目录

概述

Trie树，又称为字典树、单词查找树或者前缀树，是一种用于快速检索的多叉数结构。例如，英文字母的字典树是26叉数，数字的字典树是10叉树。
Trie树的基本性质有三点，归纳为：

1. 根节点不包含字符，根节点外每一个节点都只包含一个字符。
2. 从根节点到某一节点，路径上经过的字符连接起来，为该节点对应的字符串。
3. 每个节点的所有子节点包含的字符串不相同。

Trie树基本实现

我们通过LeetCode的上的一道Trie题目来描述Trie树的实现。Implement Trie(Prefix Tree)。

定义Trie树节点

class TrieNode {
    boolean isWord;
    HashMap<Character, TrieNode> nexts;

    public TrieNode() {
        nexts = new HashMap<Character, TrieNode>();
    }
}

添加操作

我们向Trie树中添加一个字符串word，具体步骤如下：

    // Inserts a word into the trie.
    public void insert(String word) {
        char[] s = word.toCharArray();

        TrieNode p = root;
        int i = 0, n = s.length;

        // traverse existing
        while (i < n) {
            TrieNode next = p.nexts.get(s[i]);
            if (next != null) {
                p = next;
                i ++;
            } else {
                break;
            }
        }

        // append new nodes
        while (i < n) {
            TrieNode newTrie = new TrieNode();
            p.nexts.put(s[i], newTrie);
            p = newTrie;
            i ++;
        }

        // set word end
        p.isWord = true;
    }

查询word是否在Trie树中

    // Returns if the word is in the trie.
    public boolean search(String word) {
        TrieNode p = root;

        for (int i = 0; i < word.length(); i ++) {
            TrieNode child = p.nexts.get(word.charAt(i));
            if (child == null) {
                return false;
            }
            p = child;
        }

        return p.isWord;
    }

    // Returns if there is any word in the trie
    // that starts with the given prefix.
    public boolean startsWith(String prefix) {
        TrieNode p = root;

        for (int i = 0; i < prefix.length(); i ++) {
            TrieNode child = p.nexts.get(prefix.charAt(i));
            if (child == null) {
                return false;
            }
            p = child;
        }

        return true;
    }

AC完整代码

import java.util.HashMap;

class TrieNode {
    boolean isWord;
    HashMap<Character, TrieNode> nexts;

    public TrieNode() {
        nexts = new HashMap<Character, TrieNode>();
    }
}


public class Trie {
    private TrieNode root;

    public Trie() {
        root = new TrieNode();
    }

    // Inserts a word into the trie.
    public void insert(String word) {
        char[] s = word.toCharArray();

        TrieNode p = root;
        int i = 0, n = s.length;

        // traverse existing
        while (i < n) {
            TrieNode next = p.nexts.get(s[i]);
            if (next != null) {
                p = next;
                i ++;
            } else {
                break;
            }
        }

        // append new nodes
        while (i < n) {
            TrieNode newTrie = new TrieNode();
            p.nexts.put(s[i], newTrie);
            p = newTrie;
            i ++;
        }

        // set word end
        p.isWord = true;
    }

    // Returns if the word is in the trie.
    public boolean search(String word) {
        TrieNode p = root;

        for (int i = 0; i < word.length(); i ++) {
            TrieNode child = p.nexts.get(word.charAt(i));
            if (child == null) {
                return false;
            }
            p = child;
        }

        return p.isWord;
    }

    // Returns if there is any word in the trie
    // that starts with the given prefix.
    public boolean startsWith(String prefix) {
        TrieNode p = root;

        for (int i = 0; i < prefix.length(); i ++) {
            TrieNode child = p.nexts.get(prefix.charAt(i));
            if (child == null) {
                return false;
            }
            p = child;
        }

        return true;
    }

    public static void main(String[] args) {
        Trie trie = new Trie();
        trie.insert("keydsdsds");
        System.out.println(trie.startsWith("key"));
    }
}