Getting the lowest possible sum from numbers' difference

Question

I have to find the lowest possible sum from numbers\' difference.

Let\'s say I have 4 numbers. 1515, 1520, 1500 and 1535. The lowest sum of difference is 30, becaus

Answer 1

I know you said you did not need code but it is the best way for me to describe a set based solution. The solution runs under SQL Server 2008. Included in the code is the data for the two examples you give. The sql solution could be done with a single self joining table but I find it easier to explain when there are multiple tables.

    --table 1 holds the values

declare @Table1 table (T1_Val int)
Insert @Table1 
--this data is test 1
--Select (1515) Union ALL
--Select (1520) Union ALL
--Select (1500) Union ALL
--Select (1535) 

--this data is test 2
Select (1731) Union ALL
Select (1572) Union ALL
Select (2041) Union ALL
Select (1561) Union ALL
Select (1682) Union ALL
Select (1572) Union ALL
Select (1609) Union ALL
Select (1731) 
--Select * from @Table1

--table 2 holds the sorted numbered list
Declare @Table2 table (T2_id int identity(1,1), T1_Val int)
Insert @Table2 Select T1_Val from @Table1 order by T1_Val

--table 3 will hold the sorted pairs
Declare @Table3 table (T3_id int identity(1,1), T21_id int, T21_Val int, T22_id int, T22_val int)
Insert @Table3
Select T2_1.T2_id, T2_1.T1_Val,T2_2.T2_id, T2_2.T1_Val from @Table2 AS T2_1
LEFT Outer join @Table2 AS T2_2 on T2_1.T2_id = T2_2.T2_id +1

--select * from @Table3
--remove odd numbered rows
delete from @Table3 where T3_id % 2 > 0 

--select * from @Table3
--show the diff values
--select *, ABS(T21_Val - T22_val) from @Table3
--show the diff values in order
--select *, ABS(T21_Val - T22_val) from @Table3 order by ABS(T21_Val - T22_val)
--display the two lowest
select TOP 2 CAST(T22_val as varchar(24)) + ' and ' + CAST(T21_val as varchar(24)) as 'The minimum difference pairs are'
, ABS(T21_Val - T22_val) as 'Difference'
from @Table3
ORDER by ABS(T21_Val - T22_val)