sqlite3 recursive aggregation of data - recursion

Question

This may be a kind of the Knapsack problem.
I need to traverse a data table, group it by a column, choosing ones with better time.
Then repeat the previous step until a limit given by column CAPACITY is not reached.
This is the demo scenario:
create table if not exists data( vid num, size num, epid num, sid num, capacity num, dt );
delete from data;
insert into data(vid,size,epid,sid,capacity,dt)
values
(0,20,1,1,50,1100), -- 2nd choice
(0,20,1,1,50,1000), -- 1st choice
(0,20,1,1,50,1200), -- last choice excluded because out of capacity
(1,20,2,2,50,1100), -- 2nd choice
(1,20,2,2,50,1000), -- 1st choice
(1,20,2,2,50,1200); -- last choice excluded because out of capacity
This is the non recursive solution:
with best0 as (
select a.rowid as tid,a.vid,a.sid,a.size,a.dt,a.capacity-a.size as remains,0 as level
from data a
group by a.sid
having min(a.dt)
),
best1 as (
select a.tid,a.vid,a.sid,a.size,a.dt,a.remains, a.level
from (
select
a.rowid as tid,a.sid,a.vid,a.size,a.capacity,a.dt,b.remains-a.size as remains,
b.level+1 as level
from data a
join best0 b on b.sid=a.sid -- and b.level=a.level-1
where not a.rowid in (select tid from best0)
and b.remains-a.size>0
) a group by a.sid having min(a.dt)
),
best2 as (
select a.tid,a.vid,a.sid,a.size,a.dt,a.remains, a.level
from (
select
a.rowid as tid,a.sid,a.vid,a.size,a.capacity,a.dt,b.remains-a.size as remains,
b.level+1 as level
from data a
join best1 b on b.sid=a.sid -- and b.level=a.level-1
where not a.rowid in (select tid from best0 union all select tid from best1)
and b.remains-a.size>0
) a group by a.sid having min(a.dt)
)
select * from best0
union all
select * from best1
union all
select * from best2
And this the result:
tid | vid | sid | size | Dtime | capacity | group_level
--- | --- | --- | ---- | ----- | -------- | -----------
2 | 0 | 1 | 20 | 1000 | 30 | 0
5 | 1 | 2 | 20 | 1000 | 30 | 0
1 | 0 | 1 | 20 | 1100 | 10 | 1
4 | 1 | 2 | 20 | 1100 | 10 | 1
This is the recursive version that give error: "recursive reference in a subquery: best"
with recursive best(tid,vid,sid,size,dt,remains,level)
as (
select a.rowid as tid,a.vid,a.sid,a.size,a.dt,a.capacity-a.size as remains,0 as level
from data a
group by a.sid
having min(a.dt)
union all
select a.tid,a.vid,a.sid,a.size,a.dt,a.remains, a.level
from (
select
a.rowid as tid,a.sid,a.vid,a.size,a.dt,b.remains-a.size as remains,
b.level+1 as level
from data a
join best b on b.sid=a.sid -- and b.level=a.level-1
where not a.rowid in (select tid from best) and b.remains-a.size>0
) a group by a.sid having min(a.dt)
)
select * from best
I tried differents solutions even using a loop counter but everyone give the same error.