/**
* KMP algorithm is a famous way to find a substring from a text. To understand its‘ capacity, we should acquaint onself with the normal algorithm.
*/
/**
* simple algorithm
*
* workflow:
* (say, @ct means for currently position of search text)
*
* step 1: match text from index @ct with pattern.
* step 2: if success, step to next character. or,
*
* The most straightforward algorithm is to look for a character match at successive values of index @ct, the position in the string being searched, i.e. S[ct]. If the index
* if the index m reaches the end of the string, then there is no match. In which case the search is said to "fail". At each position m, the algorithm first check whether
* S[ct] and P[0] is equal. If success, check the rest of characters. if fail, check next position, ct+1;
*
* put all of detail into this code.
*/
int work( char *s, char *pat)
{
int ct = 0;
int mi = 0;
while( s[ct]!='\0' )
{
while( s[ct + mi]==pat[mi])
{
mi++;
if( pat[mi]=='\0')
return ct;
}
ct++;
}
return -1;
}
/**
* It‘s simple and have a good performance usually. But thing will become terrible when we deal with some special string. Just like:
*
* S[m] = 00000000....00000001
* P[n] = 000001
* wow, the result is really awful. In conclusion, if we take a comparison operation as the basic element, we could get the time complexity.At ideal case,
* T(m,n) = O( m+n)
*
* that is reasonable.But at worst case,
* T(m,n) = O( m*n)
*
* Now , It‘s time to KMP show its excellent performance.
*/
/**
* KMP
* KMP is a algorithm for search a substring from a string. At case above, the situation become awful, because of some special situation: we always
* be told we are wrong when we almost success. There are so many traps.
*
* Q: Could I do something with those traps?
*/
/*
* Of course, we can. Image this, you encounter a trap when you check substring from position S[ct], and you realize this when you match S[ct+m] with P[m].
* At this moment ,except for fail, we also know another thing.
*
* S[ct]S[ct+1]....S[ct+m-1] = P[0]P[1]....p[m-1]
*
* Have you find anything ?
* All of traps must be the substring of the pattern and must be started by index 0. That‘s means we can do some funny thing , since we know what we will face. Now,
* pick a trap up to analysis. In the case above
*
* P[0]P[1]P[2]....P[m].
*
* what we are interested is whether a really substring is remain under this.
*
* Q: How can we know that?
*/
/*
* if a really substring is remain under this substring, It must have
*
* P[0]P[1]P[2]....P[n] = P[m-n]...P[m-1]P[m] n<m
* (this is the key point for the KMP algorithm.)
*
* Of course, some other false one may meet with this formula. But who care about it, we just want to find the doubtful one. So , by the help of this conclusion,
* we could know whether a doubtful substring is here and where is it. Then if we know where is the doubtful substring, we could skip some undoubtful one.That‘s all.
*/
/*
* Here is a examples for KMP.
*/
#include <stdio.h>
#include <iostream>
typedef int INDEX;
class KMP {
public:
KMP( );
~KMP( );
bool set( char *s, char *patt );
bool work( void);
bool showPT( void);
bool show( void);
private:
/*
* initialize the table of partial match string.
*/
bool createPT( void);
bool computePTV( INDEX mmi);
/*
* text string
*/
char *str;
/*
* pattern string
*/
char *pattern;
/*
* the length of pattern
*/
int p_len;
/*
* a pointer for the table of
*/
int *ptab;
INDEX ip; //index position of the string
};
KMP::KMP( )
{
this->str = NULL;
this->pattern = NULL;
this->p_len = 0;
this->ptab = NULL;
this->ip = -1;
}
KMP::~KMP()
{
if( this->ptab!=NULL)
{
delete []this->ptab;
this->ptab = NULL;
}
}
bool KMP::set(char * s,char * patt)
{
this->str = s;
this->pattern = patt;
this->ip = -1;
this->p_len = strlen( this->pattern);
this->ptab = new int[this->p_len];
return true;
}
bool KMP::work(void)
{
/*
* As the analysis above, To skip some traps, we need a table to record
* some information about those traps.
*/
this->createPT( );
// current match index
INDEX cmi = 0;
//index of text string, this is a relative length
INDEX si = 0 ;
//index of pattern
//INDEX pi = 0;
/*
* the process of search is almost same as the simple algorithm. The difference
* of operation is occur when we encounter a trap. Based on our theory, we
* could skip some traps.
*/
while( this->str[cmi]!='\0' )
{
/*
* match pattern with the text, this is same as the normal algorithm.
*/
while( this->str[cmi + si]==this->pattern[si] )
{
si++;
//pi++;
if( this->pattern[si]=='\0')
{
this->ip = cmi;
return true;
}
}
/*
* when we encounter a trap, we need to revise the start position
* in next search. In this expression, @(cmi + si) is the last position
* in the text where we compare with our pattern. @( this->ptab[si])
* is the length of possible string in this template.
*/
cmi = cmi + si -this->ptab[si];
/*
* update the relative length to the corresponding value.
*/
if( si!=0)
{
si = this->ptab[si];
//pi = this->ptab[pi];
}
}
return false;
}
/**
*
*/
bool KMP::createPT( void)
{
//mismatch index
INDEX mmi = 1;
/*
* deal with every template string that is possible to become a trap.
*/
while( mmi<this->p_len)
{
this->computePTV( mmi);
mmi++;
}
/*
* Actually, the following is not a trap, but for make our program
* more concise , we do a trick.
*/
this->ptab[0] = -1;
return true;
}
/**
* This function work for compute the max match string. That's comformation
* will be used to skip some traps.
*/
bool KMP::computePTV( INDEX mmi)
{
//max match index
INDEX max_mi = mmi -1;
//initial position for search substring
INDEX i = max_mi -1;
//the length of substring
INDEX ss_len = 0;
while( i>=0 )
{
while( this->pattern[ max_mi - ss_len]==this->pattern[ i-ss_len] )
{
if( i==ss_len)
{
this->ptab[ mmi] = ss_len + 1;
return true;
}
ss_len ++;
}
ss_len = 0;
i--;
}
this->ptab[ mmi] = 0;
return false;
}
bool KMP::showPT(void)
{
int i = 0;
for( i=0; i<this->p_len; i++)
{
printf( "%2c", this->pattern[i] );
}
printf("\n");
for( i=0; i<this->p_len; i++)
{
printf("%2d", this->ptab[i]);
}
printf("\n");
return true;
}
bool KMP::show(void)
{
printf("text: %s\n", this->str);
printf("pattern: %s\n", this->pattern);
printf(" index = %d\n", this->ip);
return true;
}
#define TEXT "aababcaababcabcdabbabcdabbaababcabcdabbaababaababcabcdabbcaabaacaabaaabaabaababcabcdabbabcabcdaababcabcdabbabbcdabb"
#define PATTERN "abaabcac"
int main( )
{
KMP kmp;
kmp.set( TEXT, PATTERN);
kmp.work( );
kmp.showPT( );
kmp.show( );
return 0;
}
字符串查找算法-KMP