Find all combinations - sql

Question

My teacher asks an algorithm that find all combinations. I have a set of data and the length can be variable. So combinations should be like this:
a
b
c
aa
ab
ac
...
ccbc
ccca
cccb
cccc
They will be stored in the "word" table that contains a single varchar field.
I did it with loop because I don't like recursivity and jt has better performance:
DROP PROCEDURE combi;
CREATE PROCEDURE combi
AS
BEGIN
DELETE FROM word
DECLARE #i BIGINT
DECLARE #j INT
DECLARE #word NVARCHAR(24)
DECLARE #str NVARCHAR(62)
DECLARE #combinations BIGINT
DECLARE #currentlength TINYINT
DECLARE #maxcurrentlength TINYINT
SET #maxcurrentlength=4
SET #str='azertyuiopqsdfghjklmwxcvbnAZERTYUIOPQSDFGHJKLMWXCVBN0123456789' -- length=62
SET #currentlength=1
-- loop on the length of the text
WHILE #currentlength<=#maxcurrentlength BEGIN
SET #combinations=POWER(62,#currentlength)
SET #i=0
-- get all combinations
WHILE i<#combinations BEGIN
SET #word=''
SET #j=0
-- generate word
WHILE #j<#currentlength BEGIN
SET #word=#word+SUBSTRING(#str, (FLOOR(#i / POWER(62,#currentlength-#j-1) ) % 62) +1, 1)
SET #j=#j+1
END
INSERT INTO word VALUES (#word)
SET #i=#i+1
END
SET #currentlength=#currentlength+1
END
END;
EXEC combi;
The problem is when I use a length of 8, my server crashes: it seems that POWER(62,#currentlength-#j-1) is the problem.

Answer 1

I'm slightly confused about how you ask the question. You ask to "find all combinations" which could very easily be done with CROSS JOIN. If you need to get a length of 4 then you join the table with available values to itself 4 times and you are pretty much done. If you need to get the strings in 1 field you could concatenate them in the select. Like this:
declare #values table (
value nvarchar(100))
insert #values values ('a'),('b'),('c')
select v1.value+v2.value+v3.value+v4.value
from #values v1 cross join
#values v2 cross join
#values v3 cross join
#values v4
order by v1.value+v2.value+v3.value+v4.value

Answer 2

Here is a generic solution using a recursive CTE:
CREATE TABLE t (i nchar(1))
INSERT INTO t VALUES ('a'),('b'),('c')
;WITH cte AS (
SELECT cast(i AS nvarchar(4000)) AS combo, 1 AS ct
FROM t
UNION ALL
SELECT cte.combo + t.i, ct + 1
FROM cte
CROSS JOIN t
WHERE ct <= 4 -- your maximum length
)
SELECT combo
FROM cte
ORDER BY ct, combo
SQL Fiddle.
You must be aware that the number of results grows exponentially with the maximum length, so performance deteriorates rapidly with growing maximum length.

Answer 3

You are likely overflowing the int type you are passing to POWER() as the documentation for power suggests POWER() returns the same type you feed it.
Try using:
SET #word=#word+SUBSTRING(#str, (FLOOR(#i / POWER(CAST(62 AS BIGINT),#currentlength-#j-1) ) % 62) +1, 1)

Answer 4

If you need to parameterise it so that you can set the required length then this algorithm would do it and it's more relational database orientated.
declare #characters table (character nchar(1))
declare #words table (word nvarchar(100))
insert #characters values ('a'),('b'),('c')
INSERT #words (word ) VALUEs ('')
DECLARE #Required_length int
DECLARE #length int
SET #Required_length = 4
SET #length = 0
WHILE #length <= #Required_length
BEGIN
SET #length = #length+1
INSERT #words (word )
SELECT w.word + c.character
FROM #words w JOIN #characters c ON LEN(w.word) = #length-1
END
SELECT word from #words where len(word) = #Required_length
Start with a zero length word
Add all the possible characters to the zero length word to get all
the one character words
Add all the possible characters to the end of all the one character
words to get all the two character words
Add all the possible characters to the end of all the two character words
to get all the three character words
etc....
You can make it run more efficiently by including the length as a column in the word table so that you don't need to calculate the lengths when you're filtering by them but as this has been set by your teacher I'm not going to do all your work for you

Answer 5

First insert of all characters
SET NOCOUNT ON;
create table ##chars (col char(1))
declare #i int
set #i=65
while #i<=90 /* A-Z */
begin
insert into ##chars values( CHAR(#i))
set #i=#i+1
end
set #i=97
while #i<=122 /* a-z */
begin
insert into ##chars values( CHAR(#i))
set #i=#i+1
end
set #i=48
while #i<=57 /* 0-9 */
begin
insert into ##chars values( CHAR(#i))
set #i=#i+1
end
Now, set number for combinations
create table ##result(word varchar(10))
declare #wide int
set #wide=4 /* set how many combinations are calculated */
insert into ##result select * from ##chars
while #wide>1
begin
begin tran w
insert into ##result select a.word+b.col from ##result a, ##chars b
commit tran w
set #wide=#wide-1
end
select * from ##result
/*
drop table ##chars
drop table ##result
*/