order, res);
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// 后序遍历
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if (order == "post")
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res.add(val(i));
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}
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/* 前序遍历 */
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public List<Integer> preOrder() {
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List<Integer> res = new ArrayList<>();
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dfs(0, "pre", res);
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return res;
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}
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/* 中序遍历 */
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public List<Integer> inOrder() {
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List<Integer> res = new ArrayList<>();
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dfs(0, "in", res);
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return res;
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}
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/* 后序遍历 */
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public List<Integer> postOrder() {
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List<Integer> res = new ArrayList<>();
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dfs(0, "post", res);
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return res;
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}
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}
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public class array_binary_tree {
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public static void main(String[] args) {
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// 初始化二叉树
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// 这里借助了一个从数组直接生成二叉树的函数
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List<Integer> arr = Arrays.asList(1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15);
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TreeNode root = TreeNode.listToTree(arr);
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System.out.println("\n初始化二叉树\n");
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System.out.println("二叉树的数组表示：");
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System.out.println(arr);
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System.out.println("二叉树的链表表示：");
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PrintUtil.printTree(root);
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// 数组表示下的二叉树类
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ArrayBinaryTree abt = new ArrayBinaryTree(arr);
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// 访问节点
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int i = 1;
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Integer l = abt.left(i);
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Integer r = abt.right(i);
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Integer p = abt.parent(i);
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System.out.println("\n当前节点的索引为 " + i + " ，值为 " + abt.val(i));
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System.out.println("其左子节点的索引为 " + l + " ，值为 " + (l == null ? "null" : abt.val(l)));
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System.out.println("其右子节点的索引为 " + r + " ，值为 " + (r == null ? "null" : abt.val(r)));
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System.out.println("其父节点的索引为 " + p + " ，值为 " + (p == null ? "null" : abt.val(p)));
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// 遍历树
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List<Integer> res = abt.levelOrder();
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System.out.println("\n层序遍历为：" + res);
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res = abt.preOrder();
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System.out.println("前序遍历为：" + res);
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res = abt.inOrder();
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System.out.println("中序遍历为：" + res);
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res = abt.postOrder();
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System.out.println("后序遍历为：" + res);
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}
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}
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@ -8,61 +8,66 @@ package utils;
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import java.util.*;
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/* Definition for a binary tree node. */
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/* 二叉树节点类 */
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public class TreeNode {
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public int val; // 节点值
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public int height; // 节点高度
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public TreeNode left; // 左子节点引用
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public TreeNode right; // 右子节点引用
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/* 构造方法 */
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public TreeNode(int x) {
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val = x;
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}
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/* Generate a binary tree given an array */
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public static TreeNode listToTree(List<Integer> list) {
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int size = list.size();
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if (size == 0)
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return null;
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// 序列化编码规则请参考：
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// https://www.hello-algo.com/chapter_tree/array_representation_of_tree/
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// 二叉树的数组表示：
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// [1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, None, None, 15]
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// 二叉树的链表表示：
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// /——— 15
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// /——— 7
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// /——— 3
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// | \——— 6
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// | \——— 12
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// ——— 1
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// \——— 2
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// | /——— 9
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// \——— 4
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// \——— 8
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TreeNode root = new TreeNode(list.get(0));
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Queue<TreeNode> queue = new LinkedList<>();
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queue.add(root);
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int i = 0;
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while (!queue.isEmpty()) {
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TreeNode node = queue.poll();
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if (++i >= size)
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break;
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if (list.get(i) != null) {
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node.left = new TreeNode(list.get(i));
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queue.add(node.left);
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}
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if (++i >= size)
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break;
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if (list.get(i) != null) {
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node.right = new TreeNode(list.get(i));
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queue.add(node.right);
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}
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/* 将列表反序列化为二叉树：递归 */
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private static TreeNode listToTreeDFS(List<Integer> arr, int i) {
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if (i < 0 || i >= arr.size() || arr.get(i) == null) {
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return null;
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}
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TreeNode root = new TreeNode(arr.get(i));
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root.left = listToTreeDFS(arr, 2 * i + 1);
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root.right = listToTreeDFS(arr, 2 * i + 2);
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return root;
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}
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/* Serialize a binary tree to a list */
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public static List<Integer> treeToList(TreeNode root) {
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List<Integer> list = new ArrayList<>();
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/* 将列表反序列化为二叉树 */
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public static TreeNode listToTree(List<Integer> arr) {
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return listToTreeDFS(arr, 0);
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}
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/* 将二叉树序列化为列表：递归 */
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private static void treeToListDFS(TreeNode root, int i, List<Integer> res) {
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if (root == null)
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return list;
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Queue<TreeNode> queue = new LinkedList<TreeNode>() {{ add(root); }};
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while (!queue.isEmpty()) {
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TreeNode node = queue.poll();
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if (node != null) {
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list.add(node.val);
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queue.add(node.left);
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queue.add(node.right);
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} else {
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list.add(null);
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}
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return;
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while (i >= res.size()) {
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res.add(null);
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}
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return list;
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res.set(i, root.val);
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treeToListDFS(root.left, 2 * i + 1, res);
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treeToListDFS(root.right, 2 * i + 2, res);
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}
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/* 将二叉树序列化为列表 */
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public static List<Integer> treeToList(TreeNode root) {
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List<Integer> res = new ArrayList<>();
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treeToListDFS(root, 0, res);
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return res;
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}
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}
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