Horspool algorithm

Idea

http://www.iti.fh-flensburg.de/lang/algorithmen/pattern/horsen.htm

The Boyer-Moore algorithm uses two heuristics in order to determine the shift distance of the pattern in case of a mismatch: the bad-character and the good-suffix heuristics. Since the good-suffix heuristics is rather complicated to implement there is a need for a simple algorithm that is based merely on the bad-character heuristics. Due to an idea of Horspool [Hor 80], instead of the "bad character" that caused the mismatch, in each case the rightmost character of the current text window is used for determining the shift distance.

Example:  

0123456789...abcabdaacbabcaab       bcaab      0123456789...abcabdaacbabcaab          bcaab     (a)   Boyer-Moore (b)   Horspool   

In this example, t₀, ..., t₄  =  a b c a b is the current text window that is compared with the pattern. Its suffix a b has matched, but the comparison c-a causes a mismatch. The bad-character heuristics of the Boyer-Moore algorithm (a) uses the "bad" text character c to determine the shift distance. The Horspool algorithm (b) uses the rightmost character b of the current text window. The pattern can be shifted until the rightmost occurrence of b in the pattern matches the text character b, where the occurence at the last position of the pattern does not count.

Like the Boyer-Moore algorithm, the Horspool algorithm assumes its best case if every time in the first comparison a text symbol is found that does not occur at all in the pattern. Then the algorithm performs just O(n/m) comparisons.

 

Preprocessing

The function occ required for the bad-character heuristics is computed slightly different as in the Boyer-Moore algorithm. For every alphabet symbol a, the function value occ(p, a) is equal to the rightmost position of a in p₀ ... p_m-2, or -1, if a does not occur at all. Observe that the last symbol p_m-1 of the pattern is not taken into account.

Example:  

• occ(text, x) = 2
• occ(text, t) = 0
• occ(next, t) = -1

The occurrence function for a certain pattern p is stored in an array occ that is indexed by the alphabet symbols. For every symbol a  A the entry occ[a] holds the corresponding function value occ(p, a).

Given a pattern p, the following function horspoolInitocc computes the occurrence function.

void horspoolInitocc(){    int j;    char a;    for (a=0; a<alphabetsize; a++)        occ[a]=-1;    for (j=0; j<m-1; j++)    {        a=p[j];        occ[a]=j;    }}

Searching algorithm 

As in the Boyer-Moore algorithm, the pattern is compared from right to left with the text. After a complete match or in case of a mismatch, the pattern is shifted according to the precomputed function occ.

void horspoolSearch(){    int i=0, j;    while (i<=n-m)    {        j=m-1;        while (j>=0 && p[j]==t[i+j]) j--;        if (j<0) report(i);        i+=m-1;        i-=occ[t[i]];    }}

References 

   [Hor 80]R.N. Horspool: Practical Fast Searching in Strings. Software - Practice and Experience 10, 501-506 (1980)  [1]http://www-igm.univ-mlv.fr/~lecroq/string/  [2]http://www.inf.fh-flensburg.de/lang/algorithmen/pattern/stringmatchingclasses/HorspoolStringMatcher.java   Horspool algorithm as a Java class source file