Detailed explanation of examples of binary search tree implementation in Java

This article mainly introduces the implementation code of java binary search tree in detail. It has certain reference value. Interested friends can refer to it.

The example of this article shares with you the Java binary search tree. The specific code for forking the search tree is for your reference. The specific content is as follows

package 查找;

import edu.princeton.cs.algs4.Queue;
import edu.princeton.cs.algs4.StdOut;

public class BST<Key extends Comparable<Key>, Value> {
  private class Node {
    private Key key; // 键
    private Value value;// 值
    private Node left, right; // 指向子树的链接
    private int n; // 以该节点为根的子树中的节点总数

    public Node(Key key, Value val, int n) {
      this.key = key;
      this.value = val;
      this.n = n;
    }
  }

  private Node root;

  public int size() {
    return size(root);
  }

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

  /**
   * 如果树是空的，则查找未命中 如果被查找的键小于根节点，则在左子树中继续查找 如果被查找的键大于根节点，则在右子树中继续查找
   * 如果被查找的键和根节点的键相等，查找命中
   * 
   * @param key
   * @return
   */
  public Value get(Key key) {
    return get(root, key);
  }

  private Value get(Node x, Key key) {
    if (x == null)
      return null;
    int cmp = key.compareTo(x.key);
    if (cmp < 0)
      return get(x.left, key);
    else if (cmp > 0)
      return get(x.right, key);
    else
      return x.value;
  }

  /**
   * 二叉查找树的一个很重要的特性就是插入的实现难度和查找差不多。 当查找到一个不存在与树中的节点（null）时，new 新节点，并将上一路径指向该节点
   * 
   * @param key
   * @param val
   */
  public void put(Key key, Value val) {
    root = put(root, key, val);
  }

  private Node put(Node x, Key key, Value val) {
    if (x == null)
      return new Node(key, val, 1);
    int cmp = key.compareTo(x.key);
    if (cmp < 0)
      x.left = put(x.left, key, val);
    else if (cmp > 0)
      x.right = put(x.right, key, val);
    else
      x.value = val;
    x.n = size(x.left) + size(x.right); // 要及时更新节点的子树数量
    return x;
  }

  public Key min() {
    return min(root).key;
  }

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

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

  private Node max(Node x) {
    if (x.right == null)
      return x;
    return min(x.right);
  }

  /**
   * 向下取整：找出小于等于该键的最大键
   * 
   * @param key
   * @return
   */
  public Key floor(Key key) {
    Node x = floor(root, key);
    if (x == null)
      return null;
    else
      return x.key;
  }

  /**
   * 如果给定的键key小于二叉查找树的根节点的键，那么小于等于key的最大键一定出现在根节点的左子树中
   * 如果给定的键key大于二叉查找树的根节点，那么只有当根节点右子树中存在大于等于key的节点时，
   * 小于等于key的最大键才会出现在右子树中，否则根节点就是小于等于key的最大键
   * 
   * @param x
   * @param key
   * @return
   */
  private Node floor(Node x, Key key) {
    if (x == null)
      return null;
    int cmp = key.compareTo(x.key);
    if (cmp == 0)
      return x;
    else if (cmp < 0)
      return floor(x.left, key);
    else {
      Node t = floor(x.right, key);
      if (t == null)
        return x;
      else
        return t;
    }
  }

  /**
   * 向上取整：找出大于等于该键的最小键
   * 
   * @param key
   * @return
   */
  public Key ceiling(Key key) {
    Node x = ceiling(root, key);
    if (x == null)
      return null;
    else
      return x.key;
  }

  /**
   * 如果给定的键key大于二叉查找树的根节点的键，那么大于等于key的最小键一定出现在根节点的右子树中
   * 如果给定的键key小于二叉查找树的根节点，那么只有当根节点左子树中存在大于等于key的节点时，
   * 大于等于key的最小键才会出现在左子树中，否则根节点就是大于等于key的最小键
   * 
   * @param x
   * @param key
   * @return
   */
  private Node ceiling(Node x, Key key) {
    if (x == null)
      return null;
    int cmp = key.compareTo(x.key);
    if (cmp == 0)
      return x;
    else if (cmp > 0) {
      return ceiling(x.right, key);
    } else {
      Node t = floor(x.left, key);
      if (t == null)
        return x;
      else
        return t;
    }
  }

  /**
   * 选择排名为k的节点
   * 
   * @param k
   * @return
   */
  public Key select(int k) {
    return select(root, k).key;
  }

  private Node select(Node x, int k) {
    if (x == null)
      return null;
    int t = size(x.left);
    if (t > k)
      return select(x.left, k);
    else if (t < k)
      return select(x.right, k - t - 1);// 根节点也要排除掉
    else
      return x;
  }

  /**
   * 查找给定键值的排名
   * 
   * @param key
   * @return
   */
  public int rank(Key key) {
    return rank(key, root);
  }

  private int rank(Key key, Node x) {
    if (x == null)
      return 0;
    int cmp = key.compareTo(x.key);
    if (cmp < 0)
      return rank(key, x.left);
    else if (cmp > 0)
      return 1 + size(x.left) + rank(key, x.right);
    else
      return size(x.left);
  }
  /**
   * 删除最小键值对
   */
  public void deleteMin(){
    root = deleteMin(root);
  }
  /**
   * 不断深入根节点的左子树直到遇见一个空链接，然后将指向该节点的链接指向该结点的右子树
   * 此时已经没有任何链接指向要被删除的结点，因此它会被垃圾收集器清理掉
   * @param x
   * @return
   */
  private Node deleteMin(Node x){
    if(x.left == null) return x.right;
    x.left = deleteMin(x.left);
    x.n = size(x.left)+size(x.right) + 1;
    return x;
  }
  
  public void deleteMax(){
    root = deleteMax(root);
  }
  private Node deleteMax(Node x){
    if(x.right == null ) return x.left;
    x.right = deleteMax(x.right);
    x.n = size(x.left)+size(x.right) + 1;
    return x;
  }
  
  public void delete(Key key){
    root = delete(root,key);
  }
  private Node delete(Node x, Key key){
    if(x == null) return null;
    int cmp = key.compareTo(x.key);
    if(cmp < 0) x.left = delete(x.left,key);
    else if(cmp > 0) x.right = delete(x.right,key);
    else{
      if(x.right == null) return x.left;
      if(x.left == null ) return x.right;
      /**
       * 如果被删除节点有两个子树，将被删除节点暂记为t
       * 从t的右子树中选取最小的节点x，将这个节点x的左子树设为t的左子树
       * 这个节点x的右子树设为t的右子树中删除了最小节点的子树，这样就成功替换了t的位置
       */
      Node t = x;
      x = min(t.right);
      x.left = t.left;
      x.right = deleteMin(t.right);
    }
    x.n = size(x.left) + size(x.right) +1;
    return x;
  }
  
  public void print(){
    print(root);
  }
  private void print(Node x){
    if(x == null ) return;
    print(x.left);
    StdOut.println(x.key);
    print(x.right);
  }
  
  public Iterable<Key> keys(){
    return keys(min(),max());
  }
  public Iterable<Key> keys(Key lo, Key hi){
    Queue<Key> queue = new Queue<Key>();
    keys(root, queue, lo, hi);
    return queue;
  }
  private void keys(Node x, Queue<Key> queue, Key lo, Key hi){
    if(x == null) return;
    int cmplo = lo.compareTo(x.key);
    int cmphi = lo.compareTo(x.key);
    if(cmplo < 0 ) keys(x.left,queue,lo,hi);
    if(cmplo <= 0 && cmphi >= 0) queue.enqueue(x.key);
    if(cmphi > 0 ) keys(x.right,queue,lo,hi);
  }
}

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