Patricia前缀树(Patricia Trie)及其基本操作

Patricia前缀树(Patricia Trie)及其基本操作

Trie是一种字典树，用于存储文本字符，并利用了单词之间共享前缀的特点，所以叫做前缀树。不像平衡BST，Trie的高度只与最长的文本串的长度s有关系，而与单词的数量n无关。Trie的节点分两种：内部结点和叶子结点，内部结点用来存储单词key的成分字母，如果设字母表大小为d，那么每个内部结点最多有d个孩子，叶子结点存储该单词作为key的数据内容(data)。注意内部结点和叶子结点并不是互斥的，一个内部结点本身可以有儿子结点，同时它也可以是一个叶子结点。例如：




这里ab结点本身就是叶子结点，因为它以#结束符标记了，同时它有两个儿子结点a和c，c是叶子结点。

如果一颗Trie中有很多单词只有一个儿子结点，可以用Patricia Trie（Linux内核中叫做Radix Tree）压缩存储。由于#结束符标记被看作是一个叶子结点，那么一颗Patricia Trie的任何内部结点有2个或以上的孩子结点。

Patricia Trie的基本操作包括：插入、删除和查询。插入操作可能会涉及到split（拆分），删除操作可能会涉及到merge（合并）。基于Patricia Trie的基本性质，split和merge操作都是局部的，这样实现起来比较简单。详细内容请参考以下代码：

 

实现：

import java.util.LinkedList; import java.util.List; /** * Patricia Trie * * Copyright (c) 2011 ljs (http://blog.csdn.net/ljsspace/) * Licensed under GPL (http://www.opensource.org/licenses/gpl-license.php) * * @author ljs * 2011-06-27 * */ public class PatriciaTrie { private class PatriciaTrieNode { private String key; private Integer data; private List children = new LinkedList(); //use "#" for terminal char private boolean terminal; public PatriciaTrieNode(){ this.key = ""; } public PatriciaTrieNode(String key){ this.key = key; } public String toString(){ return this.key + (this.terminal?"#":"") + "(" + children.size() +")"; } } private PatriciaTrieNode root; //return the value of the external node if found; //otherwise, return null public Integer find(String key){ if(key == null || key.length() == 0) return null; if(root==null){ return null; }else{ return find(root,key); } } private Integer find(PatriciaTrieNode currNode,String key) { for(int i=0;ichild.key.length()){ //e.g. child="ab#", key="abc" // ab# // / / // a c# String subkey = key.substring(j); //c //recursion return find(child,subkey); }else{ //key.length()=1 //e.g. child="ab#", key="ab", currNode="a" // a# // / // ab# // / // f# child.terminal = false; //merge node for child if(child.children.size()==1){ PatriciaTrieNode singleChild = child.children.get(0); //f# child.key += singleChild.key; child.data = singleChild.data; child.terminal = singleChild.terminal; //Note: singleChild may not be external node child.children = singleChild.children; } } }else{ //e.g. child="ab", key="ab" // ab // / / // e f throw new Exception("No such key is found for removal!"); } }else if(key.length()>child.key.length()){ //e.g. child="ab#", key="abc" // ab# // / / // a c# String subkey = key.substring(j); //c //recursion delete(child,subkey); }else{ //key.length() / | / // e f insert "c" c# e f PatriciaTrieNode node = new PatriciaTrieNode(key); currNode.children.add(i,node); node.terminal = true; node.data = value; done = true; break; }else{ //key.charAt(0)>child.key.charAt(0) //don't forget to add the largest new key after iterating all children continue; } }else{//current child's key partially matches with the new key; 0 / / // e f insert "ab" e f child.terminal = true; child.data = value; } }else if(key.length()>child.key.length()){ //e.g. child="ab#" // ab# ab# // / / ==========> / | / // e f insert "abc" c# e f String subkey = key.substring(j); //recursion insert(child,subkey,value); }else{ //key.length() / // e f insert "ab" c# // / / // e f String childSubkey = child.key.substring(j); //c PatriciaTrieNode subChildNode = new PatriciaTrieNode(childSubkey); subChildNode.terminal = child.terminal; subChildNode.data = child.data; subChildNode.children = child.children; //inherited from parent child.key = key; //ab child.terminal = true; //ab# child.data = value; child.children = new LinkedList(); child.children.add(subChildNode); } }else{//0 / / // e f insert "abd" c# d# // / / // e f //split at j String childSubkey = child.key.substring(j); //c String subkey = key.substring(j); //d PatriciaTrieNode subChildNode = new PatriciaTrieNode(childSubkey); subChildNode.terminal = child.terminal; subChildNode.data = child.data; subChildNode.children = child.children; //inherited from parent //update child's key child.key = child.key.substring(0,j); //child is not terminal now due to split, it is inherited by subChildNode child.terminal = false; //Note: no need to merge subChildNode PatriciaTrieNode node = new PatriciaTrieNode(subkey); node.terminal = true; node.data = value; child.children = new LinkedList(); if(subkey.charAt(0)

 

测试输出：

| |-ab[1]# |--c[2]# |--d[4]# |---e[3]# |-dc |--a[8]# |--e[5]# |---g[7]# |---h[6]# |--f[9]# |-gh[11]# |--k[10]# |-m |--g[15]# |--n[14]# |---s[12]# |---t[13]# Found no such key: "dc" Found no such key: "d" Found key "ab" at: 1 Found no such key: "ef" Found no such key: "zz" Found no such key: "dk" Found key "dcf" at: 9 Found no such key: "dck" After delete key: abd | |-ab[1]# |--c[2]# |--de[3]# |-dc |--a[8]# |--e[5]# |---g[7]# |---h[6]# |--f[9]# |-gh[11]# |--k[10]# |-m |--g[15]# |--n[14]# |---s[12]# |---t[13]# **************************** | |-b |--e |---ar[1]# |---ll[2]# |--id[3]# |--u |---ll[4]# |---y[5]# |-s |--ell[6]# |--to |---ck[7]# |---p[8]# **************************** | |-a |--l |---l[3]# |----o |-----t[1]# |-----y[2]# |---oe[4]# |--n[6]# |---t[5]# |--re[7]# |--te[8]# |-be[9]# **************************** | |-e[7]# |-i |--mize[3]# |--nimize[1]# |--ze[5]# |-mi |--nimize[0]# |--ze[4]# |-nimize[2]# |-ze[6]# Found key "ize" at: 5 Found no such key: "zee" Found key "mize" at: 4 After delete key: mize | |-e[7]# |-i |--mize[3]# |--nimize[1]# |--ze[5]# |-minimize[0]# |-nimize[2]# |-ze[6]#