Selecting rows only if meeting criteria - postgresql

Question

I am new to PostgreSQL and to database queries in general.
I have a list of user_id with university courses taken, date started and finished.
Some users have multiple entries and sometimes the start date or finish date (or both) are missing.
I need to retrieve the longest course taken by a user or, if start date is missing, the latest.
If multiple choices are still available, then pick random among the multiple options.
For example
on user 2 (below) I want to get only "Economics and Politics" because it has the latest date;
on user 6, only "Electrical and Electronics Engineering" because it is the longer course.
The query I did doesn't work (and I think I am off-track):
(SELECT Q.user_id, min(Q.started_at) as Started_on, max(Q.ended_at) as Completed_on,
q.field_of_study
FROM
(select distinct(user_id),started_at, Ended_at, field_of_study
from educations
) as Q
group by Q.user_id, q.field_of_study )
order by q.user_id
as the result is:
User_id Started_on Completed_on Field_of_studies
2 "2001-01-01" "" "International Economics"
2 "" "2002-01-01" "Economics and Politics"
3 "1992-01-01" "1999-01-01" "Economics, Management of ..."
5 "2012-01-01" "2016-01-01" ""
6 "2005-01-01" "2009-01-01" "Electrical and Electronics Engineering"
6 "2011-01-01" "2012-01-01" "Finance, General"
6 "" "" ""
6 "2010-01-01" "2012-01-01" "Financial Mathematics"

Answer 1

I think this query should do what you need, it relies on calculating the difference in days between ended_at and started_at, and uses 0001-01-01 if the started_at is null (making it a really long interval):
select
educations.user_id,
max(educations.started_at) started_at,
max(educations.ended_at) ended_at,
max(educations.field_of_study) field_of_study
from educations
join (
select
user_id,
max(
ended_at::date
-
coalesce(started_at, '0001-01-01')::date
) max_length
from educations
where (started_at is not null or ended_at is not null)
group by user_id
) x on educations.user_id = x.user_id
and ended_at::date
-
coalesce(started_at, '0001-01-01')::date
= x.max_length
group by educations.user_id
;
Sample SQL Fiddle