Editing String-searching algorithm (section)

== Overview ==
The most basic case of string searching involves one (often very long) string, sometimes called the ''haystack'', and one (often very short) string, sometimes called the ''needle''. The goal is to find one or more occurrences of the needle within the haystack.  For example, one might search for ''to'' within:

 Some books are to be tasted, others to be swallowed, and some few to be chewed and digested.

One might request the first occurrence of "to", which is the fourth word; or all occurrences, of which there are 3; or the last, which is the fifth word from the end.

Very commonly, however, various constraints are added. For example, one might want to match the "needle" only where it consists of one (or more) complete words—perhaps defined as ''not'' having other letters immediately adjacent on either side. In that case a search for "hew" or "low" should fail for the example sentence above, even though those literal strings do occur.

Another common example involves "normalization". For many purposes, a search for a phrase such as "to be" should succeed even in places where there is something else intervening between the "to" and the "be":
*More than one space
*Other "whitespace" characters such as tabs, non-breaking spaces, line-breaks, etc.
*Less commonly, a hyphen or soft hyphen
*In structured texts, [[Markup language|tags]] or even arbitrarily large but "parenthetical" things such as footnotes, list-numbers or other markers, embedded images, and so on.

Many symbol systems include characters that are synonymous (at least for some purposes):
*Latin-based alphabets distinguish lower-case from upper-case, but for many purposes string search is expected to ignore the distinction.
*Many languages include [[Typographic ligature|ligature]]s, where one composite character is equivalent to two or more other characters.
*Many writing systems involve [[diacritical marks]] such as accents or [[Vowel pointing (disambiguation)|vowel points]], which may vary in their usage, or be of varying importance in matching.
*DNA sequences can involve [[non-coding]] segments which may be ignored for some purposes, or polymorphisms that lead to no change in the encoded proteins, which may not count as a true difference for some other purposes.
* Some languages have rules where a different character or form of character must be used at the start, middle, or end of words.

Finally, for strings that represent natural language, aspects of the language itself become involved. For example, one might wish to find all occurrences of a "word" despite it having alternate spellings, prefixes or suffixes, etc.

Another more complex type of search is [[regular expression]] searching, where the user constructs a pattern of characters or other symbols, and any match to the pattern should fulfill the search. For example, to catch both the American English word "color" and the British equivalent "colour", instead of searching for two different literal strings, one might use a regular expression such as:

 colou?r

where the "?" conventionally makes the preceding character ("u") optional.

This article mainly discusses algorithms for the simpler kinds of string searching.

A similar problem introduced in the field of bioinformatics and genomics is the maximal exact matching (MEM).<ref>{{Cite journal|last1=Kurtz|first1=Stefan|last2=Phillippy|first2=Adam|last3=Delcher|first3=Arthur L|last4=Smoot|first4=Michael|last5=Shumway|first5=Martin|last6=Antonescu|first6=Corina|last7=Salzberg|first7=Steven L|date=2004|title=Versatile and open software for comparing large genomes |journal=Genome Biology |volume=5|issue=2|pages=R12|doi=10.1186/gb-2004-5-2-r12|issn=1465-6906 |pmc= 395750|pmid=14759262 |doi-access=free }}</ref> Given two strings, MEMs are common substrings that cannot be extended left or right without causing a mismatch.<ref>{{Cite journal|last1=Khan|first1=Zia|last2=Bloom|first2=Joshua S.|last3=Kruglyak|first3=Leonid|last4=Singh|first4=Mona|date=2009-07-01|title=A practical algorithm for finding maximal exact matches in large sequence datasets using sparse suffix arrays|url= |journal=Bioinformatics |volume=25|issue=13|pages=1609–1616|doi=10.1093/bioinformatics/btp275 |pmc=2732316|pmid=19389736}}</ref>