mysql, update foreach category - mysql

Question

it is a really simple question. it is only 1 table!
i have a table of books which each book have a category and a number.
SO I WANNA TRANSFORM THIS
+--------------------------+
| book_id | category | num |
+--------------------------+
| 1 | a | 7 |
| 2 | a | 5 |
| 3 | a | 3 |
| 4 | b | 9 |
| 5 | b | 8 |
| 6 | b | 1 |
+--------------------------+
INTO THIS,
+--------------------------+
| book_id | category | num |
+--------------------------+
| 3 | a | 3 |
| 2 | a | 5 |
| 1 | a | 7 |
| 6 | b | 1 |
| 5 | b | 8 |
| 4 | b | 9 |
+--------------------------+
AND THEN THIS!
+--------------------------+
| book_id | category | num |
+--------------------------+
| 3 | a | 1 |
| 2 | a | 2 |
| 1 | a | 3 |
| 6 | b | 1 |
| 5 | b | 2 |
| 4 | b | 3 |
+--------------------------+
BUT HOW?!?!?!?!
script to create table...
drop table if exists books;
CREATE TABLE books(
id int AUTO_INCREMENT,
category varchar(30),
num int,
PRIMARY KEY (id)
);
insert into books (category,num)
values
('a',7),
('a',5),
('a',3),
('b',9),
('b',8),
('b',1);

Answer 1

You can use user variables to generate the sequence numbers within each category in the order of increasing id.
If you just want to query the table, use:
select
b.id,
b.category,
#rn := if(#category = category, #rn + 1, if (#category := category, 1, 1)) num
from books b, (select #category := null, #rn := 0) t2
order by b.category, b.id
If you want to update your table, use:
update books b1
join (
select
b.id,
#rn := if(#category = category, #rn + 1, if (#category := category, 1, 1)) num
from books b, (select #category := null, #rn := 0) t2
order by b.category, b.id
) b2 on b1.id = b2.id
set b1.num = b2.num;
Demo
EDIT:
As per the edited question, you can use order by b.category, b.num instead.