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这个结点新节点的Base我置为0

传统的Trie实现简单,但是占用的空间实在是难以接受,特别是当字符集不仅限于英文26个字符的时候,爆炸起来的空间根本无法接受。

双数组Trie就是优化了空间的Trie树,原理本文就不讲了,请参考An Efficient
Implementation of Trie Structures,本程序的编写也是参考这篇论文的。

关于几点论文没有提及的细节和与论文不一一致的实现:

1.对于插入字符串,如果有一个字符串是另一个字符串的子串的话,我是将结束符也作为一条边,产生一个新的结点,这个结点新节点的Base我置为0

所以一个字符串结束也有2中情况:一个是Base值为负,存储剩余字符(可能只有一个结束符)到Tail数组;另一个是Base为0。

所以在查询的时候要考虑一下这两种情况

2.对于第一种冲突(论文中的Case
3),可能要将Tail中的字符串取出一部分,作为边放到索引中。论文是使用将尾串左移的方式,我的方式直接修改Base值,而不是移动尾串。

下面是java实现的代码,可以处理相同字符串插入,子串的插入等情况

/*  
 * Name:   Double Array Trie  
 * Author: Yaguang Ding  
 * Mail: dingyaguang117@gmail.com  
 * Blog: blog.csdn.net/dingyaguang117  
 * Date:   2012/5/21  
 * Note: a word ends may be either of these two case:  
 * 1. Base[cur_p] == pos  ( pos<0 and Tail[-pos] == 'END_CHAR' )  
 * 2. Check[Base[cur_p] + Code('END_CHAR')] ==  cur_p  
 */ 

import java.util.ArrayList;  
import java.util.HashMap;  
import java.util.Map;  
import java.util.Arrays;  

public class DoubleArrayTrie {  
    final char END_CHAR = '';  
    final int DEFAULT_LEN = 1024;  
    int Base[]  = new int [DEFAULT_LEN];  
    int Check[] = new int [DEFAULT_LEN];  
    char Tail[] = new char [DEFAULT_LEN];  
    int Pos = 1;  
    Map<Character ,Integer> CharMap = new HashMap<Character,Integer>();  
    ArrayList<Character> CharList = new ArrayList<Character>();  

    public DoubleArrayTrie()  
    {  
        Base[1] = 1;  

        CharMap.put(END_CHAR,1);  
        CharList.add(END_CHAR);  
        CharList.add(END_CHAR);  
        for(int i=0;i<26;++i)  
        {  
            CharMap.put((char)('a'+i),CharMap.size()+1);  
            CharList.add((char)('a'+i));  
        }  

    }  
    private void Extend_Array()  
    {  
        Base = Arrays.copyOf(Base, Base.length*2);  
        Check = Arrays.copyOf(Check, Check.length*2);  
    }  

    private void Extend_Tail()  
    {  
        Tail = Arrays.copyOf(Tail, Tail.length*2);  
    }  

    private int GetCharCode(char c)  
    {  
        if (!CharMap.containsKey(c))  
        {  
            CharMap.put(c,CharMap.size()+1);  
            CharList.add(c);  
        }  
        return CharMap.get(c);  
    }  
    private int CopyToTailArray(String s,int p)  
    {  
        int _Pos = Pos;  
        while(s.length()-p+1 > Tail.length-Pos)  
        {  
            Extend_Tail();  
        }  
        for(int i=p; i<s.length();++i)  
        {  
            Tail[_Pos] = s.charAt(i);  
            _Pos++;  
        }  
        return _Pos;  
    }  

    private int x_check(Integer []set)  
    {  
        for(int i=1; ; ++i)  
        {  
            boolean flag = true;  
            for(int j=0;j<set.length;++j)  
            {  
                int cur_p = i+set[j];  
                if(cur_p>= Base.length) Extend_Array();  
                if(Base[cur_p]!= 0 || Check[cur_p]!= 0)  
                {  
                    flag = false;  
                    break;  
                }  
            }  
            if (flag) return i;  
        }  
    }  

    private ArrayList<Integer> GetChildList(int p)  
    {  
        ArrayList<Integer> ret = new ArrayList<Integer>();  
        for(int i=1; i<=CharMap.size();++i)  
        {  
            if(Base[p]+i >= Check.length) break;  
            if(Check[Base[p]+i] == p)  
            {  
                ret.add(i);  
            }  
        }  
        return ret;  
    }  

    private boolean TailContainString(int start,String s2)  
    {  
        for(int i=0;i<s2.length();++i)  
        {  
            if(s2.charAt(i) != Tail[i+start]) return false;  
        }  

        return true;  
    }  
    private boolean TailMatchString(int start,String s2)  
    {  
        s2 += END_CHAR;  
        for(int i=0;i<s2.length();++i)  
        {  
            if(s2.charAt(i) != Tail[i+start]) return false;  
        }  
        return true;  
    }  

    public void Insert(String s) throws Exception  
    {  
        s += END_CHAR;  

        int pre_p = 1;  
        int cur_p;  
        for(int i=0; i<s.length(); ++i)  
        {  
            //获取状态位置  
            cur_p = Base[pre_p]+GetCharCode(s.charAt(i));  
            //如果长度超过现有,拓展数组  
            if (cur_p >= Base.length) Extend_Array();  

            //空闲状态  
            if(Base[cur_p] == 0 && Check[cur_p] == 0)  
            {  
                Base[cur_p] = -Pos;  
                Check[cur_p] = pre_p;  
                Pos = CopyToTailArray(s,i+1);  
                break;  
            }else 
            //已存在状态  
            if(Base[cur_p] > 0 && Check[cur_p] == pre_p)  
            {  
                pre_p = cur_p;  
                continue;  
            }else 
            //冲突 1:遇到 Base[cur_p]小于0的,即遇到一个被压缩存到Tail中的字符串  
            if(Base[cur_p] < 0 && Check[cur_p] == pre_p)  
            {  
                int head = -Base[cur_p];  

                if(s.charAt(i+1)== END_CHAR && Tail[head]==END_CHAR)    //插入重复字符串  
                {  
                    break;  
                }  

                //公共字母的情况,因为上一个判断已经排除了结束符,所以一定是2个都不是结束符  
                if (Tail[head] == s.charAt(i+1))  
                {  
                    int avail_base = x_check(new Integer[]{GetCharCode(s.charAt(i+1))});  
                    Base[cur_p] = avail_base;  

                    Check[avail_base+GetCharCode(s.charAt(i+1))] = cur_p;  
                    Base[avail_base+GetCharCode(s.charAt(i+1))] = -(head+1);  
                    pre_p = cur_p;  
                    continue;  
                }  
                else 
                {  
                    //2个字母不相同的情况,可能有一个为结束符  
                    int avail_base ;  
                    avail_base = x_check(new Integer[]{GetCharCode(s.charAt(i+1)),GetCharCode(Tail[head])});  

                    Base[cur_p] = avail_base;  

                    Check[avail_base+GetCharCode(Tail[head])] = cur_p;  
                    Check[avail_base+GetCharCode(s.charAt(i+1))] = cur_p;  

                    //Tail 为END_FLAG 的情况  
                    if(Tail[head] == END_CHAR)  
                        Base[avail_base+GetCharCode(Tail[head])] = 0;  
                    else 
                        Base[avail_base+GetCharCode(Tail[head])] = -(head+1);  
                    if(s.charAt(i+1) == END_CHAR)   
                        Base[avail_base+GetCharCode(s.charAt(i+1))] = 0;  
                    else 
                        Base[avail_base+GetCharCode(s.charAt(i+1))] = -Pos;  

                    Pos = CopyToTailArray(s,i+2);  
                    break;  
                }  
            }else 
            //冲突2:当前结点已经被占用,需要调整pre的base  
            if(Check[cur_p] != pre_p)  
            {  
                ArrayList<Integer> list1 = GetChildList(pre_p);  
                int toBeAdjust;  
                ArrayList<Integer> list = null;  
                if(true)  
                {  
                    toBeAdjust = pre_p;  
                    list = list1;  
                }  

                int origin_base = Base[toBeAdjust];  
                list.add(GetCharCode(s.charAt(i)));  
                int avail_base = x_check((Integer[])list.toArray(new Integer[list.size()]));  
                list.remove(list.size()-1);  

                Base[toBeAdjust] = avail_base;  
                for(int j=0; j<list.size(); ++j)  
                {  
                    //BUG   
                    int tmp1 = origin_base + list.get(j);  
                    int tmp2 = avail_base + list.get(j);  

                    Base[tmp2] = Base[tmp1];  
                    Check[tmp2] = Check[tmp1];  

                    //有后续  
                    if(Base[tmp1] > 0)  
                    {  
                        ArrayList<Integer> subsequence = GetChildList(tmp1);  
                        for(int k=0; k<subsequence.size(); ++k)  
                        {  
                            Check[Base[tmp1]+subsequence.get(k)] = tmp2;  
                        }  
                    }  

                    Base[tmp1] = 0;  
                    Check[tmp1] = 0;  
                }  

                //更新新的cur_p  
                cur_p = Base[pre_p]+GetCharCode(s.charAt(i));  

                if(s.charAt(i) == END_CHAR)  
                    Base[cur_p] = 0;  
                else 
                    Base[cur_p] = -Pos;  
                Check[cur_p] = pre_p;  
                Pos = CopyToTailArray(s,i+1);  
                break;  
            }  
        }  
    }  

    public boolean Exists(String word)  
    {  
        int pre_p = 1;  
        int cur_p = 0;  

        for(int i=0;i<word.length();++i)  
        {  
            cur_p = Base[pre_p]+GetCharCode(word.charAt(i));  
            if(Check[cur_p] != pre_p) return false;  
            if(Base[cur_p] < 0)  
            {  
                if(TailMatchString(-Base[cur_p],word.substring(i+1)))  
                    return true;  
                return false;  
            }  
            pre_p = cur_p;  
        }  
        if(Check[Base[cur_p]+GetCharCode(END_CHAR)] == cur_p)  
            return true;  
        return false;  
    }  

    //内部函数,返回匹配单词的最靠后的Base index,  
    class FindStruct  
    {  
        int p;  
        String prefix="";  
    }  
    private FindStruct Find(String word)  
    {  
        int pre_p = 1;  
        int cur_p = 0;  
        FindStruct fs = new FindStruct();  
        for(int i=0;i<word.length();++i)  
        {  
            // BUG  
            fs.prefix += word.charAt(i);  
            cur_p = Base[pre_p]+GetCharCode(word.charAt(i));  
            if(Check[cur_p] != pre_p)  
            {  
                fs.p = -1;  
                return fs;  
            }  
            if(Base[cur_p] < 0)  
            {  
                if(TailContainString(-Base[cur_p],word.substring(i+1)))  
                {  
                    fs.p = cur_p;  
                    return fs;  
                }  
                fs.p = -1;  
                return fs;  
            }  
            pre_p = cur_p;  
        }  
        fs.p =  cur_p;  
        return fs;  
    }  

    public ArrayList<String> GetAllChildWord(int index)  
    {  
        ArrayList<String> result = new ArrayList<String>();  
        if(Base[index] == 0)  
        {  
            result.add("");  
            return result;  
        }  
        if(Base[index] < 0)  
        {  
            String r="";  
            for(int i=-Base[index];Tail[i]!=END_CHAR;++i)  
            {  
                r+= Tail[i];  
            }  
            result.add(r);  
            return result;  
        }  
        for(int i=1;i<=CharMap.size();++i)  
        {  
            if(Check[Base[index]+i] == index)  
            {  
                for(String s:GetAllChildWord(Base[index]+i))  
                {  
                    result.add(CharList.get(i)+s);  
                }  
                //result.addAll(GetAllChildWord(Base[index]+i));  
            }  
        }  
        return result;  
    }  

    public ArrayList<String> FindAllWords(String word)  
    {  
        ArrayList<String> result = new ArrayList<String>();  
        String prefix = "";  
        FindStruct fs = Find(word);  
        int p = fs.p;  
        if (p == -1) return result;  
        if(Base[p]<0)  
        {  
            String r="";  
            for(int i=-Base[p];Tail[i]!=END_CHAR;++i)  
            {  
                r+= Tail[i];  
            }  
            result.add(fs.prefix+r);  
            return result;  
        }  

        if(Base[p] > 0)  
        {  
            ArrayList<String> r =  GetAllChildWord(p);  
            for(int i=0;i<r.size();++i)  
            {  
                r.set(i, fs.prefix+r.get(i));  
            }  
            return r;  
        }  

        return result;  
    }  

}

测试代码:

import java.io.BufferedReader;  
import java.io.FileInputStream;  
import java.io.IOException;  
import java.io.InputStream;  
import java.io.InputStreamReader;  
import java.util.ArrayList;  
import java.util.Scanner;  

import javax.xml.crypto.Data;  

public class Main {  

    public static void main(String[] args) throws Exception {  
        ArrayList<String> words = new ArrayList<String>();  
        BufferedReader reader = new BufferedReader(new InputStreamReader(new FileInputStream("E:/兔子的试验学习中心[课内]/ACM大赛/ACM第四届校赛/E命令提示/words3.dic")));  
        String s;  
        int num = 0;  
        while((s=reader.readLine()) != null)  
        {  
            words.add(s);  
            num ++;  
        }  
        DoubleArrayTrie dat = new DoubleArrayTrie();  

        for(String word: words)  
        {  
            dat.Insert(word);  
        }  

        System.out.println(dat.Base.length);  
        System.out.println(dat.Tail.length);  

        Scanner sc = new Scanner(System.in);  
        while(sc.hasNext())  
        {  
            String word = sc.next();  
            System.out.println(dat.Exists(word));  
            System.out.println(dat.FindAllWords(word));  
        }  

    }  

}

下面是测试结果,构造6W英文单词的DAT,大概需要20秒

我增长数组的时候是每次长度增加到2倍,初始1024

Base和Check数组的长度为131072

Tail的长度为262144

图片 1

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