0 课程地址
https://coding.imooc.com/lesson/207.html#mid=14350
1 重点关注
1.1 破坏二分搜索树的四种情况
1.2 左左情况解析
1.3 左左情况解决：右旋转（图中应该是右旋转）
// 对节点y进行向右旋转操作，返回旋转后新的根节点x // y x // / \ / \ // x T4 向右旋转 (y) z y // / \ - - - - - - - -> / \ / \ // z T3 T1 T2 T3 T4 // / \ // T1 T2
1.4 右右情况解决：左旋转
// 对节点y进行向左旋转操作，返回旋转后新的根节点x // y x // / \ / \ // T1 x 向左旋转 (y) y z // / \ - - - - - - - -> / \ / \ // T2 z T1 T2 T3 T4 // / \ // T3 T4
2 课程内容
3 Coding
3.1 coding
案例：傲慢与偏见 统计单词
- 关键代码
//3 递归，添加元素 public Node add(K key,V value,Node root){ //3.1 终止条件 //3.1.1 要插入的元素和二叉树原有节点相同,这个不用判断，因为已经调了containsKey方法判断了 if(root==null){ size++; return new Node(key,value); } //3.1.2 最终插入左孩子 if(key.compareTo(root.key)<0 ){ root.left = add(key,value,root.left); }else if(key.compareTo(root.key)>0){ root.right = add(key,value,root.right); }else{ root.value = value; } root.height = 1+Math.max(getHeight(root.left),getHeight(root.right)); int balanceFactor = getBalanceFactor(root); if(Math.abs(balanceFactor)>1){ System.out.println("unbalanced:"+balanceFactor); } //左左情况 if(balanceFactor>1&&getBalanceFactor(root.left)>=0){ return rightRotate(root); }else if(balanceFactor<-1&&getBalanceFactor(root.left)<=0){ return leftRotate(root); } return root; } // 对节点y进行向右旋转操作，返回旋转后新的根节点x // y x // / \ / \ // x T4 向右旋转 (y) z y // / \ - - - - - - - -> / \ / \ // z T3 T1 T2 T3 T4 // / \ // T1 T2 /** * 右旋转 * 1 旋转 * 2 变更高度 * @author weidoudou * @date 2023/4/14 7:27 * @param y 请添加参数描述 * @return com.company.AVLTree<K,V>.Node **/ private Node rightRotate(Node y){ //1 右旋转 Node x = y.left; Node T3 = x.right; x.right = y; y.left = T3; //2 变更高度 y.height = Math.max(getHeight(y.left),getHeight(y.right))+1; x.height = Math.max(getHeight(x.left),getHeight(x.left))+1; return x; } // 对节点y进行向左旋转操作，返回旋转后新的根节点x // y x // / \ / \ // T1 x 向左旋转 (y) y z // / \ - - - - - - - -> / \ / \ // T2 z T1 T2 T3 T4 // / \ // T3 T4 private Node leftRotate(Node y) { Node x = y.right; Node T2 = x.left; // 向左旋转过程 x.left = y; y.right = T2; // 更新height y.height = Math.max(getHeight(y.left), getHeight(y.right)) + 1; x.height = Math.max(getHeight(x.left), getHeight(x.right)) + 1; return x; }
- 主类：
package com.company; import java.util.ArrayList; import java.util.List; public class AVLTree<K extends Comparable<K>,V> { //1 定义Node class Node{ private K key; private V value; private Node left,right; private int height; private int balanceFactor; public Node(K key, V value){ this.key = key; this.value = value; this.left = null; this.right = null; this.height = 1; } @Override public String toString() { final StringBuffer sb = new StringBuffer("Node{"); sb.append("key=").append(key); sb.append(", value=").append(value); sb.append('}'); return sb.toString(); } } //2 定义属性 private int size; private Node root; /** * getHeight * @author weidoudou * @date 2023/4/1 11:34 * @param node 请添加参数描述 * @return int **/ private int getHeight(Node node){ if(null==node){ return 0; } return node.height; } /** * getBalanceFactor * @author weidoudou * @date 2023/4/1 11:36 * @param node 请添加参数描述 * @return int **/ private int getBalanceFactor(Node node){ if(null==node){ return 0; } return getHeight(node.left) - getHeight(node.right); } /** * 无参构造函数 * @author weidoudou * @date 2023/1/1 11:09 * @return null **/ public AVLTree(){ this.size = 0; this.root = null; } public boolean isEmpty() { return size==0?true:false; } public int getSize() { return size; } //3 定义包含函数 private Node containsKey(K key,Node node){ //结束条件 if(null==node){ return null; } //循环条件 if(key.compareTo(node.key)<0){ return containsKey(key,node.left); }else if(key.compareTo(node.key)>0){ return containsKey(key, node.right); }else{//key.compareTo(node.key)=0 其实这个也是结束条件 return node; } } public boolean contains(K key) { return containsKey(key,root)==null?false:true; } public V get(K key) { Node node = containsKey(key,root); if(null!=node){ return node.value; } return null; } //3 递归，添加元素 public Node add(K key,V value,Node root){ //3.1 终止条件 //3.1.1 要插入的元素和二叉树原有节点相同,这个不用判断，因为已经调了containsKey方法判断了 if(root==null){ size++; return new Node(key,value); } //3.1.2 最终插入左孩子 if(key.compareTo(root.key)<0 ){ root.left = add(key,value,root.left); }else if(key.compareTo(root.key)>0){ root.right = add(key,value,root.right); }else{ root.value = value; } root.height = 1+Math.max(getHeight(root.left),getHeight(root.right)); int balanceFactor = getBalanceFactor(root); if(Math.abs(balanceFactor)>1){ System.out.println("unbalanced:"+balanceFactor); } //左左情况 if(balanceFactor>1&&getBalanceFactor(root.left)>=0){ return rightRotate(root); }else if(balanceFactor<-1&&getBalanceFactor(root.left)<=0){ return leftRotate(root); } return root; } // 对节点y进行向右旋转操作，返回旋转后新的根节点x // y x // / \ / \ // x T4 向右旋转 (y) z y // / \ - - - - - - - -> / \ / \ // z T3 T1 T2 T3 T4 // / \ // T1 T2 /** * 右旋转 * 1 旋转 * 2 变更高度 * @author weidoudou * @date 2023/4/14 7:27 * @param y 请添加参数描述 * @return com.company.AVLTree<K,V>.Node **/ private Node rightRotate(Node y){ //1 右旋转 Node x = y.left; Node T3 = x.right; x.right = y; y.left = T3; //2 变更高度 y.height = Math.max(getHeight(y.left),getHeight(y.right))+1; x.height = Math.max(getHeight(x.left),getHeight(x.left))+1; return x; } // 对节点y进行向左旋转操作，返回旋转后新的根节点x // y x // / \ / \ // T1 x 向左旋转 (y) y z // / \ - - - - - - - -> / \ / \ // T2 z T1 T2 T3 T4 // / \ // T3 T4 private Node leftRotate(Node y) { Node x = y.right; Node T2 = x.left; // 向左旋转过程 x.left = y; y.right = T2; // 更新height y.height = Math.max(getHeight(y.left), getHeight(y.right)) + 1; x.height = Math.max(getHeight(x.left), getHeight(x.right)) + 1; return x; } public void add(K key, V value) { Node node = containsKey(key,root); //未找到，插值 if(node==null){ //2.1 考虑特殊情况,如果是第一次调用，root为null if(root==null){ root = new Node(key,value); size++; }else{ //2.2 添加递归方法 add(key,value,root); } }else{ node.value = value; } //找到后，更新值 } public void set(K key, V value) { Node node = containsKey(key,root); if(node == null){ throw new IllegalArgumentException("要修改的值不存在"); } node.value = value; } private Node remove(Node node,K key){ //终止条件1 基本判断不到，因为已经判断了containskey /*if(node==null){ return null; }*/ //递归 if(key.compareTo(node.key)<0){ node.left = remove(node.left,key); return node; }else if(key.compareTo(node.key)>0){ node.right = remove(node.right,key); return node; }else{ //已找到要删除的元素 //1 如果只有左子节点或只有右子节点，则直接将子节点替换 if(node.left==null){ return node.right; }else if(node.right==null){ return node.left; }else{ //2 如果有左子节点和右子节点，则寻找前驱或后继 对当前节点替换掉 Node nodeMain = findMin(node.right); nodeMain.right = removMin(node.right);//这块一箭双雕，既把后继节点问题解决了，也把后继删除了 nodeMain.left = node.left; node.left = node.right = null; return node; } } } private Node findMin(Node node){ //1 终止条件 if(node.left==null){ return node; } //2 递归 return findMin(node.left); } private Node removMin(Node node){ //终止条件 if(node.left==null){ Node rightNode = node.right; node.right = null; return rightNode; } //递归 node.left = removMin(node.left); return node; } /** * 删除任意元素 若删除元素节点下只有一个节点直接接上即可，若有两个节点，则找前驱或后继，本节找前驱 * @author weidoudou * @date 2023/1/1 11:52 * @param key 请添加参数描述 * @return V **/ public V remove(K key) { Node node = containsKey(key,root); if(node == null){ throw new IllegalArgumentException("要修改的值不存在"); } size--; return remove(root, key).value; } //1 校验二分搜索树(中序遍历参考之前的中序遍历一节) public boolean judgeBST(){ List<K> list = new ArrayList<>(); inOrder(root,list); for(int i=1;i<list.size();i++){ if(list.get(i-1).compareTo(list.get(i))>0){ return false; } } return true; } private void inOrder(Node root, List<K> list){ if(root==null){ return; } inOrder(root.left,list); list.add(root.key); inOrder(root.right,list); } //2 校验平衡二叉树 public boolean judgeBalance(){ return judgeBalance(root); } private boolean judgeBalance(Node node){ if(root == null){ return true; } if(Math.abs(getBalanceFactor(node))>1){ return false; } return judgeBalance(node.left)&&judgeBalance(node.right); } public static void main(String[] args) { System.out.println("Pride and Prejudice"); ArrayList<String> words = new ArrayList<>(); if(FileOperation.readFile("pride-and-prejudice.txt",words)){ System.out.println("Total words: "+words.size()); AVLTree<String,Integer> avlTree = new AVLTree<>(); for(String word:words){ if(avlTree.contains(word)){ avlTree.set(word,avlTree.get(word)+1); }else{ avlTree.add(word,1); } } System.out.println("Total different words:"+avlTree.getSize()); System.out.println("judge BST:"+avlTree.judgeBST()); System.out.println("judge Balance:"+avlTree.judgeBalance()); } } }