Smarter SQL UPDATE between two tables (bill and bill rows)

Question

I have these two SQL tables:

Bills (BillId, Folio, Date, ProductId)
BillsRows (BillRowId, BillId, ProductId, Lot, Quantity, Price)

• ProductId is optional in Bills
• ProductId is mandatory in BillsRows
• If all the rows of a bill have the same ProductId then the bill will have that ProductId
• If there are mixed ProductId within a bill, then the bill will have ProductId = NULL

Visual example:

I have created the following SQL UPDATE but I'm not sure it is efficient:

update Bills
set ProductId = (
    select top 1 ProductId
    from BillsRows
    group by ProductId, BillId
    having count(*) = (select count(*) from BillsRows where BillId = Bills.BillId)
    and BillId = Bills.BillId
)

The fact that I'm counting all the rows is what makes me think it is not quite efficient.

Is there any smarter alternative than this?

Update: added two samples

Sample 1: Bill should be updated to ProductId=1 because all of the rows have ProductId=1

insert into Bills (BillId, Folio, Date, ProductId) values (1, 324, '2022-04-14', null)
insert into BillsRows (BillRowId, BillId, ProductId) values (1, 1, 1111)
insert into BillsRows (BillRowId, BillId, ProductId) values (2, 1, 1111)
insert into BillsRows (BillRowId, BillId, ProductId) values (3, 1, 1111)

Sample 2: Bill should be updated to ProductId=NULL because it has different products

insert into Bills (BillId, Folio, Date, ProductId) values (2, 325, '2022-04-14', null)
insert into BillsRows (BillRowId, BillId, ProductId) values (4, 2, 1111)
insert into BillsRows (BillRowId, BillId, ProductId) values (5, 2, 2222)
insert into BillsRows (BillRowId, BillId, ProductId) values (6, 2, 3333)

Answer 1

Maybe something like this

update B
set B.ProductId =R.ProductID
from Bills B inner join
BillsRows R on R.BillID=B.BillID
where not exists
(
    select 1
    from BillsRows BR where BR.BillId = R.BillId 
    and B.ProductID<> BR.ProductId
)

Answer 2

Please try below query. It should be faster.

update Bills
set ProductId = (
    select max(ProductId)
    from BillsRows
    group by BillId
    having count(distinct ProductId) =1
    and BillId = Bills.BillId
)

Answer 3

I think this update might be more efficient than what I initially posted:

update Bills
set 
Bills.ProductId = (
    select 
        top 1 ProductId
    from BillsRows
    where BillsRows.BillId = Bills.BillId
)
where BillId in (
    select 
        BillsRowsGrouped.BillId
    from (
        select 
            BillsRows.BillId, 
            BillsRows.ProductId
        from BillsRows
        group by 
            BillsRows.BillId,
            BillsRows.ProductId
    ) as BillsRowsGrouped
    group by BillsRowsGrouped.BillId
    having count(*) = 1
)

If we read from inside to outside...

First we have this:

        select 
            BillsRows.BillId, 
            BillsRows.ProductId
        from BillsRows
        group by 
            BillsRows.BillId,
            BillsRows.ProductId

(This returns a virtual table with two columns: BillId and ProductId)

Then, I group again, by BillId, and stick with those with count(*) = 1

    select 
        BillsRowsGrouped.BillId
    from (...) as BillsRowsGrouped
    group by BillsRowsGrouped.BillId
    having count(*) = 1

Finally, I update using the top 1 result from BillsRows and making sure BillId is in the previous query:

update Bills
set 
Bills.ProductId = (
    select 
        top 1 ProductId
    from BillsRows
    where BillsRows.BillId = Bills.BillId
)
where BillId in (...)