字典树

字典树又叫 前缀树， 是一种树形数据结构，用于高效地存储和检索字符串数据集中的键。这一数据结构有相当多的应用情景，例如自动补全和拼写检查。

LC208 创建字典树

这是一个字符串字典树的典型例子，字符串中只包含26个小写字母。

代码为：

class Trie {

    class Node{
        boolean end;
        Node[] son = new Node[26];
    }

    private Node root;

    public Trie() {
        root = new Node(); //伪根
        
    }
    
    public void insert(String word) {
        Node cur = root;
        for(int i = 0; i < word.length(); i++){
            char c = word.charAt(i);
            if(cur.son[c - 'a'] == null){
                cur.son[c - 'a'] = new Node();
            }
            cur = cur.son[c - 'a'];
        }
        cur.end = true;
        
    }
    
    public boolean search(String word) {
        Node cur = root;
        for(char ch : word.toCharArray()){
            ch -= 'a';
            if(cur.son[ch] == null){
                return false;
            }
            cur = cur.son[ch];
        }
        if(cur.end != true){
            return false;
        }
        return true;
        
    }
    
    public boolean startsWith(String prefix) {
        Node cur = root;
        for(char ch : prefix.toCharArray()){
            ch -= 'a';
            if(cur.son[ch] == null){
                return false;
            }
            cur = cur.son[ch];
        }
        return true;
        
    }
}

0-1字典树

应用：求最大异或和

代码如下：

import java.io.*;
import java.util.List;
import java.util.ArrayList;

class Main{

    static class Node{
        Node[] son = new Node[2];
        int count = 0;
    }

    static void insert(Node root, int num){
        Node cur = root;
        cur.count++;
        for(int i = 31; i >= 0; i--){
            int bit = (num >> i) & 1;
            if(cur.son[bit] == null){
                cur.son[bit] = new Node();
            }
            cur = cur.son[bit];
            cur.count++;
        }

    }

    static void remove(Node root, int num){
        Node cur = root;
        cur.count--;
        for(int i = 31; i >= 0; i--){
            int bit = (num >> i) & 1;
            cur = cur.son[bit];
            cur.count--;  //不物理上删除任何节点，采用count来表示节点删除
        }
    }

    static int query(Node root, int num){
        Node cur = root;
        if(root.count == 0){
            return -1;
        }
        int res = 0;
        for(int i = 31; i >= 0; i--){
            int bit = (num >> i) & 1;
            int orBit = 1 - bit;
            if(cur.son[orBit] != null && cur.son[orBit].count > 0){
                res += (1 << i);
                cur = cur.son[orBit];
            } else {
                cur = cur.son[bit];
            }
        }
        return res;
    }
    
    

    public static void main(String[] args) throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StreamTokenizer st = new StreamTokenizer(br);
        st.parseNumbers();
        st.nextToken();
        int n = (int)st.nval;
        
        Node root = new Node();
        
        for(int k = 0; k < n; k++){
            st.nextToken();
            int ops = (int)st.nval;

            st.nextToken();
            int num = (int)st.nval;

            if(ops == 1){
                insert(root, num);
                

            } else if(ops == 2){
               remove(root, num);
                
            } else {
                
                int res = query(root, num);
                System.out.println(res);

            }
        }
    }   

}