PostgreSQL Select the r.* by MIN() with group-by on two columns

Question

The example schema of a table called results

id	user_id	activity_id	activity_type_id	start_date_local	elapsed_time
1	100	11111	1	2014-01-07 04:34:38	4444
2	100	22222	1	2015-04-14 06:44:42	5555
3	100	33333	1	2015-04-14 06:44:42	7777
4	100	44444	2	2014-01-07 04:34:38	12345
5	200	55555	1	2015-12-22 16:32:56	5023

The problem

Select the results of fastest activities (i.e. minimum elapsed time) of each user by activity_type_id and year.

(Basically, in this simplified example, record ID=3 should be excluded from the selection, because record ID=2 is the fastest for user 100 of the given activity_type_id 1 and the year of 2015)

What I have tried

SELECT user_id,
       activity_type_id,
       EXTRACT(year FROM start_date_local) AS year,
       MIN(elapsed_time) AS fastest_time
FROM results
GROUP BY activity_type_id, user_id, year
ORDER BY activity_type_id, user_id, year;

Actual

Which selects the correct result set I want, but only contains the grouped by columns

user_id	activity_type_id	year	fastest_time
100	1	2014	4444
100	1	2015	5555
100	2	2014	12345
200	1	2015	5023

Goal

To have the actual full record with all columns. i.e. results.* + year

id	user_id	activity_id	activity_type_id	start_date_local	year	elapsed_time
1	100	11111	1	2014-01-07 04:34:38	2014	2014
2	100	22222	1	2015-04-14 06:44:42	2015	5555
4	100	44444	2	2014-01-07 04:34:38	2014	12345
5	200	55555	1	2015-12-22 16:32:56	2015	5023

Answer 1

I think you want this:

SELECT DISTINCT ON (user_id, activity_type_id, EXTRACT(year FROM start_date_local)) 
     *, EXTRACT(year FROM start_date_local) AS year
FROM results
ORDER BY user_id, activity_type_id, year, elapsed_time;