postgresql cumulative counts in date range I'm trying to get the cumulative count of rows (by group_id) between two dates that represent a time period where the row was active.

I have a table like this:

 group_id |   id   | type | start_date |  end_date
----------+--------+------+------------+------------
       33 | 119435 | AAA  | 2013-05-21 | 2014-05-19
       33 |  15144 | AAA  | 2013-05-21 | 2015-05-18
       33 |  29393 | AAA  | 2013-05-21 | 2016-05-23
       33 | 119437 | AAA  | 2013-05-21 | 2017-05-15
       33 |  62380 | AAA  | 2013-05-21 | 2099-12-31
       33 | 119436 | AAA  | 2013-05-21 | 2099-12-31
       33 |  27346 | AAA  | 2013-05-21 | 2099-12-31
       33 |  28529 | AAA  | 2014-05-20 | 2099-12-31
       33 | 221576 | AAA  | 2015-05-19 | 2099-12-31
       33 | 253893 | AAA  | 2016-05-24 | 2099-12-31
       33 | 251589 | AAA  | 2017-05-16 | 2099-12-31
       33 | 285245 | AAA  | 2019-01-24 | 2099-12-31
       34 | 253893 | AAA  | 2016-05-24 | 2099-12-31
       34 | 251589 | AAA  | 2017-05-16 | 2099-12-31
       34 | 285245 | AAA  | 2019-01-24 | 2099-12-31
       34 | 285246 | AAA  | 2019-05-31 | 2099-12-31


... and I need to get active counts for each of those date ranges like this: 

 group_id | start_date |  end_date  | active
----------+------------+------------+--------
       33 | 2013-05-21 | 2014-05-19 |      7
       33 | 2013-05-21 | 2015-05-18 |      8
       33 | 2013-05-21 | 2016-05-23 |      9
       33 | 2013-05-21 | 2017-05-15 |     10
       33 | 2013-05-21 | 2099-12-31 |     12
       33 | 2013-05-21 | 2099-12-31 |     12
       33 | 2013-05-21 | 2099-12-31 |     12
       33 | 2014-05-20 | 2099-12-31 |     11
       33 | 2015-05-19 | 2099-12-31 |     10
       33 | 2016-05-24 | 2099-12-31 |      9
       33 | 2017-05-16 | 2099-12-31 |      8
       33 | 2019-01-24 | 2099-12-31 |      8
       34 | 2016-05-24 | 2099-12-31 |      1
       34 | 2017-05-16 | 2099-12-31 |      2
       34 | 2019-01-24 | 2099-12-31 |      3
       34 | 2019-05-31 | 2099-12-31 |      4


I've tried various combinations of LAG and LEAD, with and without CTEs, but cannot come up with a solution.

Is there a way to do this in a single query? If not a single query, perhaps a combination of queries in a UDF?

UPDATE

Per @jjanes comment below, I believe my source table is setup incorrectly. I think I should create the source table like this instead:

 group_id |   id   | type | start_date |  end_date
----------+--------+------+------------+------------
  ... (skipped group 33) ...
       34 | 253893 | AAA  | 2016-05-24 | 2017-05-15
       34 | 253893 | AAA  | 2017-05-16 | 2019-01-23
       34 | 253893 | AAA  | 2019-01-24 | 2019-05-30
       34 | 253893 | AAA  | 2019-05-31 | 2099-12-31
       34 | 251589 | AAA  | 2017-05-16 | 2019-01-23
       34 | 251589 | AAA  | 2019-01-24 | 2019-05-30
       34 | 251589 | AAA  | 2019-05-31 | 2099-12-31
       34 | 285245 | AAA  | 2019-01-24 | 2019-05-30
       34 | 285245 | AAA  | 2019-05-31 | 2099-12-31
       34 | 285246 | AAA  | 2019-05-31 | 2099-12-31


With that change in the source data, the outcome of actives (showing only group 34 here) would be like this:

 group_id | start_date |  end_date  | active
----------+------------+------------+--------
       34 | 2016-05-24 | 2017-05-15 |      1
       34 | 2017-05-16 | 2019-01-23 |      2
       34 | 2019-01-24 | 2019-05-30 |      3
       34 | 2019-05-31 | 2099-12-31 |      4
You should explain your logic in more detail.  If I implement what you seem to be asking for, it generates your desired result for 33, but not for 34.

If you don't count overlapping rows "below" you, then how can the first row of 33 have a count of 7?  And if you do count overlapping rows "below" you, then how can the first row of 34 have a count of 1?

select group_id, start_date, end_date, (
    select count(*) from foobar f2 where 
        f2.group_id=foobar.group_id and
        daterange(foobar.start_date,foobar.end_date) &amp;&amp; daterange(f2.start_date,f2.end_date)
    ) as active 
from foobar;


 group_id | start_date |  end_date  | active 
----------+------------+------------+--------
       33 | 2013-05-21 | 2014-05-19 |      7
       33 | 2013-05-21 | 2015-05-18 |      8
       33 | 2013-05-21 | 2016-05-23 |      9
       33 | 2013-05-21 | 2017-05-15 |     10
       33 | 2013-05-21 | 2099-12-31 |     12
       33 | 2013-05-21 | 2099-12-31 |     12
       33 | 2013-05-21 | 2099-12-31 |     12
       33 | 2014-05-20 | 2099-12-31 |     11
       33 | 2015-05-19 | 2099-12-31 |     10
       33 | 2016-05-24 | 2099-12-31 |      9
       33 | 2017-05-16 | 2099-12-31 |      8
       33 | 2019-01-24 | 2099-12-31 |      8
       34 | 2016-05-24 | 2099-12-31 |      4
       34 | 2017-05-16 | 2099-12-31 |      4
       34 | 2019-01-24 | 2099-12-31 |      4
       34 | 2019-05-31 | 2099-12-31 |      4