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update avl tree
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@l81893521
l81893521 committed May 24, 2018
1 parent 94fd2c9 commit ee080d8
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3 changes: 2 additions & 1 deletion README.md
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### AVL树
1. [计算节点高度和平衡因子](https://github.com/l81893521/basic-data-structure/blob/master/src/main/java/will/zhang/avlTree/AAVLTree.java)
2. [检查二分搜索树性质和平衡性](https://github.com/l81893521/basic-data-structure/blob/master/src/main/java/will/zhang/avlTree/BAVLTree.java)
2. [检查二分搜索树性质和平衡性](https://github.com/l81893521/basic-data-structure/blob/master/src/main/java/will/zhang/avlTree/BAVLTree.java)
3. [左旋转和右旋转的实现](https://github.com/l81893521/basic-data-structure/blob/master/src/main/java/will/zhang/avlTree/CAVLTree.java)
354 changes: 354 additions & 0 deletions src/main/java/will/zhang/avlTree/CAVLTree.java
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package will.zhang.avlTree;


import java.util.ArrayList;

/**
* AVL树, 是一颗基于二分搜索树实现的平衡二叉树
*/
public class CAVLTree<K extends Comparable, V>{

//根节点
private Node root;
private int size;

public CAVLTree(){
root = null;
size = 0;
}

/**
* 往二分搜索树添加一个节点
* @param key
* @param value
*/
public void add(K key, V value) {
root = add(root, key, value);
}

/**
* 以node为根的二分搜索树插入元素(key, value)
* @param node
* @param key
* @param value
* @Return 返回插入新节点后二分搜索树的根
*/
private Node add(Node node, K key, V value){
if(node == null){
size++;
return new Node(key, value);
}

if(key.compareTo(node.key) < 0){
node.left = add(node.left, key, value);
}else if(key.compareTo(node.key) > 0){
node.right = add(node.right, key, value);
}else{
//之前如果e和node.e相等, 按照自己要求做处理, 这里不做任何处理
//但是在映射(Map)中, 通常用户都是想修改该key的值, 所以改变了一下处理方式
node.value = value;
}
//更新Height
//取当前节点的左子树和右子树高度较高的再加上1
node.height = 1 + Math.max(getHeight(node.left), getHeight(node.right));

//计算平衡因子
int balanceFactor = getBalanceFactor(node);
//平衡因子大于1, 已经不满足平衡二叉树的条件了
if(Math.abs(balanceFactor) > 1){
System.out.println("unbalanced : " + balanceFactor);
}

//平衡维护, 进行右旋转操作
if(balanceFactor > 1 && getBalanceFactor(node.left) >= 0){
return rightRotate(node);
}
//平衡维护, 进行左旋转操作
if(balanceFactor < -1 && getBalanceFactor(node.right) <= 0){
return leftRotate(node);
}
return node;
}

public V remove(K key) {
Node node = getNode(root, key);
if(node != null){
remove(root, key);
return node.value;
}
return null;
}

/**
* 删除以node为根的二分搜索树键为key的节点
* 返回删除节点之后新的二分搜索树的根
* @param node
* @param key
*/
private Node remove(Node node, K key){
if(node == null){
return null;
}

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{ //e == node.e
//如果待删除的节点, 没有左子树
if(node.left == null){
Node rightNode = node.right;
node.right = null;
size--;
return rightNode;
}

if(node.right == null){ //如果待删除的节点, 没有右子树
Node leftNode = node.left;
node.left = null;
size--;
return leftNode;
}

//如果同时存在左右子树
//找出待删除节点的右子树中的最小值的节点, 也就是前驱(也可以找左子树中的最大值, 后继)
Node successor = minimum(node.right);
//把前驱的右子树, 指向删除最小值后的右子树(删除前驱原来所在的位置的节点)
successor.right = removeMin(node.right);
//前驱的左子树和右子树已经正确连接上
successor.left = node.left;
//清除原来的引用
node.left = node.right = null;
//返回
return successor;
}
}

public boolean contains(K key) {
return getNode(root, key) != null;
}

public V get(K key) {
Node node = getNode(root, key);
return node == null ? null : node.value;
}

public void set(K key, V newValue) {
Node node = getNode(root, key);
if(node == null){
throw new IllegalArgumentException(key + " doesn't exist!");
}
node.value = newValue;
}

public int getSize() {
return size;
}

public boolean isEmpty() {
return size == 0;
}

/**
* 在以node为根的二分搜索树中
* 返回key所在的节点
* @param node
* @param key
* @return
*/
private Node getNode(Node node, K key){
if(node == null){
return null;
}

if(key.compareTo(node.key) == 0){
return node;
}else if(key.compareTo(node.key) < 0){
return getNode(node.left, key);
}else{
return getNode(node.right, key);
}
}

/**
* 返回以node为根的二分搜索树的最小值所在的节点
* @param node
* @return
*/
private Node minimum(Node node){
if(node.left == null){
return node;
}
return minimum(node.left);
}

/**
* 删除以node为根的二分搜索树的最小值的节点
* 返回删除节点之后新的二分搜索树的根
* @param node
* @return
*/
private Node removeMin(Node node){
if(node.left == null){
Node rightNode = node.right;
node.right = null;
size--;
return rightNode;
}

node.left = removeMin(node.left);
return node;
}

/**
* 获得节点的高度值
* @param node
* @return
*/
private int getHeight(Node node){
if(node == null){
return 0;
}
return node.height;
}

/**
* 获取节点Node的平衡因子
* @param node
* @return
*/
private int getBalanceFactor(Node node){
if(node == null){
return 0;
}
//左子树的高度减去右子树的高度
return getHeight(node.left) - getHeight(node.right);
}

/**
* 判断该二叉树是否是一颗二分搜索树
* @return
*/
private boolean isBinarySearchTree(){
ArrayList<K> keys = new ArrayList<>();
//进行中序遍历, 这个时候keys应该是升序排列的
inOrder(root, keys);
//检验是否是升序
for (int i = 1; i < keys.size(); i++) {
//如果i-1比i还大, 代表有问题
if(keys.get(i - 1).compareTo(keys.get(i)) > 0){
return false;
}
}
return true;
}

/**
* 判断该二叉树是否是一颗平衡二叉树
* @return
*/
private boolean isBalanced(){
return isBalanced(root);
}

/**
* 判断以node为根的二叉树是否是一颗平衡二叉树
* @param node
* @return
*/
private boolean isBalanced(Node node){
if(node == null){
return true;
}
//如果平衡因子的绝对值 > 1, 直接返回false
int balanceFactor = getBalanceFactor(node);
if(Math.abs(balanceFactor) > 1){
return false;
}
return isBalanced(node.left) && isBalanced(node.right);
}

/**
* 对以node为根的二分搜索树进行中序遍历
* 并将结果保存到keys中
* @param node
* @param keys
*/
private void inOrder(Node node, ArrayList<K> keys){
if(node == null){
return;
}
inOrder(node.left, keys);
keys.add(node.key);
inOrder(node.right, keys);

}

// 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
private Node rightRotate(Node y){
Node x = y.left;
Node t3 = x.right;
//右旋
x.right = y;
y.left = t3;
//更新高度值,必须先更新y, 因为x的高度值和y是相关的
y.height = Math.max(getHeight(y.left), getHeight(y.right)) + 1;
x.height = Math.max(getHeight(x.left), getHeight(x.right)) + 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;
//进行左旋转
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;
}

/**
* 节点
* avl树的私有类
* 对用户屏蔽, 用户无需知道
*/
private class Node{
//这里用了K key和V value分别存放映射的键和值
public K key;
public V value;
//左节点和右节点
public Node left, right;
//记录每一个节点的高度值
public int height;

public Node(K key, V value){
this.key = key;
this.value = value;
left = null;
right = null;
//初始化的时候节点的高度值为1
height = 1;
}
}
}

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