BST.java

import java.util.LinkedList;
import java.util.Queue;
import java.util.Stack;

public class BST<E extends Comparable<E>> {
    private class Node {
        public E e;
        public Node left, right;

        public Node(E e) {
            this.e = e;
            left = null;
            right = null;
        }
    }

    private Node root;
    private int size;

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

    public int size() {
        return size;
    }

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

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

    // 向以node为根的二分搜索树中插入元素e，递归算法
    private Node add(Node node, E e) {
        if (node == null) {
            size++;
            return new Node(e);
        }

        if (e.compareTo(node.e) > 0)
            node.left = add(node.left, e);
        else if (e.compareTo(node.e) < 0)
            node.right = add(node.right, e);

        return node;
    }

    // 查看二分搜索树种是否包含元素e
    private boolean contains(E e) {
        return contains(root, e);
    }

    // 以node 为根的二分搜索树中是否包含元素e，递归算法
    private boolean contains(Node node, E e) {
        if (node == null)
            return false;

        if (e.compareTo(node.e) == 0)
            return true;
        else if (e.compareTo(node.e) < 0)
            return contains(node.left, e);
        else// e.compareTo(node.e) > 0
            return contains(node.right, e);
    }

    // 二分搜索树的递归前序遍历
    public void preOrder() {
        preOrder(root);
    }

    private void preOrder(Node node) {
        if (node == null)
            return;

        System.out.println(node.e);
        preOrder(node.left);
        preOrder(node.right);
    }


    // 二分搜索树的中序遍历
    public void inOrder() {
        inOrder(root);
    }

    private void inOrder(Node node) {
        if (node == null)
            return;

        preOrder(node.left);
        System.out.println(node.e);
        preOrder(node.right);
    }

    // 二分搜索树的后序遍历
    public void postOrder() {
        postOrder(root);
    }

    private void postOrder(Node node) {
        if (node == null)
            return;

        preOrder(node.left);
        preOrder(node.right);
        System.out.println(node.e);
    }


    // 二分搜索树的非递归前序遍历
    public void preOrderNR() {
        Stack<Node> stack = new Stack<>();
        stack.push(root);
        while (!stack.isEmpty()) {
            Node cur = stack.pop();
            System.out.println(cur.e);

            if (cur.right != null) {
                stack.push(cur.right);

            }
            if (cur.left != null) {
                stack.push(cur.left);

            }
        }
    }

    // 二分搜索树的层序遍历
    public void levelOrder() {
        Queue<Node> q = new LinkedList<>();
        ((LinkedList<Node>) q).add(root);
        while (!q.isEmpty()) {
            Node cur = q.remove();
            System.out.println(cur.e);

            if (cur.right != null) {
                ((LinkedList<Node>) q).add(cur.right);

            }
            if (cur.left != null) {
                ((LinkedList<Node>) q).add(cur.left);

            }
        }
    }

    // 寻找二分搜索树的最小元素
    public E minmum() {
        if (size == 0)
            throw new IllegalArgumentException("BST is empty!");

        return minmum(root).e;
    }

    private Node minmum(Node node) {
        if (node.left == null)
            return node;
        return minmum(node);
    }

    // 寻找二分搜索树的最大元素
    public E maxmum() {
        if (size == 0)
            throw new IllegalArgumentException("BST is empty!");

        return maxmum(root).e;
    }

    private Node maxmum(Node node) {
        if (node.right == null)
            return node;
        return maxmum(node);
    }

    // 删除二分搜索树的最小元素所在节点，返回最小值
    public E removeMin() {
        E ret = minmum();
        root = removeMin(root);
        return ret;
    }

    // 删除以node为根的二分搜索树中的最小节点
    // 返回删除节点后新的二分搜索树的根
    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;
    }

    public E removeMax() {
        E ret = maxmum();
        root = removeMax(root);
        return ret;
    }

    public Node removeMax(Node node) {
        if (node.right == null) {
            Node nodeLeft = node.left;
            node.left = null;
            return nodeLeft;
        }

        node.right = removeMax(node.right);
        return node;
    }

    // 从二分搜索树中删除元素为e的节点
    public void remove(E e) {
        root = remove(root, e);
    }

    private Node remove(Node node, E e) {
        if (node == null)
            return null;

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

            // 待删除节点左子树为空
            if (node.left == null) {
                Node rightNode = node.right;
                node.right = null;
                size--;
                return rightNode;
            }
            // 待删除节点右子树为空
            if (node.right == null) {
                Node leftNode = node.left;
                node.left = null;
                size--;
                return 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 = minmum(node.right);
            successor.right = removeMin(node.right);
            successor.left = node.left;

            node.left = node.right = null;

            return successor;
        }
    }

    @Override
    public String toString() {
        StringBuilder res = new StringBuilder();
        generateBSTString(root, 0, res);
        return res.toString();
    }

    private void generateBSTString(Node node, int depth, StringBuilder res) {
        if (node == null) {
            res.append(generateBSTString(depth) + "null\n");
            return;
        }

        res.append(generateBSTString(depth) + node.e + "\n");
        generateBSTString(node.left, depth + 1, res);
        generateBSTString(node.right, depth + 1, res);
    }

    private String generateBSTString(int depth) {
        StringBuilder res = new StringBuilder();
        for (int i = 0; i < depth; i++) {
            res.append("--");
        }
        return res.toString();

    }
}