1、二叉树：

package com.datastructure.tree;
//一个常用的第三方库是Apache Commons Collections，它提供了一个名为BinaryTree的类，用于表示二叉树。
//可以使用org.apache.commons.collections4.BinaryTree类创建二叉树和进行操作。
//可以在Maven中添加以下依赖项：
//<dependency>
//<groupId>org.apache.commons</groupId>
//<artifactId>commons-collections4</artifactId>
//<version>4.4</version>
//</dependency>
public class BinaryTree {private Node root;private class Node {private int data;private Node left;private Node right;public Node(int data) {this.data = data;this.left = null;this.right = null;}}// 插入节点public void insert(int data) {root = insert(root, data);}private Node insert(Node node, int data) {if (node == null) {node = new Node(data);} else {if (data <= node.data) {node.left = insert(node.left, data);} else {node.right = insert(node.right, data);}}return node;}// 前序遍历public void preOrderTraversal() {preOrderTraversal(root);}private void preOrderTraversal(Node node) {if (node != null) {System.out.println(node.data);preOrderTraversal(node.left);preOrderTraversal(node.right);}}// 中序遍历public void inOrderTraversal() {inOrderTraversal(root);}private void inOrderTraversal(Node node) {if (node != null) {inOrderTraversal(node.left);System.out.println(node.data);inOrderTraversal(node.right);}}// 后序遍历public void postOrderTraversal() {postOrderTraversal(root);}private void postOrderTraversal(Node node) {if (node != null) {postOrderTraversal(node.left);postOrderTraversal(node.right);System.out.println(node.data);}}
}

package com.datastructure.tree;public class BinaryTreeDemo {public static void main(String[] args) {BinaryTree tree = new BinaryTree();tree.insert(5);tree.insert(3);tree.insert(7);tree.insert(2);tree.insert(4);tree.insert(6);tree.insert(8);System.out.println("前序遍历:");tree.preOrderTraversal();System.out.println("中序遍历:");tree.inOrderTraversal();System.out.println("后序遍历:");tree.postOrderTraversal();}
}

2、平衡二叉树：

package com.datastructure.tree;
//平衡树
//AVLTree是一个泛型类，可以存储任意实现了Comparable接口的类型。
//在AVLTree类中，使用Node类来表示树节点，并在节点中保存了节点值、左子节点、右子节点和节点高度。
//在插入操作中，使用递归的方式在树中查找合适的位置插入新节点，并在返回时重新平衡树。
//在插入节点之后，检查当前节点的平衡因子，如果超出范围，则通过旋转操作来恢复平衡。
//除了插入操作之外，还可以实现其他操作，例如删除节点、查找节点、遍历等。
public class AVLTreeDemo<T extends Comparable<T>> {private class Node {T value;Node left;Node right;int height;Node(T value) {this.value = value;this.height = 1;}}private Node root;private int height(Node node) {if (node == null) {return 0;}return node.height;}private int balanceFactor(Node node) {if (node == null) {return 0;}return height(node.left) - height(node.right);}private Node rotateLeft(Node x) {Node y = x.right;Node T2 = y.left;y.left = x;x.right = T2;x.height = Math.max(height(x.left), height(x.right)) + 1;y.height = Math.max(height(y.left), height(y.right)) + 1;return y;}private Node rotateRight(Node y) {Node x = y.left;Node T2 = x.right;x.right = y;y.left = T2;y.height = Math.max(height(y.left), height(y.right)) + 1;x.height = Math.max(height(x.left), height(x.right)) + 1;return x;}public void insert(T value) {root = insert(root, value);}private Node insert(Node node, T value) {if (node == null) {return new Node(value);}if (value.compareTo(node.value) < 0) {node.left = insert(node.left, value);} else if (value.compareTo(node.value) > 0) {node.right = insert(node.right, value);} else {return node; // 不允许插入重复的值}node.height = Math.max(height(node.left), height(node.right)) + 1;int balance = balanceFactor(node);if (balance > 1 && value.compareTo(node.left.value) < 0) {return rotateRight(node);}if (balance < -1 && value.compareTo(node.right.value) > 0) {return rotateLeft(node);}if (balance > 1 && value.compareTo(node.left.value) > 0) {node.left = rotateLeft(node.left);return rotateRight(node);}if (balance < -1 && value.compareTo(node.right.value) < 0) {node.right = rotateRight(node.right);return rotateLeft(node);}return node;}public void delete(T value) {root = delete(root, value);}private Node delete(Node node, T value) {if (node == null) {return null;}if (value.compareTo(node.value) < 0) {node.left = delete(node.left, value);} else if (value.compareTo(node.value) > 0) {node.right = delete(node.right, value);} else {if (node.left == null || node.right == null) {Node temp = null;if (node.left != null) {temp = node.left;} else {temp = node.right;}if (temp == null) {temp = node;node = null;} else {node = temp;}} else {Node temp = minValueNode(node.right);node.value = temp.value;node.right = delete(node.right, temp.value);}}if (node == null) {return node;}node.height = Math.max(height(node.left), height(node.right)) + 1;int balance = balanceFactor(node);if (balance > 1 && balanceFactor(node.left) >= 0) {return rotateRight(node);}if (balance > 1 && balanceFactor(node.left) < 0) {node.left = rotateLeft(node.left);return rotateRight(node);}if (balance < -1 && balanceFactor(node.right) <= 0) {return rotateLeft(node);}if (balance < -1 && balanceFactor(node.right) > 0) {node.right = rotateRight(node.right);return rotateLeft(node);}return node;}private Node minValueNode(Node node) {Node current = node;while (current.left != null) {current = current.left;}return current;}// 其他操作方法...// 中序遍历public void inorderTraversal() {inorderTraversal(root);}private void inorderTraversal(Node node) {if (node != null) {inorderTraversal(node.left);System.out.print(node.value + " ");inorderTraversal(node.right);}}
}

package com.datastructure.tree;
//可以在项目中添加Apache Commons Collections库的依赖。
//可以在Maven项目中的pom.xml文件中添加以下代码片段：
//<dependency>
//<groupId>org.apache.commons</groupId>
//<artifactId>commons-collections4</artifactId>
//<version>4.4</version>
//</dependency>
//import org.apache.commons.collections4.map.AVLTree;
public class AVLTreeDemoMain {public static void main(String[] args) {AVLTreeDemo<Integer> tree = new AVLTreeDemo<>();tree.insert(5);tree.insert(10);tree.insert(3);tree.insert(7);tree.insert(8);tree.insert(1);System.out.println("Inorder Traversal:");tree.inorderTraversal();tree.delete(5);System.out.println("nAfter deleting 5:");tree.inorderTraversal();}
}