# String matching

## Horspool algorithm  ### Idea

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...
abcabdaacba
bcaab
bcaab

0123456789...
abcabdaacba
bcaab
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 ... 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

### 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)
 [Web 1] http://www-igm.univ-mlv.fr/~lecroq/string/ [Web 2] http://www.inf.fh-flensburg.de/lang/algorithmen/pattern/stringmatchingclasses/HorspoolStringMatcher.java   Horspool algorithm as a Java class source file

 Next:   [Sunday algorithm]   or  H.W. Lang   Hochschule Flensburg   lang@hs-flensburg.de   Impressum   Datenschutz   ©   Created: 22.02.2001   Updated: 04.06.2018 