Substring Online Tutorials

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.

"*string*" is a substring of "*substring*"

Prefixes and suffixes are special cases of substrings. A prefix of a string $S {\displaystyle S}$ is a substring of $S {\displaystyle S}$ that occurs at the beginning of $S {\displaystyle S}$ ; likewise, a suffix of a string $S {\displaystyle S}$ is a substring that occurs at the end of $S {\displaystyle S}$ .

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).

Substring

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

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

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

The first occurrence is obtained with $p=$ b and $s=$ na, while the second occurrence is obtained with $p=$ ban and $s {\displaystyle s}$ 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 $u {\displaystyle u}$ is a substring of $t {\displaystyle t}$ , 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 $p {\displaystyle p}$ is a prefix of a string $t {\displaystyle t}$ if there exists a string $s {\displaystyle s}$ such that $t=ps$ . 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:

banana
|||
ban

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

Suffix

A string $s {\displaystyle s}$ is a suffix^[1] of a string $t {\displaystyle t}$ if there exists a string $p {\displaystyle p}$