递归的二叉查找树Java实现

package practice;

public class TestMain {
    public static void main(String[] args) {
        int[] ao = {50,18,97,63,56,3,71,85,54,34,9,62,45,94,66,65,7,19,22,86};
        Integer[] a = new Integer[20];
        for (int i = 0; i < a.length; i++) {
            a[i] = new Integer(ao[i]);
        }
        BinarySortTree<Integer, String> tree = new BinarySortTree<Integer, String>();
        for (int i = 0; i < a.length; i++) {
            tree.put(a[i], a[i].toString());
        }
        /*tree.delete(3);
        System.out.println("min = "+tree.min()+" max = "+tree.max());
        tree.delete(97);
        System.out.println("min = "+tree.min()+" max = "+tree.max());
        tree.delete(19);
        tree.delete(18);
        tree.delete(85);
        System.out.println();
        tree.delete(99);*/

    }
}
/*
 * 二叉查找树及其操作的递归实现
 * 二叉查找树：左节点比根节点小，左节点比根节点大。
 */
class BinarySortTree<K extends Comparable<K>, V>{

    Node root;
    /*
     * Node结点类
     */
    class Node{
        private Node left, right; //左右子树
        private K key;
        private V value;
        private int N; //节点所在树的子节点数（包括自己）

        private Node(K key, V value) {
            this.key = key;
            this.value = value;
            this.N = 1;
        }        

        public K getKey() {
            return key;
        }
    }
    /*
     * 插入新节点
     * O(lgn)
     */
    public void put(K key, V value) {
        root = put(key, value, root);
    }

    private Node put(K key, V value, Node node) {
        if (node == null) { return new Node(key, value);}

        if (compare(key, node.key) == 0)     { node.value = value;} //如果key相等则更新值
        else if (compare(key, node.key) < 0) { node.left = put(key, value, node.left);} //进入左子树
        else if (compare(key, node.key) > 0) { node.right = put(key, value, node.right);} //进入右子树
        node.N = size(node.left) + size(node.right) + 1; //子节点数

        return node;
    }
    /*
     * 查找
     */
    public V get(K key) {
        return get(key, root);
    }

    private V get(K key, Node node) {
        if (node == null) { return null;}

        if (compare(key, node.key) < 0)      { return get(key, node.left);}
        else if (compare(key, node.key) > 0) { return get(key, node.right);}
        else                                 { return node.value;} //递归结束条件，找到key
    }
    /*
     * 获取最大最小值
     */
    public K min() {
        return min(root).key;
    }

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

    public K max() {
        return max(root).key;
    }

    private Node max(Node node) {
        if (node.right == null) { return node;}
        else                    { return max(node.right);}
    }
    /*
     * 获取键的排名
     */
    public int rank(K key) {
        return rank(key, root);
    }

    private int rank(K key, Node node) {
        if (node == null) { return 0;} //键不存在返回0

        if (compare(key, node.key) < 0)      { return rank(key, node.left);}
        else if (compare(key, node.key) > 0) { return size(node.left) + 1 + rank(key, node.right);}
                                             //当查找进入右子树时，加上同级左子树的大小，再加1（父节点本身）
        else                                 { return size(node.left);} //该节点左子树的大小（它的左子树的key全部比它小）
    }
    /*
     * 根据排名获取键
     */
    public Node select(int N) {
        return select(N, root);
    }

    private Node select(int N, Node node) {

        int t = size(node.left) + 1; //获取当前节点在以它为根节点的树中的排名（从1开始排）
        if (N < t)      { return select(N, node.left);} //与当前排名比较，选择进入左子树还是右子树
        else if (N > t) { return select(N - t, node.right);}
        //进入右子树时，右子树所有的节点的排名都要加上"同级左子树的大小，再加1（父节点本身）"，所以 N - t
        else            { return node;}
    }
    /*
     * 删除最小键
     */
    public void deleteMin() {
        root = deleteMin(root);
    }
    private Node deleteMin(Node node) {
        if (node.left == null) { return node.right;} //将最小节点的右子树连在他的父节点上即将它删除
        node.left = deleteMin(node.left);
        node.N = size(node.left) + size(node.right) + 1; //更新树的大小
        return node;
    }
    /*
     * 删除指定键
     */
    public void delete(K key) {
        root = delete(key, root);
    }
    private Node delete(K key, Node node) {
        if (node == null) { return null;} //找不到键，不做任何处理，原样返回

        if (compare(key, node.key) < 0)      { node.left = delete(key, node.left);} //向左向右找
        else if (compare(key, node.key) > 0) { node.right = delete(key, node.right);}
        else {
            if (node.right == null) { return node.left;} //如果要删的节点有一边时null，直接把另一条子树连到父节点上
            if (node.left== null)   { return node.right;}
            /*Node tnode = min(node.right);
            node.right = deleteMin(node.right);
            tnode.left = node.left;
            tnode.right = node.right;
            tnode.N = size(tnode.left) + size(tnode.right) + 1;
            return tnode;*/
            //上下两段代码实现了同样的功能，充分体现了差距
            Node tnode = node;  //将右子树中的最小值（后继节点）连到父节点上，或左子树中的最大值（前趋节点）也可以
            node = min(tnode.right);
            node.right = deleteMin(tnode.right); //把将要连到父节点上的那个后继节点在当前位置删除
            node.left = tnode.left; //更新左右子树
        }

        node.N = size(node.left) + size(node.right) + 1; //更新树的大小
        return node;
    }
    /*
     * key1 <  key2 -1
     * key1 >  key2  1
     * key1 == key2  0
     */
    private int compare(K key1, K key2) {
        return key1.compareTo(key2);
    }

    private int size(Node node) {
        if (node == null) { return 0;}
        else              { return node.N;}
    }

    /*
     * 中序遍历
     */
    public void print(Node node) {
        if (node == null) {
            return;
        }
        print(node.left);
        System.out.print(node.key+" ");
        print(node.right);
    }
}

算法动态演示

http://www.cs.usfca.edu/~galles/visualization/BST.html