前言
上篇文章介绍《Rabin-Karp字符串匹配算法》。这里介绍有限自己主动机(Finite Automata)字符串匹配算法，有限自己主动机(Finite Automata)字符串匹配算法最基本的是计算出转移函数。
即给定一个当前状态k和一个字符x。计算下一个状态；计算方法为：找出模式pat的最长前缀prefix。同一时候也是pat[0...k-1]x(注意：字符串下标是从0開始)的后缀，则prefix的长度即为下一个状态。匹配的过程是比較输入文本子串和模式串的状态值，若相等则存在。若不想等则不存在。
有关理论知识參考《算法导论》，这里不正确理论知识进行解说。
有限自己主动机字符串匹配算法
若模式串pat的长度为m。则状态值为0-m，即有m+1个状态，初始状态为0。当中numbers=NO_OF_CHARS为输入字符表的个数，从下面的源代码能够知道，计算转移函数(即预处理)的时间复杂度为
，匹配时间复杂度为
。
该算法能够依据后面介绍的KMP算法进行改进，对求解转移函数的过程进行改进能够得到比較好的时间复杂度
。
下面是模式串为P=abababaca的自己主动机运行过程
源代码实现
#include<iostream>
#include<string>
using namespace std;
const int NO_OF_CHARS = 256;//the numbers of input alphabet
int getNextState(const string &pat, int M, int state, int x)
{
// If the character c is same as next character in pattern,
// then simply increment state
if (state < M && x == pat[state])
return state+1;
int ns, i; // ns stores the result which is next state
// ns finally contains the longest prefix which is also suffix
// in "pat[0..state-1]c"
// Start from the largest possible value and stop when you find
// a prefix which is also suffix
for (ns = state; ns > 0; ns--)
{
if(pat[ns-1] == x)
{
for(i = 0; i < ns-1; i++)
{
if (pat[i] != pat[state-ns+1+i])
break;
}
if (i == ns-1)
return ns;
}
}
return 0;
}
/* This function builds the TF table which represents Finite Automata for a
given pattern */
void compute_Transition_Function(const string &pat, int M, int TF[][NO_OF_CHARS])
{
int state, x;
for (state = 0; state <= M; ++state)
for (x = 0; x < NO_OF_CHARS; ++x)//for each charater c in the inout alphabet table
TF[state][x] = getNextState(pat, M, state, x);
}
/* Prints all occurrences of pat in txt */
void Finite_Automata_search(const string &pat, const string &txt)
{
int M = pat.length();
int N = txt.length();
int TF_len = M+1;
//this is supported by C++11
int TF[TF_len][NO_OF_CHARS];//the state of transform table, stores the states.
compute_Transition_Function(pat, M, TF);//compute the state of Transition Function
// Process txt over FA.
int state=0;//inite the state
for (int i = 0; i < N; i++)
{
state = TF[state][txt[i]];
if (state == M)
cout<<"patterb found at index is:"<<i-M+1<<endl;
}
}
int main()
{
string txt = "Finite Automata Algorithm: Finite Automata";
string pat = "Auto";
Finite_Automata_search(pat, txt);
system("pause");
return 0;
}
參考资料：
《算法导论》
http://www.geeksforgeeks.org/searching-for-patterns-set-5-finite-automata/
http://my.oschina.net/amince/blog/182210
本文转自mfrbuaa博客园博客，原文链接：http://www.cnblogs.com/mfrbuaa/p/4914074.html，如需转载请自行联系原作者
