Substring

---

title: "Substring" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["string-(computer-science)", "formal-languages"] description: "Contiguous part of a sequence of symbols" topic_path: "technology/computing" source: "https://en.wikipedia.org/wiki/Substring" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::summary Contiguous part of a sequence of symbols ::

::callout[type=note] the definition of a substring ::

::figure[src="https://upload.wikimedia.org/wikipedia/commons/3/3f/Substring.png" caption=""''string''" is a substring of "''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 S is a substring of S that occurs at the beginning of S; likewise, a suffix of a string S is a substring that occurs at the end of S.

The substrings of the string "" would be: "", "", "", "", "", "", "", "", "", "", "", "", "" "", "" (note the empty string at the end).

Substring

A string u is a substring (or factor) of a string t if there exists two strings p and s such that t = pus. In particular, the empty string is a substring of every string.

Example: The string u=\texttt{ana} is equal to substrings (and subsequences) of t=\texttt{banana} at two different offsets:

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

The first occurrence is obtained with p=\texttt{b} and s=\texttt{na}, while the second occurrence is obtained with p=\texttt{ban} and s 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 u is a substring of t, 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 (in America) or factors (in Europe).

Prefix

A string p is a prefix of a string t if there exists a string s such that t = ps. 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 (and substring and subsequence) of the string banana:

banana ||| ban

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

Suffix

A string s is a suffix of a string t if there exists a string p such that t = ps. 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 (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.

Border

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

Superstring

A superstring of a finite set P of strings is a single string that contains every string in P as a substring. For example, \texttt{bcclabccefab} is a superstring of P = {\texttt{abcc}, \texttt{efab}, \texttt{bccla}}, and \texttt{efabccla} is a shorter one. Concatenating all members of P, in arbitrary order, always obtains a trivial superstring of P. 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.

References

::callout[type=info title="Wikipedia Source"] This article was imported from Wikipedia and is available under the Creative Commons Attribution-ShareAlike 4.0 License. Content has been adapted to SurfDoc format. Original contributors can be found on the article history page. ::