Java递归实现二分搜索树

淩亂°似流年 2021-12-23 07:11 302阅读 0赞

**导读**: 本文分为两部分: 1.实现代码 2.测试代码

实现代码如下:

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
        // 返回插入新节点后的二分搜索树的根
        private Node add(Node node, E e) {
            if (node == null){
                size++;
                return new Node(e);
            }
            if (e.compareTo(node.e) > 0) {
                node.right = add(node.right, e);
            } else
                node.left = add(node.left, e);
            return node;
        }
    
        // 搜索二分搜索树是否包含元素e
        public boolean contains(E e){
            return contains(root ,e);
        }
    
        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.right, e);
            else
                return contains(node.left, e);
        }
    
        // 前序遍历
        public void perOrder(){
            perOrder(root);
        }
    
        // 递归写法
        private void perOrder(Node node){
            if (node != null){
                System.out.print(node.e+" ");
                perOrder(node.left);
                perOrder(node.right);
            }
        }
    
        // 中序遍历
        public void inOrder(){
            inOrder(root);
        }
    
        private void inOrder(Node node){
            if (node == null)
                return;
            inOrder(node.left);
            System.out.print(node.e+" ");
            inOrder(node.right);
        }
    
        // 后续遍历
        public void  postOrder(){
            postOrder(root);
        }
    
        private void postOrder(Node node){
            if (node != null){
                postOrder(node.left);
                postOrder(node.right);
                System.out.print(node.e + " ");
            }
        }
    
        @Override
        public String toString(){
            StringBuilder res = new StringBuilder();
            generateBSTString(root,0,res);
            return res.toString();
        }
    
        // 生成以node为根节点, 深度为depth的描述二叉树的字符串
        private void generateBSTString(Node node, int depth, StringBuilder res) {
    
            if (node == null){
                res.append(generateDepthString(depth)+"null\n");
                return;
            }
    
            res.append(generateDepthString(depth) + node.e + "\n");
            generateBSTString(node.left, depth+1, res);
            generateBSTString(node.right, depth+1, res);
        }
    
        private String generateDepthString(int depth) {
            StringBuilder res = new StringBuilder();
            for (int i = 0; i < depth; i++) {
                res.append("--");
            }
            return res.toString();
        }
    
        // 返回最小元素
        public E minimum(){
            if (size == 0)
                throw new IllegalArgumentException("BST is empty!");
            return minimum(root).e;
        }
    
        private Node minimum(Node node){
            if (node.left == null)
                return node;
            return minimum(node.left);
        }
    
        // 返回最大元素
        public E maximum(){
            if (size == 0)
                throw new IllegalArgumentException("BST is empty!");
            return maximum(root).e;
        }
    
        private Node maximum(Node node){
            if (node.right == null)
                return node;
            return maximum(node.right);
        }
    
        // 从二分搜索树中删除最小值所在节点,返回最小值
        public E removeMin(){
            E ret = minimum();
            root = removeMin(root);
            return ret;
        }
    
        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;
        }
    
        // 从二分搜索树中删除最大值所在节点,返回最大值
        public E removeMax(){
            E ret = maximum();
            root = removeMax(root);
            return ret;
        }
    
        private Node removeMax(Node node){
    
            if (node.right == null){
                Node leftNode = node.left;
                node.left = null;
                size -- ;
                return leftNode;
            }
    
            node.right = removeMax(node.right);
            return node;
        }
    
        // 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 == node.e
                if (node.left == null){
                    Node rightNode = node.right;
                    node.right = null;
                    size --;
                    return rightNode;
                }
                if (node.right == null){
                    Node leftNode = node.left;
                    node.left = null;
                    size --;
                    return leftNode;
                }
    
                Node successor = minimum(node.right);
                successor.right = removeMin(node.right);
                successor.left = node.left;
    
                node.left = node.right = null;
                return successor;
            }
        }
    
    }

测试代码如下:

BST<Integer> bst = new BST<>();
            for (int i = 0; i < 100; i++) {
                bst.add(new Random().nextInt(1000));
            }
            
            // 前序遍历
            bst.perOrder();
            System.out.println();
            
            // 中序遍历
            bst.inOrder();
            System.out.println();
            
            // 后序遍历
            bst.postOrder();
            System.out.println();
            System.out.println(bst.toString());
        }