平衡树和 AVL (3) —— AVL 树删除节点

1 平衡树删除节点

• AVLTree.java

package avltree;

import java.util.ArrayList;

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

    public 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颗二分搜索树
    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);

    }


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

    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);
    }


    public 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
    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));

        x.height = Math.max(getHeight(x.left), getHeight(x.right));


        return x;

    }

    // 对 y 进行左旋转操作，返回旋转后新的根节点
    //          y                        x
    //        /   \                    /    \
    //       T1     x                 y       z
    //             /  \              / \     / \
    //            T2   z            T1  T2  T3 T4
    //                / \
    //               T3  T4

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

        // 向左旋转的过程
        x.left = y;
        y.right = T2;

        y.height = Math.max(getHeight(y.left), getHeight(y.right));
        x.height = Math.max(getHeight(x.left), getHeight(x.right));

        return x;

    }


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

    // 以 node 为根的二分搜索树中插入元素 (key,value)
    // 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 {
            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);

        if (Math.abs(balanceFactor) > 1) {
            System.out.println("unbalanced: " + balanceFactor);
        }

        // 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);
    }

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

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

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

            /*
             * 待删除节点左右子树均不为空
             *
             * 找到比待删除节点大的最小节点，即到删除节点左子树的最小节点
             * 用这个节点顶替待删除节点的位置
             *
             * */
            Node successor = minimum(node.right);
            successor.right = 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);

        if (Math.abs(balanceFactor) > 1) {
            System.out.println("unbalanced: " + balanceFactor);
        }

        // 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;

    }

}