Merge continuous rows with Postgresql - sql

Question

I have a slots table like this :
Column | Type |
------------+-----------------------------+
id | integer |
begin_at | timestamp without time zone |
end_at | timestamp without time zone |
user_id | integer |
and I like to select merged rows for continuous time. Let's say I have (simplified) data like :
(1, 5:15, 5:30, 1)
(2, 5:15, 5:30, 2)
(3, 5:30, 5:45, 2)
(4, 5:45, 6:00, 2)
(5, 8:15, 8:30, 2)
(6, 8:30, 8:45, 2)
I would like to know if it's possible to select rows formatted like :
(5:15, 5:30, 1)
(5:15, 6:00, 2) // <======= rows id 2,3 and 4 merged
(8:15, 8:45, 2) // <======= rows id 5 and 6 merged
EDIT:
Here's the SQLfiddle
I'm using Postgresql, version 9.3!
Thank you!

Answer 1

Here is one method for solving this problem. Create a flag that determines if a one record does not overlap with the previous one. This is the start of a group. Then take the cumulative sum of this flag and use that for grouping:
select user_id, min(begin_at) as begin_at, max(end_at) as end_at
from (select s.*, sum(startflag) over (partition by user_id order by begin_at) as grp
from (select s.*,
(case when lag(end_at) over (partition by user_id order by begin_at) >= begin_at
then 0 else 1
end) as startflag
from slots s
) s
) s
group by user_id, grp;
Here is a SQL Fiddle.

Answer 2

Gordon Linoff already provided the answer (I upvoted).
I've used the same approach, but wanted to deal with tsrange type.
So I came up with this construct:
SELECT min(id) b_id, min(begin_at) b_at, max(end_at) e_at, grp, user_id
FROM (
SELECT t.*, sum(g) OVER (ORDER BY id) grp
FROM (
SELECT s.*, (NOT r -|- lag(r,1,r)
OVER (PARTITION BY user_id ORDER BY id))::int g
FROM (SELECT id,begin_at,end_at,user_id,
tsrange(begin_at,end_at,'[)') r FROM slots) s
) t
) u
GROUP BY grp, user_id
ORDER BY grp;
Unfortunately, on the top level one has to use min(begin_at) and max(end_at), as there're no aggregate functions for the range-based union operator +.
I create ranges with exclusive upper bounds, this allows me to use “is adjacent to” (-|-) operator. I compare current tsrange with the one on the previous row, defaulting to the current one in case there's no previous. Then I negate the comparison and cast to integer, which gives me 1 in cases when new group starts.