AVL树

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;
    }

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

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

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

    // 添加元素
    public void add(K key, V value) {
        root = add(root, key, value);
    }

    // 向以node为根的二分搜索树种插入元素E
    private Node add(Node node, K key, V value) {
        // 当我们递归到null的时候就一定要创建一个节点
        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;
        }
        
        // 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,插入的元素在不平衡的节点的左侧的左侧 LL
        if (balanceFactor > 1 && getBalanceFactor(node.left) >= 0) {
            return rightRotate(node);
        }
        // 平衡维护,插入的元素在不平衡的节点的右侧的右侧 RR
        if (balanceFactor < -1 && getBalanceFactor(node.right) <= 0) {
            return leftRotate(node);
        }
        // 平衡维护,插入的元素在不平衡的节点的左侧的右侧 LR
        if (balanceFactor > 1 && getBalanceFactor(node.left) < 0) {
            node.left = leftRotate(node.left);
            return rightRotate(node);
        }
        // 平衡维护,插入的元素在不平衡的节点的右侧的左侧 RL
        if (balanceFactor < -1 && getBalanceFactor(node.right) > 0) {
            node.right = rightRotate(node.right);
            return leftRotate(node);
        }
        return node;
    }


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

    private Node leftRotate(Node y) {
        Node x = y.right;
        Node T2 = x.left;
        x.left = y;
        y.right = T2;

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

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

    // 判断该二叉树是不是一颗平衡搜索树
    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;
    }

    // 判断以Node为节点的二叉树是不是一颗平衡二叉树
    public boolean isBalanced() {
        return isBalanced(root);
    }

    private boolean isBalanced(Node node) {
        if (node == null) {
            return true;
        }
        int balanceFactor = getBalanceFactor(node);
        if (balanceFactor > 1) {
            return false;
        }
        return isBalanced(node.left) && isBalanced(node.right);
    }

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

    }

    private Node getNode(Node node, K key) {
        if (node == null) {
            return null;
        }
        if (key.compareTo(node.key) < 0) {
            return getNode(node.left, key);
        } else if (key.compareTo(node.key) > 0) {
            return getNode(node.right, key);
        } else {
            return node;
        }
    }

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

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

    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);
            retNode = node;
        } else if (key.compareTo(node.key) > 0) {
            node.right = remove(node.right, key);
            retNode = node;
        } else {
            // 3种情况
            // 待删除节点左子树为空
            if (node.left == null) {
                Node rightNode = node.right;
                node.right = null;
                size--;
                retNode = rightNode;
            } else if (node.right == null) {
                // 待删除节点右子树为空
                Node leftNode = node.left;
                node.left = null;
                size--;
                retNode = leftNode;
            } else {
                // 待删除节点左右子树均不为空的情况
                // 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);
                // 这里我们进行了删除size进行了减操作
                successor.right = remove(node.right, successor.key);
                successor.left = node.left;
                node.left = node.right = null;
                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,插入的元素在不平衡的节点的左侧的左侧 LL
        if (balanceFactor > 1 && getBalanceFactor(retNode.left) >= 0) {
            return rightRotate(retNode);
        }
        // 平衡维护,插入的元素在不平衡的节点的右侧的右侧 RR
        if (balanceFactor < -1 && getBalanceFactor(retNode.right) <= 0) {
            return leftRotate(retNode);
        }
        // 平衡维护,插入的元素在不平衡的节点的左侧的右侧 LR
        if (balanceFactor > 1 && getBalanceFactor(retNode.left) < 0) {
            retNode.left = leftRotate(retNode.left);
            return rightRotate(retNode);
        }
        // 平衡维护,插入的元素在不平衡的节点的右侧的左侧 RL
        if (balanceFactor < -1 && getBalanceFactor(retNode.right) > 0) {
            retNode.right = rightRotate(retNode.right);
            return leftRotate(retNode);
        }
        return retNode;
    }

    // 最小值
    public V minimum() {
        if (size == 0) {
            throw new IllegalArgumentException("BST is empty");
        }
        return minimum(root).value;
    }

    // 返回已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);
    }
}