Substring
In formal language theory and computer science, 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". 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. A [|prefix] of a string is a substring of that occurs at the beginning of ; likewise, a [|suffix] of a string is a substring that occurs at the end of.
The substrings of the string "" would be:
"", "", "", "", "",
"", "", "", "",
"", "",
"", ""
"", ""
.
Substring
A string is a substring of a string if there exists two strings and such that. In particular, the empty string is a substring of every string.Example: The string is equal to substrings of at two different offsets:
banana
|||||
ana||
|||
ana
The first occurrence is obtained with and, while the second occurrence is obtained with and being the empty string.
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. If is a substring of, it is also a subsequence, which is a more general concept. The occurrences of a given pattern in a given string can be found 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.In the mathematical literature, substrings are also called subwords or factors.
Prefix
A string is a prefix of a string if there exists a string such that. A proper prefix of a string is not equal to the string itself; some sources 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 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.
Suffix
A string is a suffix of a string if there exists a string such that. A proper suffix of a string is not equal to the string itself. A more restricted interpretation is that it is also not empty. A suffix can be seen as a special case of a substring.Example: The string
nana is equal to a suffix 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.
Border
A border is suffix and prefix of the same string, e.g. "" is a border of "".Superstring
A superstring of a finite set of strings is a single string that contains every string in as a substring. For example, is a superstring of, and is a shorter one. Concatenating all members of, 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.