A Sudoku solution with set based T-SQL utilizing binary operators

Use tempDB
GO
--==================================================================
-- Step 1 Setup the auxiliary table containing possible values and their binary values
--==================================================================
IF OBJECT_ID(N'dbo.numBinaryDigits', N'U') IS NOT NULL DROP TABLE dbo.numBinaryDigits;
GO
Create table dbo.numBinaryDigits( vInt int, vBinary int)
Declare @i int
Set @i = 1
While @i <= 9 Begin
    insert into numBinaryDigits select @i, power(2, @i-1)
    set @i = @i +1
end
--==================================================================
-- Step 2: Convert a binary value to decimal list delimited by comma, for output
--==================================================================
IF OBJECT_ID(N'dbo.udfConvertBinaryToDecimalString', N'FN') IS NOT NULL DROP FUNCTION dbo.udfConvertBinaryToDecimalString;
GO
Create Function dbo.udfConvertBinaryToDecimalString (@i int) 
returns varchar(100) 
Begin
    Return stuff( ( select ', '+ltrim(str(vInt)) from numBinaryDigits where @i & vBinary >0 For xml path('') ) , 1,1,'' ) 
End

GO
--==================================================================
-- Step 3: Create the solution procedure. @T is the original puzzle in form of 81 characters, 0 for empty cells
--==================================================================
IF OBJECT_ID(N'dbo.uspSolveSudoku', N'P') IS NOT NULL DROP PROCEDURE dbo.uspSolveSudoku;
GO
Create procedure dbo.uspSolveSudoku ( @t varchar(100), @Trace bit = 0 )
AS
Set nocount on
declare @datetime datetime; 
select @datetime = getdate();
---------------------------------------
--Step 1: Setup working table #s. 
-- r for Row#, 
-- c for Column#, 
-- b for Block#, 
-- v for Value
-- d for current # of possible values
---------------------------------------
Create table #s ( r int, c int, b int, v int, d int)
Declare    @i int
set    @i = 0
while    @i < 81 Begin
 insert into #s 
 select    @i/9 +1,
    (@i % 9) +1,
    (@i / 27)*3 + ((@i%9)/3+1) ,
    case when substring(@t,@i+1,1)>0 then power(2, substring(@t,@i+1,1)-1) else 511 end,
    0
 set @i= @i + 1
End;
---------------------------------------
--Step 2: Solve the puzzle. A "range" means a single row, column or block
---------------------------------------
Declare    @SQL varchar(2000), 
    @SQL0 varchar(2000), 
    @SQL1 varchar(2000), 
    @SQL2 varchar(2000), 
    @SQL3 varchar(2000) 

-- Update the number of possible values in each cell
Set @SQL0 = 'Update #s set d = (select count(*) from numBinaryDigits where (v & vBinary)>0);'
-- query to eliminate determined values from un-determined cells in the same range
Set @SQL1 = 
'update #s set v = v - (v & sumv) 
from ( select Range as Range1, sum(v) as sumv 
 from #s where d = 1 
 group by Range
 ) as Range 
where Range= Range1 and d >1;' + @SQL0
-- query to determin the cell that solely contains a possible value in the same range
Set @SQL2 = 
'Update #s set v=VBinary 
from ( select Range as Range1, VBinary
 from #s cross apply (select * from numBinaryDigits where (v & vBinary)>0) as vb
 where d >1 
 group by Range, VBinary having count (*) =1
 ) as t
where (Range = Range1) and d >1 and (v & t.VBinary >0)' + @SQL0
-- if 2 cells in the same range have the same pair of possible values, eliminate the pair of values from other cells in the same range
Set @SQL3 = 
'Update #s set v = v- (v & v2) 
from ( select Range as Range1, v as v2
 from #s 
 where d= 2 group by Range,v having count(*) =2
 ) as t 
where Range1 = Range and v<> v2; ' + @SQL0

Exec (@SQL0);
Declare @Count1 smallint, -- Count of determined cells, before updates
 @Count2 smallint, -- Count of determined cells, after updates
 @CountSecondRuleExecTimes int ;
Select @Count1 = 0, @CountSecondRuleExecTimes = 0;

Select @Count2 = Count(*) from #s where d=1
While @Count2 < 81 and @CountSecondRuleExecTimes < 100 Begin
 
 While @Count1 <> @Count2 and @Count2 < 81 Begin
 Select @Count1 = count(*) from #s where d = 1

 Set @SQL = replace(@SQL1, 'Range','r'); Exec (@SQL); 
 If @Trace= 1 print Char(13)+Char(10)+@SQL

 Set @SQL = replace(@SQL1, 'Range','c'); Exec (@SQL); 
 If @Trace= 1 print Char(13)+Char(10)+@SQL

 Set @SQL = replace(@SQL1, 'Range','b'); Exec (@SQL); 
 If @Trace= 1 print Char(13)+Char(10)+@SQL

 Select @Count2 = count(*) from #s where d = 1
 End

 If @Count2 < 81 Begin
 Set @SQL = replace (    case when (@CountSecondRuleExecTimes % 6) <3 then @SQL2 else @SQL3 end, 
            'Range', 
            case (@CountSecondRuleExecTimes % 3) when 0 then 'r' when 1 then 'c' when 2 then 'b' end)
 If @Trace= 1 print Char(13)+Char(10)+@SQL
 Exec (@SQL); 

 Select @Count2 = count(*) from #s where d = 1
 Select @CountSecondRuleExecTimes = @CountSecondRuleExecTimes + 1 
 if @Count1<> @Count2 AND @Trace = 1 Print replace(@SQL, char(13)+char(10),'')

 End
End ;
---------------------------------------
OutputSudoku:
---------------------------------------
with a as (
 select r as 'Row', c as c, v = CASE WHEN d = 1 THEN dbo.udfConvertBinaryToDecimalString(v) 
 ELSE case @Trace when 1 then dbo.udfConvertBinaryToDecimalString(v) else '_' end 
 END
 from #s
) 
select * from a pivot ( max(v) for c in ([1],[2],[3],[4],[5],[6],[7],[8],[9]) ) as p

If @Trace = 1 select datediff(ms, @datetime, getdate()), @CountSecondRuleExecTimes
GO
exec uspSolveSudoku '029000008030000010000520097070056100000000000006310070760041000050000020800000630' , 1
GO
exec uspSolveSudoku '200060000000900871740008006006080030003000100090030400300700018972005000000090002' , 1
GO
/* Code Clean Up
IF OBJECT_ID(N'dbo.numBinaryDigits', N'U') IS NOT NULL DROP TABLE dbo.numBinaryDigits;
IF OBJECT_ID(N'dbo.udfConvertBinaryToDecimalString', N'FN') IS NOT NULL DROP FUNCTION dbo.udfConvertBinaryToDecimalString;
IF OBJECT_ID(N'dbo.uspSolveSudoku', N'P') IS NOT NULL DROP PROCEDURE dbo.uspSolveSudoku;
*/