JAVA數據結構之AVLTree平衡二叉樹

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;

   //空參構造函數
   public AVLTree(){
       root = null;
       size = 0;
   }

   publi int getSize(){
       return size;
   }

   public boolean isEmpty(){
       return size == 0;
   }
   /**************檢測是否符合AVLTree*********************/
   //1. 檢測是否滿足二分搜索樹
   //2. 檢測是否滿足節點平衡因子小於1


   //檢查是否還是一顆二分搜索樹
   //通過中序遍歷，是否滿足降序排列
   public boolean isBST(){
       ArrayList<K> keys = new ArrayList<>();
       inOrder(root,key);
       for(int i = 0;i < keys.size(); i++){
           if(keys.get(i-1).compareTo(keys.get(i)>0{
               return false;
           }
       }
   }

   private node inOrder(Node node, ArrayList<K> keys){
       if(node == null){
           return ;
       }
       inOrder(node.left, keys);
       keys.add(node.key);
       inOrder(node.right,key);
   }

    //判斷該二叉樹是否一顆平衡二叉樹
    public boolean isBalanced() {
        return isBalanced(root);
    }

    /*判斷node爲根的二叉樹是否是一顆二叉樹，遞歸算法*/
    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);

    }

    //獲取node的高度

    private int getHeight(Node node){
        if(node == null){
            return 0;
        }
        return node.height;
    }

    //獲取node的平衡因子

    private int getBalanceFactor(Node node){
        if(node == null){
            return 0;
        }
        return getHeight(node.left) - getHeight(node.right);
    }    

    /***************************************************************************************/

    // 對節點y進行向右旋轉操作，返回旋轉後新的根節點x
    //        y                              x
    //       / \                           /   \
    //      x   T4     向右旋轉 (y)        z     y
    //     / \       - - - - - - - ->    / \   / \
    //    z   T3                       T1  T2 T3 T4
    //   / \
    // T1   T2

    private Node rightRotate (Node y){
        Node x = y.left;
        Node T3 = x.right;

        //向右旋轉
        x.left = y;
        y.right = T3;

        //維護高度
        y.height = Math.max(getHeight(y.left),getHeight(y.right))+1;
        x.height = Math.max(getHeight(x.left),getHeightx.right))+1;

        return x;
    }

    // 對節點y進行向左旋轉操作，返回旋轉後新的根節點x
    //    y                             x
    //  /  \                          /   \
    // T1   x      向左旋轉 (y)       y     z
    //     / \   - - - - - - - ->   / \   / \
    //   T2  z                     T1 T2 T3 T4
    //      / \
    //     T3 T4
    private Node leftRotate(Node y) {
        Node x = y.right;
        Node T2 = x.left;

        //向左旋轉過程
        x.left = y;
        y.right = T2;

        //更新height; x;y節點的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;
    }

    //向二分搜索樹中添加新的元素

    public void add (K key, V value){
        root = add(root, key, value);
    }

    // 向以node爲根的二分搜索樹中插入元素(key, value)，遞歸算法
    // 返回插入新節點後二分搜索樹的根

    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));

        //計算平衡因子
        int balanceFactory = getBalanceFactory(node);

        //平衡維護
        //LL
        if(balanceFactory > 1 && getBalanceFactory(node.left) >= 0){
            return rightRotate(node);
        }
        //RR
        if(balanceFactory < -1 && getBalanceFactory(node.right) <= 0){
            return leftRotate(node);
        }

        //LR
        if(balanceFactory > 1 && getBalanceFactory(node.left) < 0){
            //node.left進行左旋轉，轉化成LL型
            node.left = leftRotate(node.left);

            return rightRotate(node);
        }

        //RL
        if(balanceFactory < -1 && getBalanceFactory(node.right) > 0){
            //node.left進行左旋轉，轉化成RR型
            node.right = leftRotate(node.right);

            return leftRotate(node);
        }

        return node;
    }

    // 返回以node爲根節點的二分搜索樹中，key所在的節點

    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);
        }
    }

    //查找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爲根的二分搜索樹的最小值所在的節點
    private Node minimum(Node node){
        if(node.left == null){
            return node;
        }
        return minim(node.left);
    }

    // 從二分搜索樹中刪除鍵爲key的節點
    public V remove(K key) {

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

    //返回的節點是刪除節點後返回的二叉搜索樹的新的節點
    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);
            retNode = node;

        } else if(key.compareTo(node.key) > 0)){
            node.right = remove(node.right,key);
            retNode = node;

        }else{ // key.compareTo(node.key) == 0
            //待刪除節點左子樹爲空的情況

            if(node.left == null){
                node.rightNode = node.right;
                node.right = null;
                size--;
                retNode = rightNode;
            }

            //待刪除節點右子樹爲空的情況
            else if(node.right == null){
                Node leftNode = node.left;
                node.left = null;
                size --;
                retNode = leftNode;
            }
            //待刪除節點左子樹均不爲空

            //找到比該待刪除節點大的最小節點，即待刪除節點右子樹的最小節點
            //用這個節點頂替待刪除節點的位置
            else {
                Node successor = minimum(node.right);
                /*
                    successor.right = node.right;

                */
                successor.right = remove(node.right,successor.key);
                successor.left = node.left；
                //爲了儘快回收
                node.left = node.right = null;
                retNode = successor
            }
        }

        //判斷刪除節點是否是葉子節點，如果是葉子節點，直接返回
        if (retNode == null) {
            return null;
        }
        //更新height
        retNode.height = 1 + Math.max(getHeight(retNode.left), getHeight(retNode.right));

        // 計算平衡因子
        int balanceFactory = getBalanceFactory(retNode);

        // 平衡維護
        // LL
        if (balanceFactory > 1 && getBalanceFactory(retNode.left) >= 0) {
            //當前節點平衡因子大於1，並且左孩子的平衡因子大於0，那麼右旋轉
            return rightRotate(retNode);
        }
        //RR
        if (balanceFactory < -1 && getBalanceFactory(retNode.right) <= 0) {
            //當前節點平衡因子小於-1，並且左孩子的平衡因子小於0，那麼左旋轉
            return leftRotate(retNode);
        }
        //LR
        if (balanceFactory > 1 && getBalanceFactory(retNode.left) < 0) {
            retNode.left = leftRotate(retNode.left);
            return rightRotate(retNode);
        }
        //RL
        if (balanceFactory < -1 && getBalanceFactory(retNode.right) > 0) {
            retNode.right = rightRotate(retNode.right);
            return leftRotate(retNode);
        }
        return retNode;
    }
}