TSql Challenge 56 is over .... So I can safetly ask doubt on that
I have tried to solve the problem as under
WITH CTE AS
(
SELECT
id ,
level ,
1 AS row ,
REPLICATE('X', POWER(3, level)) AS carpet
FROM TC56
UNION ALL
SELECT id ,
level ,
row + 1 ,
carpet
FROM CTE
WHERE Row < POWER(3, level)
)
SELECT
id
,row
,carpet
FROM CTE
ORDER BY id,row
But the output is not at par with the one specified.. My output is as under
id row carpet
1 1 X
2 1 XXX
2 2 XXX
2 3 XXX
3 1 XXXXXXXXX
3 2 XXXXXXXXX
3 3 XXXXXXXXX
3 4 XXXXXXXXX
3 5 XXXXXXXXX
3 6 XXXXXXXXX
3 7 XXXXXXXXX
3 8 XXXXXXXXX
3 9 XXXXXXXXX
The problem is that I am not able to fill positions that needs to be filled with empty spaces
Help needed
Here's a solution that can be extended to be able to generate Sierpinski carpets of greater orders. Currently it can correctly generate Sierpinski carpets up to the 3rd order.
By 'correctly' I mean, it can produce all the necessary rows for greater order patterns, but presently additional columns need to be added (those sortN ones) to provide the correct arrangement of the rows. I've added comments where modifications are required.
WITH TC56 (id, level) AS (
SELECT 1, 0 UNION ALL
SELECT 2, 1 UNION ALL
SELECT 3, 2
),
x AS (
SELECT CAST('X' AS varchar(max)) AS x
),
rec_cte AS (
SELECT
x,
level = 0,
sort1 = 0,
sort2 = 0,
sort3 = 0
/* add new columns here */
FROM x
UNION ALL
SELECT
x = CAST(x.x + CASE TC56.level WHEN 1 THEN SPACE(LEN(x.x)) ELSE x.x END + x.x
AS varchar(max)),
level = x.level + 1,
sort1 = TC56.level,
sort2 = (TC56.level * 3 + x.sort1) % 3,
sort3 = ((TC56.level * 3 + x.sort1) * 3 + x.sort2) % 3
/* computations of the new columns' values follow the above pattern; e.g.
sort4 = (((TC56.level * 3 + x.sort1) * 3 + x.sort2) * 3 + x.sort3) % 3 */
FROM rec_cte x
CROSS JOIN TC56
WHERE x.level < 3 /* the necessary level to generate;
the last sortN's N number defines the maximum value
for which the pattern produced is guaranteed to be correct;
in this script the last sort column is sort3, so
the maximum 'supported' order is 3 */
)
SELECT * FROM rec_cte
ORDER BY level, sort1, sort2, sort3 /* add the new columns here */
Here's the result:
x level sort1 sort2 sort3
------------------------------ ----------- ----------- ----------- -----------
X 0 0 0 0
XXX 1 0 0 0
X X 1 1 0 0
XXX 1 2 0 0
XXXXXXXXX 2 0 0 0
X XX XX X 2 0 1 0
XXXXXXXXX 2 0 2 0
XXX XXX 2 1 0 0
X X X X 2 1 1 0
XXX XXX 2 1 2 0
XXXXXXXXX 2 2 0 0
X XX XX X 2 2 1 0
XXXXXXXXX 2 2 2 0
XXXXXXXXXXXXXXXXXXXXXXXXXXX 3 0 0 0
X XX XX XX XX XX XX XX XX X 3 0 0 1
XXXXXXXXXXXXXXXXXXXXXXXXXXX 3 0 0 2
XXX XXXXXX XXXXXX XXX 3 0 1 0
X X X XX X X XX X X X 3 0 1 1
XXX XXXXXX XXXXXX XXX 3 0 1 2
XXXXXXXXXXXXXXXXXXXXXXXXXXX 3 0 2 0
X XX XX XX XX XX XX XX XX X 3 0 2 1
XXXXXXXXXXXXXXXXXXXXXXXXXXX 3 0 2 2
XXXXXXXXX XXXXXXXXX 3 1 0 0
X XX XX X X XX XX X 3 1 0 1
XXXXXXXXX XXXXXXXXX 3 1 0 2
XXX XXX XXX XXX 3 1 1 0
X X X X X X X X 3 1 1 1
XXX XXX XXX XXX 3 1 1 2
XXXXXXXXX XXXXXXXXX 3 1 2 0
X XX XX X X XX XX X 3 1 2 1
XXXXXXXXX XXXXXXXXX 3 1 2 2
XXXXXXXXXXXXXXXXXXXXXXXXXXX 3 2 0 0
X XX XX XX XX XX XX XX XX X 3 2 0 1
XXXXXXXXXXXXXXXXXXXXXXXXXXX 3 2 0 2
XXX XXXXXX XXXXXX XXX 3 2 1 0
X X X XX X X XX X X X 3 2 1 1
XXX XXXXXX XXXXXX XXX 3 2 1 2
XXXXXXXXXXXXXXXXXXXXXXXXXXX 3 2 2 0
X XX XX XX XX XX XX XX XX X 3 2 2 1
XXXXXXXXXXXXXXXXXXXXXXXXXXX 3 2 2 2
