List combination of numbers which have same sum - sql

Question

**N** is a prositive number
Need list of scenarios which have sum equal N
For example if N=4
ScenarioId Value
---------- -----
1 1
1 1
1 1
1 1
2 2
2 1
2 1
3 2
3 2
4 3
4 1
5 4
above list is required. If you sum by ScenarioId all sum must equal to N
UPDATE
Here is my own solution. however, I am not sure about the multiplication of two different number sets would not be equal at any time.
My current question is
Is there any possibilities a + b + c = d + e + f and a * b * c = d * e * f
Test link is here
DECLARE #N int = 4;
SELECT
[Value] = CAST(number + 1 as tinyint)
INTO #Values
FROM master.dbo.spt_values
WHERE number < #N
AND [Type] = 'p'
;WITH COMBINATIONS AS(
SELECT ScenarioKey = CAST(NULL AS nvarchar(MAX)), [Value], Total = 0, Multipication = 1, MemeberCount = 0
FROM #Values
UNION ALL
SELECT ScenarioKey = ISNULL(S.ScenarioKey, '') + IIF(S.ScenarioKey IS NULL, '', N'-') + CAST(P.[Value] AS nvarchar(10)), S.[Value], Total = S.Total + P.[Value], Multipication = S.Multipication * P.[Value], MemeberCount = MemeberCount + 1
FROM #Values P
JOIN COMBINATIONS AS S ON S.Total < S.[Value]
),
SCENARIOS AS(
SELECT
ScenarioKey
,ScenarioId = ROW_NUMBER() OVER(ORDER BY ScenarioKey)
,[Value]
FROM
(
SELECT
ScenarioKey
,[Value]
,Multipication
,MemeberCount
-- this will prevent dublications. because 1 * 2 * 3 = 3 * 2 * 1
-- however, I am not sure about multipication of two different number sets would not be equal any time
,RowNo = ROW_NUMBER() OVER(PARTITION BY [Value],Multipication,MemeberCount ORDER BY [Value],ScenarioKey)
FROM COMBINATIONS
WHERE Total = #N
) X
WHERE RowNo = 1 AND [Value] = #N
)
SELECT
R.ScenarioId
,[Value] = S.[value]
FROM SCENARIOS R
CROSS APPLY (SELECT [value] FROM STRING_SPLIT(R.ScenarioKey, '-')) S
DROP TABLE #Values

Answer 1

It's too long for comment, so I post this as an answer. I want to note, that this is a static example, but I hope it can be easily translated as a dynamic statement.
Steps are written as comments in the statement:
WITH rcte AS
(
-- Recursive query to generate all numbers from 1 to 4
SELECT 0 AS Number
UNION ALL
SELECT Number + 1
FROM rcte
WHERE Number < 4
), permutations AS (
-- All possible permutations with sum equal to 4
-- There is additional column DuplicateMarker.
-- It will be used later, because 0,0,0,4 and 0,4,0,0 are the same
SELECT
t1.Number AS Number1,
t2.Number AS Number2,
t3.Number AS Number3,
t4.Number AS Number4,
CONCAT(LTRIM(STR(t1.Number)), '.', LTRIM(STR(t2.Number)), '.', LTRIM(STR(t3.Number)), '.', LTRIM(STR(t4.Number))) AS DuplicateMarker
FROM rcte t1, rcte t2, rcte t3, rcte t4
WHERE (t1.Number + t2.Number + t3.Number + t4.Number) = 4
), duplicates AS (
-- Get data with splitted DuplicateMarker column
SELECT *
FROM permutations
CROSS APPLY (SELECT [value] FROM STRING_SPLIT(DuplicateMarker, '.')) t
), results AS (
-- Get unique combinations
-- WITHIN GROUP (ORDER BY) will order strings and 0.0.0.4 and 0.4.0.0 will be the same
SELECT DISTINCT STRING_AGG([value], '.') WITHIN GROUP (ORDER BY [value]) AS ScenarioValue
FROM duplicates
GROUP BY Number1, Number2, Number3, Number4
)
SELECT
DENSE_RANK() OVER (ORDER BY r.ScenarioValue) AS ScenarioID,
s.[value]
FROM results r
CROSS APPLY (SELECT [value] FROM STRING_SPLIT(r.ScenarioValue, '.')) s
WHERE [value] <> '0'
Output:
ScenarioID value
1 4
2 1
2 3
3 2
3 2
4 1
4 1
4 2
5 1
5 1
5 1
5 1
Update:
Thanks to #AndriyM's comment, I've made some changes and now you can eliminate string manipulations:
WITH rcte AS
(
-- Recursive query to generate all numbers from 0 to 4
SELECT 0 AS Number
UNION ALL
SELECT Number + 1
FROM rcte
WHERE Number < 4
), combinations AS (
-- All different combinations with sum equal to 4
SELECT
t1.Number AS Number1,
t2.Number AS Number2,
t3.Number AS Number3,
t4.Number AS Number4,
ROW_NUMBER() OVER (ORDER BY t1.Number, t2.Number, t3.Number, t4.NUmber) AS ScenarioID
FROM rcte t1, rcte t2, rcte t3, rcte t4
WHERE
((t1.Number + t2.Number + t3.Number + t4.Number) = 4) AND
(t1.Number <= t2.Number) AND
(t2.Number <= t3.Number) AND
(t3.Number <= t4.Number)
)
SELECT c.ScenarioID, v.[value]
FROM combinations c
CROSS APPLY (VALUES (c.NUmber1), (c.Number2), (c.Number3), (c.Number4)) AS v ([value])
WHERE v.[value] > 0
Update 2:
Approach using dynamic statement - probably not the best approach, but is based on statement from first update:
-- Set your #n value
DECLARE #n int
SET #n = 4
-- Declarations
DECLARE #combinationsSelect nvarchar(max)
DECLARE #combinationsRowNumber nvarchar(max)
DECLARE #combinationsFrom nvarchar(max)
DECLARE #combinationsWhere1 nvarchar(max)
DECLARE #combinationsWhere2 nvarchar(max)
DECLARE #combinationsValues nvarchar(max)
SET #combinationsSelect = N''
SET #combinationsRowNumber = N''
SET #combinationsFrom = N''
SET #combinationsValues = N''
SET #combinationsWhere1 = N''
SET #combinationsWhere2 = N''
-- Generate dynamic parts of the statement
;WITH numbers AS
(
SELECT 1 AS Number
UNION ALL
SELECT Number + 1
FROM Numbers
WHERE Number < #n
)
SELECT
#combinationsSelect = #combinationsSelect + N', t' + LTRIM(STR(Number)) + N'.Number AS Number' + LTRIM(STR(Number)),
#combinationsRowNumber = #combinationsRowNumber + N', t' + LTRIM(STR(Number)) + N'.Number',
#combinationsValues = #combinationsValues + N', (c.Number' + LTRIM(STR(Number)) + N')',
#combinationsFrom = #combinationsFrom + N', rcte t' + LTRIM(STR(Number)),
#combinationsWhere1 = #combinationsWhere1 + N'+ t' + LTRIM(STR(Number)) + N'.Number ',
#combinationsWhere2 = #combinationsWhere2 +
CASE
WHEN Number = 1 THEN N''
ELSE N'AND (t' + LTRIM(STR(Number-1)) + N'.Number <= t' + + LTRIM(STR(Number)) + N'.Number) '
END
FROM
numbers
SET #combinationsSelect = STUFF(#combinationsSelect, 1, 2, N'')
SET #combinationsRowNumber = STUFF(#combinationsRowNumber, 1, 2, N'')
SET #combinationsValues = STUFF(#combinationsValues, 1, 2, N'')
SET #combinationsFrom = STUFF(#combinationsFrom, 1, 2, N'')
SET #combinationsWhere1 = STUFF(#combinationsWhere1, 1, 2, N'')
SET #combinationsWhere2 = STUFF(#combinationsWhere2, 1, 4, N'')
-- Dynamic statement
DECLARE #stm nvarchar(max)
SET #stm =
N'WITH rcte AS (
SELECT 0 AS Number
UNION ALL
SELECT Number + 1
FROM rcte
WHERE Number < ' + LTRIM(STR(#n)) +
N'), combinations AS (
SELECT ' +
#combinationsSelect +
N', ROW_NUMBER() OVER (ORDER BY ' + #combinationsRowNumber + N') AS ScenarioID
FROM ' + #combinationsFrom +
N' WHERE ((' + #combinationsWhere1 + N') = ' + LTRIM(STR(#n)) + ') AND ' + #combinationsWhere2 +
N')
SELECT c.ScenarioID, v.[value]
FROM combinations c
CROSS APPLY (VALUES ' + #combinationsValues + N') AS v ([value])
WHERE v.[value] > 0'
-- Execute dynamic statement
EXEC (#stm)

Answer 2

If you have sample data like below
You can write query like below
Declare #N int =4
Select T.*
From #T T
cross apply (
select S, SUM(V) Total
From #T
Group By S) Totals
Where Totals.Total=#N and T.S = Totals.S