String prefix, true prefix, suffix, true suffix, and prefix function __ function

For example, a string ababc

First, regardless of the null character, all prefixes have a, AB, ABA, Abab, ABABC, where the true prefix has a, AB, ABA, ABAB

In the same way, the suffix is understood, and the true prefix is the first (back) prefix that does not contain itself.

The prefix function Next[j] refers to the longest true suffix of a string and also the substring length of its prefix. I'm not sure I can see the following example

A-> 0

AB-> 0

ABA-> 1

Abab-> 2

ABABC-> 0

Prefix functions are used more in matching strings, such as KMP. It is mainly to indicate the maximum step length that the pattern string can move back after a match failure.