KMP algorithm, find the NEXT [J] = K function of pattern string, is it my misunderstanding or book error?

KMP finds the position of pattern string P in the main string S.

calculates the next [j] = k function of the pattern string P.

meaning:
is provided with main string S, mode string P, and the first j characters of main string S and mode string P have been completely matched (0roomjmurl, a total of j).
if there is a mismatch on P [j], that is, P [j]! = S [j].
then for the next comparison, just compare P [k] with S [j]. (0 < = k < j, and k makes P [0] ~ P [k] exactly the same as P [j-1murk] ~ P [j-1]).

the algorithm given in the book is: 

</span>


(J=2):<br>next:


Active code page: 65001
abababb
--------------------------------
j=2, J_str=ab
k=0, left_str=a, right_str=b
next[2]=0

--------------------------------
j=3, J_str=aba
k=1, left_str=ab, right_str=ba
next[3]=1

--------------------------------
j=4, J_str=abab
k=2, left_str=aba, right_str=bab
next[4]=2

--------------------------------
j=5, J_str=ababa
k=1, left_str=ab, right_str=ba
next[5]=1

--------------------------------
j=6, J_str=ababab
k=2, left_str=aba, right_str=bab
next[6]=2

=================bookNext output==============
bNext[0] = -1
bNext[1] = 0
bNext[2] = 0
bNext[3] = 1
bNext[4] = 2
bNext[5] = 3
bNext[6] = 4

D:\AtomFiles\DataStructCode\KMPstring\Debug\KMPstring.exe ( 8648): 0
...


 logically, it seems that bookNext is also wrong. 


 is it because I don"t understand the KMP algorithm, or is there something wrong in the book?
Data structure and algorithm
Oct.13,2021
The result of the

bNext array is correct. (the picture in the book should be wrong. Please tell us which book is on how many pages to make it easier for us to check.)

I didn't take a closer look at the NextJ you wrote yourself, but if you look at the results, it's not right.

For more information on next array, please see https://subetter.com/articles.

.

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