From a5e5aea86b6302f558f26a6202dd2914f461d57c Mon Sep 17 00:00:00 2001 From: Yudong Jin Date: Sat, 10 Dec 2022 20:46:47 +0800 Subject: [PATCH] Update avl_tree.java --- codes/java/chapter_tree/avl_tree.java | 218 ++++++++++++++++++++++++++ codes/java/include/TreeNode.java | 7 +- 2 files changed, 222 insertions(+), 3 deletions(-) create mode 100644 codes/java/chapter_tree/avl_tree.java diff --git a/codes/java/chapter_tree/avl_tree.java b/codes/java/chapter_tree/avl_tree.java new file mode 100644 index 0000000..5666b5d --- /dev/null +++ b/codes/java/chapter_tree/avl_tree.java @@ -0,0 +1,218 @@ +/* + * File: avl_tree.java + * Created Time: 2022-12-10 + * Author: Krahets (krahets@163.com) + */ + + package chapter_tree; + + import include.*; + + // Tree class + class AVLTree { + TreeNode root; // 根节点 + + /* 获取结点高度 */ + public int height(TreeNode node) { + // 空结点高度为 -1 ，叶结点高度为 0 + return node == null ? -1 : node.height; + } + + /* 更新结点高度 */ + private void updateHeight(TreeNode node) { + node.height = Math.max(height(node.left), height(node.right)) + 1; + } + + /* 获取平衡因子 */ + public int balanceFactor(TreeNode node) { + if (node == null) + return 0; + return height(node.left) - height(node.right); + } + + /* 右旋操作 */ + private TreeNode rightRotate(TreeNode node) { + TreeNode child = node.left; + TreeNode grandChild = child.right; + child.right = node; + node.left = grandChild; + updateHeight(node); + updateHeight(child); + return child; + } + + /* 左旋操作 */ + private TreeNode leftRotate(TreeNode node) { + TreeNode child = node.right; + TreeNode grandChild = child.left; + child.left = node; + node.right = grandChild; + updateHeight(node); + updateHeight(child); + return child; + } + + /* 执行旋转操作，使该子树重新恢复平衡 */ + private TreeNode rotate(TreeNode node) { + int balanceFactor = balanceFactor(node); + // 根据失衡情况分为四种操作：右旋、左旋、先左后右、先右后左 + if (balanceFactor > 1) { + if (balanceFactor(node.left) >= 0) { + // 右旋 + return rightRotate(node); + } else { + // 先左旋后右旋 + node.left = leftRotate(node.left); + return rightRotate(node); + } + } + if (balanceFactor < -1) { + if (balanceFactor(node.right) <= 0) { + // 左旋 + return leftRotate(node); + } else { + // 先右旋后左旋 + node.right = rightRotate(node.right); + return leftRotate(node); + } + } + return node; + } + + /* 插入结点 */ + public TreeNode insert(int val) { + root = insertHelper(root, val); + return root; + } + + /* 递归插入结点 */ + private TreeNode insertHelper(TreeNode node, int val) { + // 1. 查找插入位置，并插入结点 + if (node == null) + return new TreeNode(val); + if (val < node.val) + node.left = insertHelper(node.left, val); + else if (val > node.val) + node.right = insertHelper(node.right, val); + else + return node; // 重复结点则直接返回 + // 2. 更新结点高度 + updateHeight(node); + // 3. 执行旋转操作，使该子树重新恢复平衡 + node = rotate(node); + // 返回该子树的根节点 + return node; + } + + /* 删除结点 */ + public TreeNode remove(int val) { + root = removeHelper(root, val); + return root; + } + + /* 递归删除结点 */ + private TreeNode removeHelper(TreeNode node, int val) { + // 1. 查找结点，并删除之 + if (node == null) + return null; + if (val < node.val) + node.left = removeHelper(node.left, val); + else if (val > node.val) + node.right = removeHelper(node.right, val); + else { + if (node.left == null || node.right == null) { + TreeNode child = node.left != null ? node.left : node.right; + // 子结点数量 = 0 ，直接删除 node 并返回 + if (child == null) + return null; + // 子结点数量 = 1 ，直接删除 node + else + node = child; + } else { + // 子结点数量 = 2 ，则将中序遍历的下个结点删除，并用该结点替换当前结点 + TreeNode temp = minNode(node.right); + node.right = removeHelper(node.right, temp.val); + node.val = temp.val; + } + } + // 2. 更新结点高度 + updateHeight(node); + // 3. 执行旋转操作，使该子树重新恢复平衡 + node = rotate(node); + // 返回该子树的根节点 + return node; + } + + /* 获取最小结点 */ + private TreeNode minNode(TreeNode node) { + if (node == null) return node; + // 循环访问左子结点，直到叶结点时为最小结点，跳出 + while (node.left != null) { + node = node.left; + } + return node; + } + + /* 查找结点 */ + public TreeNode search(int val) { + TreeNode cur = root; + // 循环查找，越过叶结点后跳出 + while (cur != null) { + // 目标结点在 root 的右子树中 + if (cur.val < val) cur = cur.right; + // 目标结点在 root 的左子树中 + else if (cur.val > val) cur = cur.left; + // 找到目标结点，跳出循环 + else break; + } + // 返回目标结点 + return cur; + } + } + + + public class avl_tree { + static void testInsert(AVLTree tree, int val) { + tree.insert(val); + System.out.println("\n插入结点 " + val + " 后，AVL 树为"); + PrintUtil.printTree(tree.root); + } + + static void testRemove(AVLTree tree, int val) { + tree.remove(val); + System.out.println("\n删除结点 " + val + " 后，AVL 树为"); + PrintUtil.printTree(tree.root); + } + + public static void main(String[] args) { + /* 初始化空 AVL 树 */ + AVLTree avlTree = new AVLTree(); + + /* 插入结点 */ + // 请关注插入结点后，AVL 树是如何保持平衡的 + testInsert(avlTree, 1); + testInsert(avlTree, 2); + testInsert(avlTree, 3); + testInsert(avlTree, 4); + testInsert(avlTree, 5); + testInsert(avlTree, 8); + testInsert(avlTree, 7); + testInsert(avlTree, 9); + testInsert(avlTree, 10); + testInsert(avlTree, 6); + + /* 插入重复结点 */ + testInsert(avlTree, 7); + + /* 删除结点 */ + // 请关注删除结点后，AVL 树是如何保持平衡的 + testRemove(avlTree, 8); // 删除度为 0 的结点 + testRemove(avlTree, 5); // 删除度为 1 的结点 + testRemove(avlTree, 4); // 删除度为 2 的结点 + + /* 查询结点 */ + TreeNode node = avlTree.search(7); + System.out.println("\n查找到的结点对象为 " + node + "，结点值 = " + node.val); + } + } + \ No newline at end of file diff --git a/codes/java/include/TreeNode.java b/codes/java/include/TreeNode.java index 6541064..98b9f82 100755 --- a/codes/java/include/TreeNode.java +++ b/codes/java/include/TreeNode.java @@ -12,9 +12,10 @@ import java.util.*; * Definition for a binary tree node. */ public class TreeNode { - public int val; - public TreeNode left; - public TreeNode right; + public int val; // 结点值 + public int height; // 结点高度 + public TreeNode left; // 左子结点引用 + public TreeNode right; // 右子结点引用 public TreeNode(int x) { val = x;