0042数据结构之AVL树

------------------------AVL树--------------------------

自平衡树:AVL树是一颗二分搜索树,同时左右子树的高度差不超过1,AVL是自平衡的

主要是通过左旋和右旋来维护平衡

统计一本书中共出现多少个单词,每个单词出现了多少次:使用AVL树实现Set和Map,Set用于统计共出现了多少个不同的单词,Map用于容纳每个单词出现的次数。

AVLTree实现如下:
package avl;

import java.util.ArrayList;

public class AVLTree<K extends Comparable<K>, V> {

    private class Node{
        public K key;
        public V value;
        public Node left, right;
        public int height;

        public Node(K key, V value){
            this.key = key;
            this.value = value;
            left = null;
            right = null;
            height = 1;
        }
    }

    private Node root;
    private int size;

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

    public int getSize(){
        return size;
    }

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

    // 判断该二叉树是否是一棵二分搜索树
   
public boolean isBST(){

        ArrayList<K> keys = new ArrayList<>();
        inOrder(root, keys);
        for(int i = 1 ; i < keys.size() ; i ++)
            if(keys.get(i - 1).compareTo(keys.get(i)) > 0)
                return false;
        return true;
    }

    private void inOrder(Node node, ArrayList<K> keys){

        if(node == null)
            return;

        inOrder(node.left, keys);
        keys.add(node.key);
        inOrder(node.right, keys);
    }

    // 判断该二叉树是否是一棵平衡二叉树
   
public boolean isBalanced(){
        return isBalanced(root);
    }

    // 判断以Node为根的二叉树是否是一棵平衡二叉树,递归算法
   
private boolean isBalanced(Node node){

        if(node == null)
            return true;

        int balanceFactor = getBalanceFactor(node);
        if(Math.abs(balanceFactor) > 1)
            return false;
        return isBalanced(node.left) && isBalanced(node.right);
    }

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

    // 获得节点node的平衡因子
   
private int getBalanceFactor(Node node){
        if(node == null)
            return 0;
        return getHeight(node.left) - getHeight(node.right);
    }

    // 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;

        // 向右旋转过程
       
x.right = y;
        y.left = T3;

        // 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;
    }

    // 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;
    }

    // 向二分搜索树中添加新的元素(key, value)
   
public void add(K key, V value){
        root = add(root, key, value);
    }

    // 向以node为根的二分搜索树中插入元素(key, value),递归算法
   
// 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 // key.compareTo(node.key) == 0
           
node.value = value;

        // 更新height
       
node.height = 1 + Math.max(getHeight(node.left), getHeight(node.right));

        // 计算平衡因子
       
int balanceFactor = getBalanceFactor(node);

        // 平衡维护
       
// LL
       
if (balanceFactor > 1 && getBalanceFactor(node.left) >= 0)
            return rightRotate(node);

        // RR
       
if (balanceFactor < -1 && getBalanceFactor(node.right) <= 0)
            return leftRotate(node);

        // LR
       
if (balanceFactor > 1 && getBalanceFactor(node.left) < 0) {
            node.left = leftRotate(node.left);
            return rightRotate(node);
        }

        // RL
       
if (balanceFactor < -1 && getBalanceFactor(node.right) > 0) {
            node.right = rightRotate(node.right);
            return leftRotate(node);
        }

        return node;
    }

    // 返回以node为根节点的二分搜索树中,key所在的节点
   
private Node getNode(Node node, K key){

        if(node == null)
            return null;

        if(key.equals(node.key))
            return node;
        else if(key.compareTo(node.key) < 0)
            return getNode(node.left, key);
        else // if(key.compareTo(node.key) > 0)
           
return getNode(node.right, key);
    }

    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;
    }

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

    // 从二分搜索树中删除键为key的节点
   
public V remove(K key){

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

    private Node remove(Node node, K key){

        if( node == null )
            return null;

        Node retNode;
        if( key.compareTo(node.key) < 0 ){
            node.left = remove(node.left , key);
            // return node;
           
retNode = node;
        }
        else if(key.compareTo(node.key) > 0 ){
            node.right = remove(node.right, key);
            // return node;
           
retNode = node;
        }
        else{   // key.compareTo(node.key) == 0

            //
待删除节点左子树为空的情况
           
if(node.left == null){
                Node rightNode = node.right;
                node.right = null;
                size --;
                // return rightNode;
               
retNode = rightNode;
            }

            // 待删除节点右子树为空的情况
           
else if(node.right == null){
                Node leftNode = node.left;
                node.left = null;
                size --;
                // return leftNode;
               
retNode = leftNode;
            }

            // 待删除节点左右子树均不为空的情况
           
else{
                // 找到比待删除节点大的最小节点, 即待删除节点右子树的最小节点
               
// 用这个节点顶替待删除节点的位置
               
Node successor = minimum(node.right);
                //successor.right = removeMin(node.right);
               
successor.right = remove(node.right, successor.key);
                successor.left = node.left;

                node.left = node.right = null;

                // return successor;
               
retNode = successor;
            }
        }

        if(retNode == null)
            return null;

        // 更新height
       
retNode.height = 1 + Math.max(getHeight(retNode.left), getHeight(retNode.right));

        // 计算平衡因子
       
int balanceFactor = getBalanceFactor(retNode);

        // 平衡维护
       
// LL
       
if (balanceFactor > 1 && getBalanceFactor(retNode.left) >= 0)
            return rightRotate(retNode);

        // RR
       
if (balanceFactor < -1 && getBalanceFactor(retNode.right) <= 0)
            return leftRotate(retNode);

        // LR
       
if (balanceFactor > 1 && getBalanceFactor(retNode.left) < 0) {
            retNode.left = leftRotate(retNode.left);
            return rightRotate(retNode);
        }

        // RL
       
if (balanceFactor < -1 && getBalanceFactor(retNode.right) > 0) {
            retNode.right = rightRotate(retNode.right);
            return leftRotate(retNode);
        }

        return retNode;
    }

}
AVLSet实现如下:
package avl;

public class AVLSet<E extends Comparable<E>> implements Set<E> {

    private AVLTree<E, Object> avl;

    public AVLSet(){
        avl = new AVLTree<>();
    }

    @Override
    public int getSize(){
        return avl.getSize();
    }

    @Override
    public boolean isEmpty(){
        return avl.isEmpty();
    }

    @Override
    public void add(E e){
        avl.add(e, null);
    }

    @Override
    public boolean contains(E e){
        return avl.contains(e);
    }

    @Override
    public void remove(E e){
        avl.remove(e);
    }
}
AVLMap实现如下:
package avl;

public class AVLMap<K extends Comparable<K>, V> implements Map<K, V> {

    private AVLTree<K, V> avl;

    public AVLMap(){
        avl = new AVLTree<>();
    }

    @Override
    public int getSize(){
        return avl.getSize();
    }

    @Override
    public boolean isEmpty(){
        return avl.isEmpty();
    }

    @Override
    public void add(K key, V value){
        avl.add(key, value);
    }

    @Override
    public boolean contains(K key){
        return avl.contains(key);
    }

    @Override
    public V get(K key){
        return avl.get(key);
    }

    @Override
    public void set(K key, V newValue){
        avl.set(key, newValue);
    }

    @Override
    public V remove(K key){
        return avl.remove(key);
    }
}

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转载自www.cnblogs.com/xiao1572662/p/12128289.html