Sum duration of overlapping periods with priority by excluding the overlap itself

Question

I have an R code and I am trying to rewrite it in PostgreSQL that feeds grafana dashboard. I do have the basics so I am almost done with the other parts of the script but what I

Answer 1

This is a type of gaps-and-islands problem. To solve this, find where the "islands" begin and then aggregate. So, to get the islands:

select a.name, min(start) as startt, max("end") as endt
from (select a.*,
             count(*) filter (where prev_end is null or prev_end < start) over (partition by name order by start, id) as grp
      from (select a.*,
                   max("end") over (partition by name
                                    order by start, id
                                    rows between unbounded preceding and 1 preceding
                                   ) as prev_end
            from activities a
           ) a
     ) a
group by name, grp;

The next step is just to aggregate again:

with islands as (
      select a.name, min(start) as startt, max("end") as endt
      from (select a.*,
                   count(*) filter (where prev_end is null or prev_end < start) over (partition by name order by start, id) as grp
            from (select a.*,
                         max("end") over (partition by name
                                          order by start, id
                                          rows between unbounded preceding and 1 preceding
                                         ) as prev_end
                  from activities a
                 ) a
           ) a
      group by name, grp
     )
select name, sum(endt - startt)
from islands i
group by name;

Here is a db<>fiddle.

Note that this uses a cumulative trailing maximum to define the overlaps. This is the most general method for determining overlaps. I think this will work on all edge cases, including:

1----------2---2----3--3-----1

It also handles ties on the start time.