PostgreSQL: Free time slot algorithm - postgresql

Question

I have a table with some time slots in it, example:
#id datet userid agentid duration
+=======================================================+
|1 |2013-08-20 08:00:00 |-1 |3 |5
|2 |2013-08-20 08:05:00 |-1 |3 |5
|3 |2013-08-20 08:10:00 | 3 |3 |5
|4 |2013-08-20 08:15:00 |-1 |3 |5
|5 |2013-08-20 08:20:00 |-1 |3 |5
|6 |2013-08-20 08:25:00 |-1 |3 |5
|7 |2013-08-20 08:30:00 |-1 |3 |5
|8 |2013-08-20 08:05:00 |-1 |7 |15
|9 |2013-08-20 08:20:00 |-1 |7 |15
+=======================================================+
In the above example, the user wit id 3 has a slot at 8:10. (if userid = -1, it means it is a free slot). He has an appointment with agent 5. For example, now user 3 would like another timeslot, but this time with agent 7. So, the algorithm should keep only the free slots for agentid 7 and the possible slots wich doesn't overlap. This would mean, only the 9th record would be a solution in this case. (But maybe in another case, there are multiple solutions). Another thing, a user can only have one appointment with the same agent.
Any ideas how to implement this? I was thinking with the OVERLAPS operator, but can't figure it out how to do so.

Answer 1

Try something like:
select *
from time_slots ts
where agentid = 7 -- or any agent
and userid = -1 -- it is free
and not exists (select 1 -- and overlaping interval does not exist
from time_slots ts_2
where ts_2.userid <> -1 -- not free
and (ts.datet, ts.datet + interval '1 hour' * ts.duration) OVERLAPS
(ts_2.datet, ts_2.datet + interval '1 hour' * ts_2.duration))