节点Node的定义

class Node {
    public K key;       // 节点key值
    public V value;     // 节点值
    public Node left;   // 左子树节点
    public Node right;  // 右子树节点
    public int height;  // 高度

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

AVL 树的结构定义

public class AVLTree<K extends Comparable<K>, V> {
    
    private Node root;  // 根节点 

    private int size;   // 节点数

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

AVL树的方法


/**
 * 获取节点高度
 **/
private int getHeight(Node node) {
    if (node==null) {
        return 0;
    }
    return node.height;
}


/**
 * 计算平衡因子
 **/
private int getBalanceFactor(Node node) {
    if (node==null) {
        return 0;
    }
    return getHeight(node.left) - getHeight(node.right);
}

/* 二分搜索树
 *
 * 二分搜索树 所有节点满足，左节点小于根节点，右节点大于根节点
 */
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);
}

public boolean isBalanced(){
    return isBalanced(root);
}

/*
 * 判断Node为根的二叉树是否平衡 即平衡因子绝对值小于2
 */
public 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);
}

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

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 {
        node.value = value;
    }

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

    int balanceFactor = getBalanceFactor(node);

    /* 判断所属情况是LL LR RL RR等情形 */

    // LL 整体顺时针旋转
    if (balanceFactor > 1 && getBalanceFactor(node.left) >= 0) {
        return rightRotate(node);
    }

    //RR 整体逆时针旋转
    if (balanceFactor < -1 && getBalanceFactor(node.right) <= 0) {
        return leftRotate(node);
    }

    //LR 左子树左旋转 转化成 LL，之后整体右旋转
    if (balanceFactor > 1 && getBalanceFactor(node.left) < 0) {
        node.left = leftRotate(node.left);
        return rightRotate(node);
    }

    //RL 右子树右旋转转化成 RR ，之后整体左旋转
    if (balanceFactor < -1 && getBalanceFactor(node.right) > 0) {
        node.right = rightRotate(node.right);
        return leftRotate(node);
    }
    return node;
}

// 右旋转 顺时针
/*
 *              y                   x
 *             / \                 / \
 *            T1  x     ----->    y   T3
 *               / \             / \
 *              T2  T3          T1 T2
 */
private Node rightRotate(Node y) {
    Node x = y.left;
    Node T3 = x.right;
    x.right = y;
    y.left = T3;

    y.height = Math.max(getHeight(y.left), getHeight(y.right)) + 1;
    x.height = Math.max(getHeight(x.left), getHeight(x.right)) + 1;
    return x;
}

// 左旋转 逆时针
private Node leftRotate(Node y) {
    Node x = y.right;
    Node T2 = x.left;
    y.right = T2;
    x.left = y;

    y.height = Math.max(getHeight(y.left), getHeight(y.right)) + 1;
    x.height = Math.max(getHeight(x.left), getHeight(x.right)) + 1;
    return x;
}

/**
 * @param node 树根节点
 * @param key  节点属性
 * @return 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 {
        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 newVal) {
    Node node = getNode(root, key);
    if (node==null) {
        throw new IllegalArgumentException(key + " 不存在");
    }
    node.value = newVal;
}

/**
 * 返回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);
}

/**
 * 删除最小节点
 *
 * @return Node 返回新树的根节点
 **/
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;
}


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 {
        //  1.左子树为空
        if (node.left==null) {
            Node rightNode = node.right;
            node.right = null;
            size--;
            retNode = rightNode;
        } else if (node.right==null) {
            Node leftNode = node.left;
            node.left = null;
            size--;
            retNode = leftNode;
        } else {

            Node successor = minimum(node.right);
            successor.right = remove(node.right, successor.key);
            successor.left = node.left;
            node.left = node.right = null;
            retNode = successor;
        }

        if (retNode==null) {
            return null;
        }
        retNode.height = 1 + Math.max(getHeight(retNode.left), getHeight(retNode.right));

        int balanceFactor = getBalanceFactor(retNode);

        //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;
}