How to compose the following SQL query?

Question

MySQL

The initial selection is sorted in ascending order by ID_1 and ID_2.
ID_2 is always greater than ID_1.

It is necessary to obtain such a selection, where the ID_2 of one record will be less than the ID_1 of the next record.
That is, for the above selection, the result will be the following:
How to create such a query and is it possible (on PostgreSql or MySql)?

Answer 1

For a primitive case, we always select the first available entry:

SET @last = 0;
SELECT `ID_1`, @last := `ID_2` AS `ID_2`
  FROM (
    SELECT `ID_1`, `ID_2` 
      FROM `table`
      ORDER BY `ID_1`, `ID_2`
  ) AS `t`
  WHERE `ID_1` > @last;

Answer 2

Look into window functions. lag and lead, in postgresql for a long time, finally appeared in mysql in 8.0. For older mysql - pervert.