Select All combinations of rows for a*b=total <=X - sql-server

Question

I have a situation about writing a query to find and insert into table B all combinations of rows from table A, where the condition is:
a x b=total from row1
c x d=total from row2 ...etc where count(total)<=X
"a" price of item
"b" quantity of item
Idea is to have all combinations like example
For 100$ dollars i can buy:
2 tshirt, 1 jacket, 1 pants
or
1 tshirt, 2 jacket, 1 pants
...etc
Creating a cursor will help me run the query for each row, but how to split the number in col.quantity in the same time ?

Answer 1

I will first write what I understood,
we would have a table of items, each item would have a price,
we have an amount of money and we want to buy as many as possible
items
we want the items to have the same weight as the two examples
provided "2 tshirt, 1 jacket, 1 pants or 1 tshirt, 2 jacket, 1 pants"
did not specify a solution with one item but tried to use all the
items.
So how to determine the Qty for each item to utilize most of the money that we have.
I think this can be described in a different way to be more clear, like for example:- one person goes in a shop and would like to buy each of the items available but if he has some more money left he want to know what other items he can buy with it. if the items are not a lot and the money is not a lot, this can be easy, but if the items are a lot and the money a lot too, I can see that this may be a problem. so lets find a solution.
Declare #Items Table (
Item varchar(250),Price decimal
)
insert into #Items values
('tshirt',30)
,('jacket',30)
,('pants' ,10)
--,('shoe' ,15) ---extra items for testing
--,('socks',5) ---extra items for testing
Declare #total int=100 -- your X
Declare #ItemsCount int
Declare #flag int
Declare #ItemsSum decimal
Declare #AllItmsQty int
select #ItemsCount=count(*),#ItemsSum=sum(price),#flag=POWER(2,count(*)) From #Items
select #AllItmsQty=#total/cast(#ItemsSum as int)
;with Numbers(n) as (
--generat numbers from 1,2,3,... #flag
select 1 union all
select (n+1) n from Numbers where n<#flag
),ItemsWithQty as (
select *,Price*n [LineTotal] from #Items,Numbers
),Combination as (
select items.*,Numbers.n-1 [CombinationId] from #Items items,Numbers
),CombinationWithSeq as (
select *
,ROW_NUMBER() over (Partition by [CombinationId] order by [CombinationId]) [seq]
from Combination
),CombinationWithSeqQty as (
select *,case when (CombinationId & power(2,seq-1))>0 then 1 else 0 end +#AllItmsQty [qty]
from CombinationWithSeq
),CombinationWithSeqQtySubTotal as (
select *,Price*qty [SubTotal] from CombinationWithSeqQty
)
select
--CombinationId,
sum(subtotal) [Total],
replace(
replace(
STRING_AGG(
case when (Qty=0) then 'NA' else (cast(Qty as varchar(5))+' '+Item)
end
,'+')
,'+NA','')
,'NA+','') [Items]
from CombinationWithSeqQtySubTotal
group by CombinationId
having sum(subtotal)<=#total
The result would be as follow:-
Total Items
===== ===========================
100 2 tshirt+1 jacket+1 pants
100 1 tshirt+2 jacket+1 pants
80 1 tshirt+1 jacket+2 pants
70 1 tshirt+1 jacket+1 pants
if I add the other two items we would get
Total Items
===== ===========================
100 1 tshirt+1 jacket+2 pants+1 shoe+1 socks
95 1 tshirt+1 jacket+1 pants+1 shoe+2 socks
90 1 tshirt+1 jacket+1 pants+1 shoe+1 socks
ok so the query is giving the final result not the table B, that you described to have a x b or item price multiplied by qty and sub total , well we can display that one very easily by filtering witch combination we selected, if we are selecting the first one that would be the nearest to the amount we can change the last part of the query to show table B you need.
),CombinationWithSeqQtySubTotal as (
select *,Price*qty [SubTotal] from CombinationWithSeqQty
),Results as (
select
CombinationId,
sum(subtotal) [Total],
replace(
replace(
STRING_AGG(
case when (Qty=0) then 'NA' else (cast(Qty as varchar(5))+' '+Item)
end
,'+')
,'+NA','')
,'NA+','') [Items]
from CombinationWithSeqQtySubTotal
group by CombinationId
having sum(subtotal)<=#total
--order by [Total] desc
)
select item, price, qty, SubTotal from CombinationWithSeqQtySubTotal t where t.CombinationId in
(select top(1) CombinationId from Results order by [Total] desc)
The result would be as below:-
item price qty SubTotal
===== ===== === =======
tshirt 30 1 30
jacket 30 1 30
pants 10 2 20
shoe 15 1 15
socks 5 1 5
or if we run it with only the items you provided the result would be as below:-
item price qty SubTotal
====== === === =======
tshirt 30 2 60
jacket 30 1 30
pants 10 1 10
if we dont want to use 'STRING_AGG' or we dont have it, we can manage its same function by adding some CTE's that will do the same job, as the 'STRING_AGG' was only combining the results in a (qty + item + comma), so the below solution may help.
Declare #Items Table (Item varchar(250),Price decimal)
insert into #Items values
('tshirt',30)
,('jacket',30)
,('pants' ,10)
--,('shoes' ,15) ---extra items for testing
--,('socks',5) ---extra items for testing
Declare #total int=100 -- your X
Declare #ItemsCount int
Declare #flag int
Declare #ItemsSum decimal
Declare #AllItmsQty int
select #ItemsCount=count(*),#ItemsSum=sum(price),#flag=POWER(2,count(*)) From #Items
select #AllItmsQty=#total/cast(#ItemsSum as int)
;with Numbers(n) as (
--generat numbers from 1,2,3,... #flag
select 1 union all
select (n+1) n from Numbers where n<#flag
),ItemsWithQty as (
select *,Price*n [LineTotal] from #Items,Numbers
),Combination as (
select items.*,Numbers.n-1 [CombinationId] from #Items items,Numbers
),CombinationWithSeq as (
select *,ROW_NUMBER() over (Partition by [CombinationId] order by [CombinationId]) [seq] from Combination
),CombinationWithSeqQty as (
select *,case when (CombinationId & power(2,seq-1))>0 then 1 else 0 end +#AllItmsQty [qty] from CombinationWithSeq
),CombinationWithSeqQtySubTotal as (
select *,Price*qty [SubTotal] from CombinationWithSeqQty
),CombinationWithTotal as (
--to find only the combinations that are less or equal to the Total
select
CombinationId,
sum(subtotal) [Total]
from CombinationWithSeqQtySubTotal
group by CombinationId
having sum(subtotal)<=#total
),DetailAnswer as (
select s.*,t.Total,cast(s.qty as varchar(20))+' ' +s.Item QtyItem from CombinationWithTotal t
inner join CombinationWithSeqQtySubTotal s on s.CombinationId=t.CombinationId
),DetailAnswerFirst as (
select *,cast(QtyItem as varchar(max)) ItemList from DetailAnswer t where t.seq=1
union all
select t.*,cast((t.QtyItem+'+'+x.ItemList) as varchar(max)) ItemList from DetailAnswer t
inner join DetailAnswerFirst x on x.CombinationId=t.CombinationId and x.seq+1=t.seq
)
select CombinationId,Total,ItemList from DetailAnswerFirst where seq=#ItemsCount order by Total desc
--select * from DetailAnswer --remark the above line and unremark this one for the details that you want to go in Table B
if any of the assumptions are wrong or if you need some description I would be happy to help.

Answer 2

Maybe the easiest way to get the possible combinations is via self-joins and joins to numbers.
If you want combinations of 3, then use 3 self-joins.
And 3 joins to a number table or CTE for each joined "Items" table.
The way the ON criteria are used, is to minimize the impact of all that joining.
You could also take the SQL from the COMBOS CTE, and use it to first insert it into a temporary table.
For example:
declare #PriceLimit decimal(10,2) = 100;
WITH COMBOS AS
(
SELECT
i1.id as id1, i2.id as id2, i3.id as id3,
n1.n as n1, n2.n as n2, n3.n as n3,
(n1.n + n2.n + n3.n) AS TotalItems,
(i1.Price * n1.n + i2.Price * n2.n + i3.Price * n3.n) as TotalCost
FROM Items i1
JOIN Items i2 ON i2.id > i1.id AND i2.Price < #PriceLimit
JOIN Items i3 ON i3.id > i2.id AND i3.Price < #PriceLimit
JOIN Nums n1
ON n1.n between 1 and FLOOR(#PriceLimit/i1.Price)
AND (i1.Price * n1.n) < #PriceLimit
JOIN Nums n2
ON n2.n between 1 and FLOOR(#PriceLimit/i2.Price)
AND (i1.Price * n1.n + i2.Price * n2.n) < #PriceLimit
JOIN Nums n3
ON n3.n between 1 and FLOOR(#PriceLimit/i3.Price)
AND (i1.Price * n1.n + i2.Price * n2.n + i3.Price * n3.n) <= #PriceLimit
AND (i1.Price * n1.n + i2.Price * n2.n + i3.Price * (n3.n+1)) > #PriceLimit
WHERE i1.Price < #PriceLimit
)
SELECT
c.TotalItems, c.TotalCost,
CONCAT (c.n1,' ',item1.Name,', ',c.n2,' ',item2.Name,', ',c.n3,' ',item3.Name) AS ItemList
FROM COMBOS c
LEFT JOIN Items item1 ON item1.id = c.id1
LEFT JOIN Items item2 ON item2.id = c.id2
LEFT JOIN Items item3 ON item3.id = c.id3
ORDER BY c.TotalCost desc, c.TotalItems desc, c.id1, c.id2, c.id3;
A test on db<>fiddle here
Test result:
TotalItems | TotalCost | ItemList
---------- | --------- | ---------------------------
7 | 100.00 | 1 pants, 1 tshirt, 5 socks
6 | 100.00 | 1 jacket, 1 tshirt, 4 socks
6 | 100.00 | 1 pants, 2 tshirt, 3 socks
5 | 100.00 | 1 jacket, 1 pants, 3 socks
5 | 100.00 | 1 jacket, 2 tshirt, 2 socks
5 | 100.00 | 1 pants, 3 tshirt, 1 socks
5 | 100.00 | 2 pants, 1 tshirt, 2 socks
3 | 90.00 | 1 jacket, 1 pants, 1 tshirt