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 $S$ is a substring of $S$ that occurs at the beginning of $S$ . A suffix of a string $S$ is a substring that occurs at the end of $S$ .

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", "".

Substring

A string $u$ is a substring (or factor)[1] 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 $u=$ 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