$($a$)$ ABCDE

j Pattern $[0..$j$-1]$ Proper prefixes Proper Suffixes next$[$j$]$

$0-$ null null $-1$

$1$

$2$

$3$

$4$

$5$

The next array is:

$($b$)$ AAAAA

j Pattern $[0..$j$-1]$ Proper prefixes Proper Suffixes next$[$j$]$

$0-$ null null $-1$

$1$

$2$

$3$

$4$

$5$

The next array is:

$($c$)$ ABABAMK

j Pattern $[0..$j$-1]$ Proper prefixes Proper Suffixes next$[$j$]$

$0-$ null null $-1$

$1$

$2$

$3$

$4$

$5$

$6$

$7$

The next array is: