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:  

0 1 2 3 4 5 6 7 8 9 ... a b c a b d a a c b a b c a a b               b c a a b		0 1 2 3 4 5 6 7 8 9 ... a b c a b d a a c b a b c a a b                     b c a a b
(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 ... pm-2,
or -1, if a does not occur at all. Observe that the last symbol pm-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