数据结构——Trie 字典树 前缀树

一、什么是Trie

Trie不同于二分搜索树、堆、线段树等二叉树结构，Trie是一个多叉树。使用场景：通讯录高效搜索，专为处理字符串设计的。

比如字典中有n条数据，如果使用树结构，查询的时间复杂度是O(logn)，如果有100万条数据的话，logn大约是20，如果有1亿条数据的话，logn大约是30(参考2的N次方计算器)

如果使用Trie这种数据结构，查询每条数据的时间复杂度和字典中一共有多少条数据没有关系！是不是屌炸天呢？

Trie查询的时间复杂度与查询的字符长度有关，时间复杂度为：O(w)，w为单词的长度。

二、构建一个Trie

Trie的基本结构与添加方法：

public class Trie {
    private class Node {
        public boolean isWord;
        public TreeMap<Character, Node> next;

        public Node(boolean isWord) {
            this.isWord = isWord;
            next = new TreeMap<>();
        }

        public Node() {
            this(false);
        }
    }

    private Node root;
    private int size;

    public Trie() {
        root = new Node();
        size = 0;
    }

    //获得Trie中存储的单词数量
    public int getSize(){
        return this.size;
    }

    //传递入一个字符串(单词),拆分成一个个的字符char
    public void add(String word){
        Node cur = root;
        for(int i = 0 ; i < word.length() ; i ++){
            char c = word.charAt(i);
            //判断当前的cur节点下一节点隐射中是否有指向c的节点
            if(cur.next.get(c) == null)
                cur.next.put(c,new Node());
            //循环结束后cur来到字符串最后一个字符所处节点，但并不一定是叶子节点,如pan和panda
            cur =  cur.next.get(c);
        }
        //如果已经存在panda,则在add(pan)时候,只是走了3遍cur =  cur.next.get(c);
        //不重复添加元素
        if(!cur.isWord) {
            cur.isWord = true;
            size++;
        }
    }
}

判断某个单词在Trie中是否存在

    public boolean contains(String word){
        Node cur = root;
        for(int i = 0 ; i < word.length() ; i++){
            char c = word.charAt(i);
            if(cur.next.get(c) == null)
                return false;
            cur = cur.next.get(c);
        }
        //循环结束后则表示到达了单词结尾的字符
        return cur.isWord;
    }

三、Trie字典树的前缀查询

    //Trie字典树的前缀查询
    public boolean isPrefix(String prefix){
        Node cur = root;
        for(int i = 0 ; i < prefix.length() ; i++){
            char c = prefix.charAt(i);
            if(cur.next.get(c) == null)
                return false;
           cur = cur.next.get(c);
        }
        return true;
    }

四、Trie字典树搜索和正则匹配

对应Leetcode  211题添加与搜索单词 

参考模型：

import java.util.TreeMap;

/**
 * Your WordDictionary object will be instantiated and called as such:
 * WordDictionary obj = new WordDictionary();
 * obj.addWord(word);
 * boolean param_2 = obj.search(word);
 */
class WordDictionary {

    private class Node{
        public boolean isWord;
        public TreeMap<Character,Node> next;

        public Node(boolean isWord){
            this.isWord = isWord;
            next = new TreeMap<>();
        }

        public Node(){
            this(false);
        }
    }
    private Node root;

    /** Initialize your data structure here. */
    public WordDictionary() {
        root = new Node();
    }
    
    /** Adds a word into the data structure. */
    public void addWord(String word) {
        Node cur = root;
        for(int i = 0 ; i < word.length() ; i++){
            char c = word.charAt(i);
            if(cur.next.get(c) == null)
                cur.next.put(c,new Node());
            cur = cur.next.get(c);
        }
        cur.isWord = true;
    }
    
    /** Returns if the word is in the data structure. A word could contain the dot character '.' to represent any one letter. */
    public boolean search(String word) {
        return match(root,word,0);
    }

    private boolean match(Node node, String word, int index) {
        if(index == word.length())
            return node.isWord;
        char c = word.charAt(index);
        if(c!='.') {
            if (node.next.get(c) == null)
                return false;
            return match(node.next.get(c),word,index + 1);
        }else{
            for(char nextChar : node.next.keySet())
                if(match(node.next.get(nextChar),word,index + 1))
                    return true;
            return false;
        }
    }
}

五、Letcode键值映射——前缀开头的键的值的总和

对应Letcode  667题  键值映射

代码实现：

class MapSum {

    private class Node{
        private int value;
        private TreeMap<Character,Node> next;

        public Node(int value){
            this.value = value;
            next = new TreeMap<>();
        }

        public Node(){
            this(0);
        }
    }

    private Node root;
    /** Initialize your data structure here. */
    public MapSum() {
        root = new Node();
    }
    
    public void insert(String word, int val) {
        Node cur = root;
        for(int i = 0 ; i < word.length() ; i++){
            char c = word.charAt(i);
            if(cur.next.get(c) == null)
                cur.next.put(c,new Node());
            cur = cur.next.get(c);
        }
        cur.value = val;
    }
    
    public int sum(String prefix) {
        Node cur = root;
        for(int i = 0 ; i < prefix.length() ; i++){
            char c = prefix.charAt(i);
            if(cur.next.get(c) == null)
                return 0;
            cur = cur.next.get(c);
        }
       return sum(cur);
    }

    private int sum(Node node) {
        int res = node.value;
        for(char c : node.next.keySet())
            res += sum(node.next.get(c));
        return res;
    }
}