Trie树(字典树)的介绍及Java实现

Z时代
2024-01-10
分类：IT

简介

Trie树，又称为前缀树或字典树，是一种有序树，用于保存关联数组，其中的键通常是字符串。与二叉查找树不同，键不是直接保存在节点中，而是由节点在树中的位置决定。一个节点的所有子孙都有相同的前缀，也就是这个节点对应的字符串，而根节点对应空字符串。

它的主要特点如下：

根节点不包含字符，除根节点外的每一个节点都只包含一个字符。

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。

每个节点的所有子节点包含的字符都不相同。

如下是一棵典型的Trie树:

Trie的来源是Retrieval,它常用于前缀匹配和词频统计。可能有人要说了，词频统计简单啊，一个hash或者一个堆就可以搞定，但问题来了，如果内存有限呢？还能这么玩吗？所以这里我们就可以用trie树来压缩下空间，因为公共前缀都是用一个节点保存的。

1、定义

这里为了简化，只考虑了26个小写字母。

首先是节点的定义:


public class TrieNode {
 public TrieNode[] children;
 public char data;
 public int freq;
 public TrieNode() {
 //因为有26个字母
 children = new TrieNode[26];
 freq = 0;
 }
}

然后是Trie树的定义:


public class TrieTree {
 private TrieNode root;
 public TrieTree(){
 root=new TrieNode();
 }
 ...
}

2、插入

由于是26叉树，故可通过charArray[index]-‘a';来得知字符应该放在哪个孩子中。


 public void insert(String word){
 if(TextUtils.isEmpty(word)){
  return;
 }
 insertNode(root,word.toCharArray(),0);
 }
 private static void insertNode(TrieNode rootNode,char[]charArray,int index){
 int k=charArray[index]-'a';
 if(k<0||k>25){
  throw new RuntimeException("charArray[index] is not a alphabet!");
 }
 if(rootNode.children[k]==null){
  rootNode.children[k]=new TrieNode();
  rootNode.children[k].data=charArray[index];
 }
 if(index==charArray.length-1){
  rootNode.children[k].freq++;
  return;
 }else{
  insertNode(rootNode.children[k],charArray,index+1);
 }
 }

3、移除节点

移除操作中，需要对词频进行减一操作。


 public void remove(String word){
 if(TextUtils.isEmpty(word)){
  return;
 }
 remove(root,word.toCharArray(),0);
 }
 private static void remove(TrieNode rootNode,char[]charArray,int index){
 int k=charArray[index]-'a';
 if(k<0||k>25){
  throw new RuntimeException("charArray[index] is not a alphabet!");
 }
 if(rootNode.children[k]==null){
  //it means we cannot find the word in this tree
  return;
 }
 if(index==charArray.length-1&&rootNode.children[k].freq >0){
  rootNode.children[k].freq--;
 }
 remove(rootNode.children[k],charArray,index+1);
 }

4、查找频率


 public int getFreq(String word){
 if(TextUtils.isEmpty(word)){
  return 0;
 }
 return getFreq(root,word.toCharArray(),0);
 }
 private static int getFreq(TrieNode rootNode,char[]charArray,int index){
 int k=charArray[index]-'a';
  if(k<0||k>25){
  throw new RuntimeException("charArray[index] is not a alphabet!");
 }
 //it means the word is not in the tree
 if(rootNode.children[k]==null){
  return 0;
 }
 if(index==charArray.length-1){
  return rootNode.children[k].freq;
 }
 return getFreq(rootNode.children[k],charArray,index+1);
 }

5、测试

测试代码如下:


 public static void test(){
 TrieTree trieTree=new TrieTree();
 String sourceStr="Democratic presumptive nominee Hillary Clintons campaign posed pounced on Trumps assertion that British term monetary turmoil might benefit his business venture in Scotland";
 //String sourceStr="the that";
 sourceStr=sourceStr.toLowerCase();
 String[]strArray=sourceStr.split(" ");
 for(String str:strArray){
  trieTree.insert(str);
 }
 String sourceStr2="Every president is tested by world events But Donald Trump thinks about how is his golf resort can profit from that";
 sourceStr2=sourceStr2.toLowerCase();
 String[]strArray2=sourceStr2.split(" ");
 for(String str:strArray2){
  trieTree.insert(str);
 }
 BinaryTree.print("frequence of 'that':"+trieTree.getFreq("that"));
 BinaryTree.print("\nfrequence of 'donald':"+trieTree.getFreq("donald"));
 trieTree.remove("that");
 BinaryTree.print("\nafter remove 'that' once,freq of 'that':"+trieTree.getFreq("that"));
 trieTree.remove("that");
 BinaryTree.print("\nafter remove 'that' twice,freq of 'that':"+trieTree.getFreq("that"));
 trieTree.remove("donald");
 BinaryTree.print("\nafter remove 'donald' once,freq of 'donald':"+trieTree.getFreq("donald"));
 BinaryTree.reallyStartPrint();
 }