给定文本txt [0..n-1]和模式pat [0..m-1] ，编写一个函数search(char pat []，char txt []) ，将所有出现的pat []都打印在txt中[] 。您可以假设n> m。
例子：
输入：txt [] =“这是一个测试文本” pat [] =“ TEST”输出：在索引10处找到的模式输入：txt [] =“ AABAACAADAABAABA” pat [] =“ AABA”输出：在索引0处找到的模式在索引9处找到的模式在索引12处找到的模式
模式搜索是计算机科学中的一个重要问题。当我们在记事本/单词文件或浏览器或数据库中搜索字符串时，将使用模式搜索算法来显示搜索结果。
在之前的文章中，我们讨论了以下算法：
天真的算法
KMP算法
Rabin Karp算法
在这篇文章中，我们将讨论基于有限自动机(FA)的模式搜索算法。在基于FA的算法中，我们预处理图案并构建一个表示有限自动机的2D数组。 FA的构建是该算法的主要难题。一旦建立了FA，搜索就很简单。在搜索中，我们只需要从自动机的第一个状态和文本的第一个字符。在每一步中，我们都会考虑文本的下一个字符，在已构建的FA中查找下一个状态，然后移至新状态。如果我们达到最终状态，则可以在文本中找到模式。搜索过程的时间复杂度为O(n)。
在讨论FA构造之前，让我们看一下以下ACACAGA模式的FA。 
上图代表ACACAGA模式的图形和表格表示。
FA中的状态数将为M + 1，其中M是模式的长度。构造FA的主要目的是为每个可能的字符从当前状态获取下一个状态。给定一个字符x和一个状态k，我们可以通过考虑字符串“ pat [0..k-1] x”来获得下一个状态，该字符串基本上是模式字符pat [0]，pat [1]…pat [ k-1]和字符x。想法是获得给定模式的最长前缀的长度，以使该前缀也为“ pat [0..k-1] x”的后缀。长度的值给我们下一个状态。例如，让我们看看如何从上图中的当前状态5和字符“ C”中获取下一个状态。我们需要考虑字符串“ pat [0..4] C”，即“ ACACAC”。模式的最长前缀的长度(使前缀为“ ACACAC”的后缀)为4(“ ACAC”)。因此，字符“ C”的下一个状态(从状态5开始)为4。
在以下代码中，computeTF()构造FA。 computeTF()的时间复杂度为O(m ^ 3 * NO_OF_CHARS)，其中m是模式的长度，NO_OF_CHARS是字母的大小(模式和文本中可能的字符总数)。该实现会尝试从可能为“ pat [0..k-1] x”后缀的最长前缀开始。在O(m * NO_OF_CHARS)中有更好的构造FA的实现(提示：我们可以在KMP算法中使用类似lps数组的构造)。我们在下一篇关于模式搜索的文章中介绍了更好的实现。
C
// C program for Finite Automata Pattern searching
// Algorithm
#include
#include
#define NO_OF_CHARS 256
int getNextState(char *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;
// ns stores the result which is next state
int ns, i;
// 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 represents4
Finite Automata for a given pattern */
void computeTF(char *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)
TF[state][x] = getNextState(pat, M, state, x);
}
/* Prints all occurrences of pat in txt */
void search(char *pat, char *txt)
{
int M = strlen(pat);
int N = strlen(txt);
int TF[M+1][NO_OF_CHARS];
computeTF(pat, M, TF);
// Process txt over FA.
int i, state=0;
for (i = 0; i < N; i++)
{
state = TF[state][txt[i]];
if (state == M)
printf ("\n Pattern found at index %d",
i-M+1);
}
}
// Driver program to test above function
int main()
{
char *txt = "AABAACAADAABAAABAA";
char *pat = "AABA";
search(pat, txt);
return 0;
} CPP
// CPP program for Finite Automata Pattern searching
// Algorithm
#include
using namespace std;
#define NO_OF_CHARS 256
int getNextState(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;
// ns stores the result which is next state
int ns, i;
// 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 represents4
Finite Automata for a given pattern */
void computeTF(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)
TF[state][x] = getNextState(pat, M, state, x);
}
/* Prints all occurrences of pat in txt */
void search(string pat, string txt)
{
int M = pat.size();
int N = txt.size();
int TF[M+1][NO_OF_CHARS];
computeTF(pat, M, TF);
// Process txt over FA.
int i, state=0;
for (i = 0; i < N; i++)
{
state = TF[state][txt[i]];
if (state == M)
cout<<" Pattern found at index "<< i-M+1< Java
// Java program for Finite Automata Pattern
// searching Algorithm
class GFG {
static int NO_OF_CHARS = 256;
static int getNextState(char[] 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;
// ns stores the result which is next state
int ns, i;
// 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 */
static void computeTF(char[] pat, int M, int TF[][])
{
int state, x;
for (state = 0; state <= M; ++state)
for (x = 0; x < NO_OF_CHARS; ++x)
TF[state][x] = getNextState(pat, M, state, x);
}
/* Prints all occurrences of pat in txt */
static void search(char[] pat, char[] txt)
{
int M = pat.length;
int N = txt.length;
int[][] TF = new int[M+1][NO_OF_CHARS];
computeTF(pat, M, TF);
// Process txt over FA.
int i, state = 0;
for (i = 0; i < N; i++)
{
state = TF[state][txt[i]];
if (state == M)
System.out.println("Pattern found "
+ "at index " + (i-M+1));
}
}
// Driver code
public static void main(String[] args)
{
char[] pat = "AABAACAADAABAAABAA".toCharArray();
char[] txt = "AABA".toCharArray();
search(txt,pat);
}
}
// This code is contributed by debjitdbb.Python
# Python program for Finite Automata
# Pattern searching Algorithm
NO_OF_CHARS = 256
def getNextState(pat, M, state, x):
'''
calculate the next state
'''
# If the character c is same as next character
# in pattern, then simply increment state
if state < M and x == ord(pat[state]):
return state+1
i=0
# 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 in range(state,0,-1):
if ord(pat[ns-1]) == x:
while(iC#
// C# program for Finite Automata Pattern
// searching Algorithm
using System;
class GFG
{
public static int NO_OF_CHARS = 256;
public static int getNextState(char[] 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 && (char)x == pat[state])
{
return state + 1;
}
// ns stores the result
// which is next state
int ns, i;
// 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] == (char)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 */
public static void computeTF(char[] pat,
int M, int[][] TF)
{
int state, x;
for (state = 0; state <= M; ++state)
{
for (x = 0; x < NO_OF_CHARS; ++x)
{
TF[state][x] = getNextState(pat, M,
state, x);
}
}
}
/* Prints all occurrences of
pat in txt */
public static void search(char[] pat,
char[] txt)
{
int M = pat.Length;
int N = txt.Length;
int[][] TF = RectangularArrays.ReturnRectangularIntArray(M + 1,
NO_OF_CHARS);
computeTF(pat, M, TF);
// Process txt over FA.
int i, state = 0;
for (i = 0; i < N; i++)
{
state = TF[state][txt[i]];
if (state == M)
{
Console.WriteLine("Pattern found " +
"at index " + (i - M + 1));
}
}
}
public static class RectangularArrays
{
public static int[][] ReturnRectangularIntArray(int size1,
int size2)
{
int[][] newArray = new int[size1][];
for (int array1 = 0; array1 < size1; array1++)
{
newArray[array1] = new int[size2];
}
return newArray;
}
}
// Driver code
public static void Main(string[] args)
{
char[] pat = "AABAACAADAABAAABAA".ToCharArray();
char[] txt = "AABA".ToCharArray();
search(txt,pat);
}
}
// This code is contributed by Shrikant13输出：
Pattern found at index 0
Pattern found at index 9
Pattern found at index 13
参考：
Thomas H. Cormen，Charles E. Leiserson，Ronald L.Rivest，Clifford Stein的算法简介