efficient merge of arrays that contain overlapping values - postgresql

Question

Given a table with arrays of integers, the arrays should be merged so that all arrays that have overlapping entries end up as a single one.
Given the table arrays
a
------------
{1,2,3}
{1,4,7}
{4,7,9}
{15,17,18}
{18,16,15}
{20}
The result should look like this
{1,2,3,4,7,9}
{15,17,18,16}
{20}
As you can see duplicate values from a merged array may be removed and the order of the resulting entries in the array is unimportant. The arrays are integer arrays so functions from the intarray module can be used.
This will be done on a quite large table so performance is critical.
My first naive approach was to self-join the table on the && operator. Like this:
SELECT DISTINCT uniq(sort(t1.a || t2.a))
FROM arrays t1
JOIN arrays t2 ON t1.a && t2.a
This leaves two problems:
It is not recursive (it merges at most 2 arrays).
This could probably be solved with a recursive CTE.
Merged arrays re-occur in the output.
Any input is very welcome.

Answer 1

do $$
declare
arr int[];
arr_id int := 0;
tmp_id int;
begin
create temporary table tmp (v int primary key, id int not null);
for arr in select a from t loop
select id into tmp_id from tmp where v = any(arr) limit 1;
if tmp_id is NULL then
tmp_id = arr_id;
arr_id = arr_id+1;
end if;
insert into tmp
select unnest(arr), tmp_id
on conflict do nothing;
end loop;
end
$$;
select array_agg(v) from tmp group by id;

Answer 2

Pure SQL version:
WITH RECURSIVE x (a) AS (VALUES ('{1,2,3}'::int2[]),
('{1,4,7}'),
('{4,7,9}'),
('{15,17,18}'),
('{18,16,15}'),
('{20}')
), y AS (
SELECT 1::int AS lvl,
ARRAY [ a::text ] AS a,
a AS res
FROM x
UNION ALL
SELECT lvl + 1,
t1.a || ARRAY [ t2.a::text ],
(SELECT array_agg(DISTINCT unnest ORDER BY unnest)
FROM (SELECT unnest(t1.res) UNION SELECT unnest(t2.a)) AS a)
FROM y AS t1
JOIN x AS t2 ON (t2.a && t1.res) AND NOT t2.a::text = ANY(t1.a)
WHERE lvl < 10
)
SELECT DISTINCT res
FROM x
JOIN LATERAL (SELECT res FROM y WHERE x.a && y.res ORDER BY lvl DESC LIMIT 1) AS z ON true