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'string' is a substring of 'substring'

A substring is a contiguous sequence of characters within a string. For instance, "the best of" is a substring of "It was the best of times". This is not to be confused with subsequence, which is a generalization of substring. For example, "Itwastimes" is a subsequence of "It was the best of times", but not a substring.

Prefix and suffix are special cases of substring. A prefix of a string is a substring of that occurs at the beginning of . A suffix of a string is a substring that occurs at the end of .

The list of all substrings of the string "apple" would be "apple", "appl", "pple", "app", "ppl", "ple", "ap", "pp", "pl", "le", "a", "p", "l", "e", "".

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SubstringEdit

A substring (or factor) of a string   is a string  , where   and  . A substring of a string is a prefix of a suffix of the string, and equivalently a suffix of a prefix. If   is a substring of  , it is also a subsequence, which is a more general concept. Given a pattern  , you can find its occurrences in a string   with a string searching algorithm. Finding the longest string which is equal to a substring of two or more strings is known as the longest common substring problem.

Example: The string ana is equal to substrings (and subsequences) of banana at two different offsets:

banana
 |||||
 ana||
   |||
   ana

In the mathematical literature, substrings are also called subwords (in America) or factors (in Europe).

Not including the empty substring, the number of substrings of a string of length   where symbols only occur once, is the number of ways to choose two distinct places between symbols to start/end the substring. Including the very beginning and very end of the string, there are   such places. So there are   non-empty substrings.

PrefixEdit

A prefix of a string   is a string  , where  . A proper prefix of a string is not equal to the string itself ( );[1] some sources[2] in addition restrict a proper prefix to be non-empty ( ). A prefix can be seen as a special case of a substring.

Example: The string ban is equal to a prefix (and substring and subsequence) of the string banana:

banana
|||
ban

The square subset symbol is sometimes used to indicate a prefix, so that   denotes that   is a prefix of  . This defines a binary relation on strings, called the prefix relation, which is a particular kind of prefix order.

In formal language theory, the term prefix of a string is also commonly understood to be the set of all prefixes of a string, with respect to that language.

SuffixEdit

A suffix of a string is any substring of the string which includes its last letter, including itself. A proper suffix of a string is not equal to the string itself. A more restricted interpretation is that it is also not empty[1]. A suffix can be seen as a special case of a substring.

Example: The string nana is equal to a suffix (and substring and subsequence) of the string banana:

banana
  ||||
  nana

A suffix tree for a string is a trie data structure that represents all of its suffixes. Suffix trees have large numbers of applications in string algorithms. The suffix array is a simplified version of this data structure that lists the start positions of the suffixes in alphabetically sorted order; it has many of the same applications.

BorderEdit

A border is suffix and prefix of the same string, e.g. "bab" is a border of "babab" (and also of "babooneatingakebab").

SuperstringEdit

Given a set of   strings  , a superstring of the set   is a single string that contains every string in   as a substring. For example, a concatenation of the strings of   in any order gives a trivial superstring of  . For a more interesting example, let  . Then   is a superstring of  , and   is another, shorter superstring of  . Generally, we are interested in finding superstrings whose length is small.[clarification needed]

See alsoEdit

ReferencesEdit

  1. ^ Kelley, Dean (1995). Automata and Formal Languages: An Introduction. London: Prentice-Hall International. ISBN 0-13-497777-7.
  2. ^ Gusfield, Dan (1999) [1997]. Algorithms on Strings, Trees and Sequences: Computer Science and Computational Biology. USA: Cambridge University Press. ISBN 0-521-58519-8.

External linksEdit