Substring

In formal language theory and computer science, a substring is a contiguous sequence of characters within a string.

[citation needed] For instance, "the best of" is a substring of "It was the best of times".

In contrast, "Itwastimes" is a subsequence of "It was the best of times", but not a substring.

Prefixes and suffixes are special cases of substrings.

; likewise, a suffix of a string

The substrings of the string "apple" would be: "a", "ap", "app", "appl", "apple", "p", "pp", "ppl", "pple", "pl", "ple", "l", "le" "e", "" (note the empty string at the end).

is a substring (or factor)[1] of a string

ana is equal to substrings (and subsequences) of

banana at two different offsets: The first occurrence is obtained with

A substring of a string is a prefix of a suffix of the string, and equivalently a suffix of a prefix; for example, nan is a prefix of nana, which is in turn a suffix of banana.

Finding the longest string which is equal to a substring of two or more strings is known as the longest common substring problem.

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

[citation needed] A string

A proper prefix of a string is not equal to the string itself;[2] some sources[3] 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: The square subset symbol is sometimes used to indicate a prefix, so that

This defines a binary relation on strings, called the prefix relation, which is a particular kind of prefix order.

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: 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.

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

[citation needed] A superstring of a finite set

, in arbitrary order, always obtains a trivial superstring of

Finding superstrings whose length is as small as possible is a more interesting problem.

A string that contains every possible permutation of a specified character set is called a superpermutation.