Find all possible combinations of array without permutations - sql

Question

Input is an array of 'n' length.
I need all combinations inside this array stored into new array.
IN: j='{A, B, C ..}'
OUT: k='{A, B, C, AB, AC, BC, ABC ..}'
Without repetitions, so without BA, CA etc.

Answer 1

Generic solution using a recursive CTE
Works for any number of elements and any base data type that supports the > operator.
WITH RECURSIVE t(i) AS (SELECT * FROM unnest('{A,B,C}'::text[])) -- provide array
, cte AS (
SELECT i::text AS combo, i, 1 AS ct
FROM t
UNION ALL
SELECT cte.combo || t.i::text, t.i, ct + 1
FROM cte
JOIN t ON t.i > cte.i
)
SELECT ARRAY (
SELECT combo
FROM cte
ORDER BY ct, combo
) AS result;
Result is an array of text in the example.
Note that you can have any number of additional non-recursive CTEs when using the RECURSIVE keyword.
More generic yet
If any of the following apply:
Array elements are non-unique (like '{A,B,B}').
The base data type does not support the > operator (like json).
Array elements are very big - for better performance.
Use a row number instead of comparing elements:
WITH RECURSIVE t AS (
SELECT i::text, row_number() OVER () AS rn
FROM unnest('{A,B,B}'::text[]) i -- duplicate element!
)
, cte AS (
SELECT i AS combo, rn, 1 AS ct
FROM t
UNION ALL
SELECT cte.combo || t.i, t.rn, ct + 1
FROM cte
JOIN t ON t.rn > cte.rn
)
SELECT ARRAY (
SELECT combo
FROM cte
ORDER BY ct, combo
) AS result;
Or use WITH ORDINALITY in Postgres 9.4+:
PostgreSQL unnest() with element number
Special case: generate decimal numbers
To generate decimal numbers with 5 digits along these lines:
WITH RECURSIVE t AS (
SELECT i
FROM unnest('{1,2,3,4,5}'::int[]) i
)
, cte AS (
SELECT i AS nr, i
FROM t
UNION ALL
SELECT cte.nr * 10 + t.i, t.i
FROM cte
JOIN t ON t.i > cte.i
)
SELECT ARRAY (
SELECT nr
FROM cte
ORDER BY nr
) AS result;
SQL Fiddle demonstrating all.

Answer 2

if n is small < 20 , all possible combinations can be found using a bitmask approach. There are 2^n different combinations of it. The number values 0 to
(2^n - 1) represents one of the combination.
e.g n=3
0 represents {},empty element
2^3-1=7= 111 b represents element, abc
pseudo code as follows
for b=0 to 2^n - 1 do #each combination
res=""
for i=0 to (n-1) do # which elements are included
if (b && (1<<i) != 0)
res= res+arr[i]
end
print res
end
end