字典树-Trie

概念

字典树，Trie (发音为 "try") 或前缀树是一种树数据结构，用于检索字符串数据集中的键。这一高效的数据结构有多种应用，如：自动补全、拼写检查、IP路由（最长前缀匹配）

特征

1. 数据结构为：Trie成员变量（Trie的指针数组、isEndOfWord结尾标志位）

2. 子节点最多有26个

插入

key为要插入的单词：

pCrawl = root

1、遍历key中的所有字母

a. 如果pCrawl.children中存在该字母，pCrawl和key继续下个迭代

b. 如果pCrawl.children中不存在该字母，则创建该字母的字典树。

2、遍历到最后，pCrawl中的变量isEndOfWord赋值为true

查询

key为要查询的单词：

pCrawl = root

1、遍历key中的所有字母

a. 如果pCrawl中存在该字母，继续下一轮循环，如果不存在该字母，返回false

2、判断pCrawl不为空，且并不是最后一个节点，则为true，否则返回false

基本实现--插入、查询

package tree;

// Java implementation of search and insert operations
// on Trie
public class Trie {

    // Alphabet size (# of symbols)
    static final int ALPHABET_SIZE = 26;

    // trie node
    static class TrieNode
    {
        TrieNode[] children = new TrieNode[ALPHABET_SIZE];

        // isEndOfWord is true if the node represents
        // end of a word
        boolean isEndOfWord;

        TrieNode(){
            isEndOfWord = false;
            for (int i = 0; i < ALPHABET_SIZE; i++)
                children[i] = null;
        }
    };

    static TrieNode root;

    // If not present, inserts key into trie
    // If the key is prefix of trie node,
    // just marks leaf node
    static void insert(String key)
    {
        int level;
        int length = key.length();
        int index;

        TrieNode pCrawl = root;

        for (level = 0; level < length; level++)
        {
            index = key.charAt(level) - 'a';
            if (pCrawl.children[index] == null)
                pCrawl.children[index] = new TrieNode();

            pCrawl = pCrawl.children[index];
        }

        // mark last node as leaf
        pCrawl.isEndOfWord = true;
    }

    // Returns true if key presents in trie, else false
    static boolean search(String key)
    {
        int level;
        int length = key.length();
        int index;
        TrieNode pCrawl = root;

        for (level = 0; level < length; level++)
        {
            index = key.charAt(level) - 'a';

            if (pCrawl.children[index] == null)
                return false;

            pCrawl = pCrawl.children[index];
        }

        return (pCrawl != null && pCrawl.isEndOfWord);
    }

    // Driver
    public static void main(String args[])
    {
        // Input keys (use only 'a' through 'z' and lower case)
        String keys[] = {"the", "a", "there", "answer", "any",
                "by", "bye", "their"};

        String output[] = {"Not present in trie", "Present in trie"};


        root = new TrieNode();

        // Construct trie
        int i;
        for (i = 0; i < keys.length ; i++)
            insert(keys[i]);

        // Search for different keys
        if(search("the") == true)
            System.out.println("the --- " + output[1]);
        else System.out.println("the --- " + output[0]);

        if(search("these") == true)
            System.out.println("these --- " + output[1]);
        else System.out.println("these --- " + output[0]);

        if(search("their") == true)
            System.out.println("their --- " + output[1]);
        else System.out.println("their --- " + output[0]);

        if(search("thaw") == true)
            System.out.println("thaw --- " + output[1]);
        else System.out.println("thaw --- " + output[0]);

    }
}
// This code is contributed by Sumit Ghosh

参考资料：

1. https://leetcode-cn.com/problems/implement-trie-prefix-tree/solution/shi-xian-trie-qian-zhui-shu-by-leetcode/

2. https://www.geeksforgeeks.org/trie-insert-and-search/