算法——字符串匹配算法自己有限的驾驶机器

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/

/article/3551273.html