Reverse join in MySQL - mysql

Question

SO,
The problem
My question is about - how to join table in MySQL with itself in reverse order? Suppose I have:
id name
1 First
2 Second
5 Third
6 Fourth
7 Fifth
8 Sixth
9 Seventh
13 Eight
14 Nine
15 Tenth
-and now I want to create a query, which will return joined records in reverse order:
left_id name right_id name
1 First 15 Tenth
2 Second 14 Nine
5 Third 13 Eight
6 Fourth 9 Seventh
7 Fifth 8 Sixth
8 Sixth 7 Fifth
9 Seventh 6 Fourth
13 Eight 5 Third
14 Nine 2 Second
15 Tenth 1 First
My approach
I have now this query:
SELECT
l.id AS left_id,
l.name,
(SELECT COUNT(1) FROM sequences WHERE id<=left_id) AS left_order,
r.id AS right_id,
r.name,
(SELECT COUNT(1) FROM sequences WHERE id<=right_id) AS right_order
FROM
sequences AS l
LEFT JOIN
sequences AS r ON 1
HAVING
left_order+right_order=(1+(SELECT COUNT(1) FROM sequences));
-see this fiddle for sample structure & code.
Some background
There's no use case for that. I was doing that in application before. Now it's mostly curiosity if there's a way to do that in SQL - that's why I'm seeking not just 'any solution' (like mine) - but as simple as possible solution. Source table will always be small (<10.000 records) - so performance is not a thing to care, I think.
The question
Can my query be simplified somehow? Also, it's important not to use variables. Order could be included in result (like in my fiddle) - but that's not mandatory.

Answer 1

The only thing i can think to be improved is
SELECT
l.id AS left_id,
l.name ln,
(SELECT COUNT(1) FROM sequences WHERE id<=left_id) AS left_order,
r.id AS right_id,
r.name rn,
(SELECT COUNT(1) FROM sequences WHERE id>=right_id) AS right_order
FROM
sequences AS l
LEFT JOIN
sequences AS r ON 1
HAVING
left_order=right_order;
There are 2 changes that should make this a little bit faster:
1) Calculating right order in reverse order in the first place
2) avoid using SELECT COUNT in the last line.
Edit: I aliased the ln,rn because i couldn't see the columns in fiddle

Answer 2

Without the SQL standard RANK() OVER(...), you have to compute the ordering yourself as you discovered.
The RANK() of a row is simply 1 + the COUNT() of all better-ranked rows. (DENSE_RANK(), for comparison, is 1 + the COUNT() of all DISTINCT better ranks.) While RANK() can be computed as a scalar subquery in your SELECT projection — as, e.g., you have done with SELECT (SELECT COUNT(1) ...), ... — I tend to prefer joins:
SELECT lft.id AS "left_id", lft.name AS "left_name",
rgt.id AS "right_id", rgt.name AS "right_name"
FROM ( SELECT s.id, s.name, COUNT(1) AS "rank" -- Left ranking
FROM sequences s
LEFT JOIN sequences d ON s.id <= d.id
GROUP BY 1, 2) lft
INNER JOIN ( SELECT s.id, s.name, COUNT(1) AS "rank" -- Right ranking
FROM sequences s
LEFT JOIN sequences d ON s.id >= d.id
GROUP BY 1, 2) rgt
ON lft.rank = rgt.rank
ORDER BY lft.id ASC;

Answer 3

SET #rank1=0;
SET #rank2=0;
SELECT *
FROM (SELECT *, #rank1 := #rank1 + 1 AS row_number FROM sequences ORDER BY ID ASC) t1
INNER JOIN (SELECT *, #rank2 := #rank2 + 1 AS row_number FROM sequences ORDER BY ID DESC) t2
on t1.row_number = t2.row_number
For some reason sql fiddler does show only 3 columns for this, not sure if my query is bad.