substring について

. For example, "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 refinements 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

.
== Substring ==

A substring (or factor) of a string

T = t_1 \dots t_n

is a string

\hat T = t_ \dots t_

, where

0 \leq i

and

m + i \leq n

. A substring of a string is a prefix of a suffix of the string, and equivalently a suffix of a prefix. If

\hat T

is a substring of

T

, it is also a subsequence, which is a more general concept. Given a pattern

P

, you can find its occurrences in a string

T

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.
Example: The string ana is equal to substrings (and subsequences) of banana at two different offsets:
banana
|||||
ana||
|||
ana
In the mathematical literature, substrings are also called subwords (in America) or factors (in Europe).
Not including the empty substring, the number of substrings of a string of length

n

where symbols only occur once, is the number of ways to choose two distinct places between symbols to start/end the substring. Including the very beginning and very end of the string, there are

n+1

such places. So there are

\tbinom = \tfrac

non-empty substrings.

抄文引用元・出典: フリー百科事典『ウィキペディア（Wikipedia）』
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