数据结构之Rabin Karp字符串匹配

The Naive String Matching algorithm slides the pattern one by one. After each slide, it one by one checks characters at the current shift and if all characters match then prints the match.

Like the Naive Algorithm, Rabin-Karp algorithm also slides the pattern one by one. But unlike the Naive algorithm, Rabin Karp algorithm matches the hash value of the pattern with the hash value of current substring of text, and if the hash values match then only it starts matching individual characters. So Rabin Karp algorithm needs to calculate hash values for following strings.

1) Pattern itself.

2) All the substrings of text of length m.

Since we need to efficiently calculate hash values for all the substrings of size m of text, we must have a hash function which has following property.

Hash at the next shift must be efficiently computable from the current hash value and next character in text or we can say hash(txt[s+1 .. s+m]) must be efficiently computable from hash(txt[s .. s+m-1]) and txt[s+m] i.e., hash(txt[s+1 .. s+m])= rehash(txt[s+m], hash(txt[s .. s+m-1]) and rehash must be O(1) operation.

The hash function suggested by Rabin and Karp calculates an integer value. The integer value for a string is numeric value of a string. For example, if all possible characters are from 1 to 10, the numeric value of “122″ will be 122. The number of possible characters is higher than 10 (256 in general) and pattern length can be large. So the numeric values cannot be practically stored as an integer. Therefore, the numeric value is calculated using modular arithmetic to make sure that the hash values can be stored in an integer variable (can fit in memory words). To do rehashing, we need to take off the most significant digit and add the new least significant digit for in hash value. Rehashing is done using the following formula.

hash( txt[s+1 .. s+m] ) = d ( hash( txt[s .. s+m-1]) – txt[s]*h ) + txt[s + m] ) mod q

hash( txt[s .. s+m-1] ) : Hash value at shift s.

hash( txt[s+1 .. s+m] ) : Hash value at next shift (or shift s+1)

d: Number of characters in the alphabet

q: A prime number

h: d^(m-1)

#include < stdio.h >

#include < string.h >

 

// d is the number of characters in input alphabet

#define d 256 

  

void Rabin_Karp_Matcher(char *pat, char *txt, int q)

{

    int M = strlen(pat);

    int N = strlen(txt);

    int i, j;

    int p = 0;  // hash value for pattern

    int t = 0; // hash value for txt

    int h = 1;

  

    // The value of h would be "pow(d, M-1)%q"

    for (i = 0; i < M-1; i++)

        h = (h*d)%q;

  

    // Calculate the hash value of pattern and first window of text

    for (i = 0; i < M; i++)

    {

        p = (d*p + pat[i])%q;

        t = (d*t + txt[i])%q;

    }

  

    // Slide the pattern over text one by one 

    for (i = 0; i <= N - M; i++)

    {

        

        // Chaeck the hash values of current window of text and pattern

        // If the hash values match then only check for characters on by one

        if ( p == t )

        {

           

            for (j = 0; j < M; j++)

            {

                if (txt[i+j] != pat[j])

                    break;

            }

            if (j == M)  // if p == t and pat[0...M-1] = txt[i, i+1, ...i+M-1]

            {

                printf("Pattern found at index %d \n", i);

            }

        }

         

        // Calulate hash value for next window of text: Remove leading digit, 

        // add trailing digit           

        if ( i < N-M )

        {

            t = (d*(t - txt[i]*h) + txt[i+M])%q;

             

            // We might get negative value of t, converting it to positive

            if(t < 0) 

              t = (t + q); 

        }

    }

}

  

int main()

{

    char *txt = "GEEKS FOR GEEKS";

    char *pat = "GEEK";

    int q = 101;  // A prime number

    Rabin_Karp_Matcher(pat, txt, q);

    getchar();

    return 0;

}