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:
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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:
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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。
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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。
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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
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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:
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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(); } |
测试结果如下:
总结
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