Min per group in SQL but with a caveat - sql

Question

I've got this table in SQL below and I need to return "the car vendors that will never be used if the car purchaser is a rational person" or "The vendor for which all car prices are more expensive then others". I've tried to do the idea of joining with itself but I am unable to get it work. The resulting output should be vendor 3 since its price for car 3 and 4 is more expensive than the other option.
id car_vendor_id vendor_name car_id price
---------------------------------------------
1 1 Vendor 1 1 25000
2 1 Vendor 1 2 40000
3 2 Vendor 2 2 35000
4 2 Vendor 2 3 25000
5 3 Vendor 3 3 28000
6 3 Vendor 3 4 40000
7 4 Vendor 4 4 35000
8 4 Vendor 4 5 20000
9 5 Vendor 5 5 18000
10 5 Vendor 5 6 32000
11 6 Vendor 6 6 30000
12 6 Vendor 6 7 20000

Answer 1

One method is row_number() and aggregation:
select car_vendor_id, vendor_name
from (select t.*,
rank() over (partition by car_id order by price) as seqnum
from t
) t
group by car_vendor_id, vendor_name
having min(seqnum) > 1;
The having clause is selecting rows where the vendor has no cars that are "first" based on price.

Answer 2

The following query uses a CTE to work out the price order for each car, so the most expensive is 1.
It then excludes rows where there is a row for the vendor where they are not the most expensive, and lastly checks they are are not the only vendor for a car.
declare #Car table(Vendor int, Car int, Price int)
insert #Car values (1,1,25000),(1,2,40000),(2,2,35000),(2,3,25000),(3,3,28000),(3,4,40000),(4,4,35000),(4,5,20000),(5,5,18000),(5,6,32000),(6,6,30000),(6,7,20000)
;with Price as (
select *, row_number() over(partition by Car order by Price desc) as r from #Car Car
)
select * from Price
where not exists(select * from Price p2 where p2.Vendor=Price.Vendor and p2.r>1)
and Vendor not in (
select Vendor from #Car where Car in (select Car from #Car group by Car having count(*)=1)
)

Answer 3

Check on the next query:
declare #car table(Vendor int, Car int, Price int);
insert #car
values
(1,1,25000),(1,2,40000),(2,2,35000),(2,3,25000),
(3,3,28000),(3,4,40000),(4,4,35000),(4,5,20000),
(5,5,18000),(5,6,32000),(6,6,30000),(6,7,20000);
with
a as (
select
vendor, price,
count(*) over(partition by car) cq,
count(*) over(partition by vendor) vcq,
max(price) over(partition by car) xcp
from #car
)
select vendor
from a
where cq > 1 and xcp = price
group by vendor, vcq
having count(*) = vcq;
To try the query online, please click here.