Postgres 13

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CREATE TABLE t (id int, mycolumn text);
INSERT INTO t VALUES (1,'A'),(2,'A,B'),(3,'A,B,C');

SELECT *,string_to_array(mycolumn,',')
FROM t
WHERE string_to_array(mycolumn,',') <@ ARRAY['A','B','C']

CREATE TABLE

INSERT 0 3

id
mycolumn
string_to_array

1
A
{A}

2
A,B
{A,B}

3
A,B,C
{A,B,C}

SELECT 3

SELECT *,string_to_array(mycolumn,',')
FROM t
WHERE string_to_array(mycolumn,',') <@ ARRAY['A','B']

id
mycolumn
string_to_array

1
A
{A}

2
A,B
{A,B}

SELECT 2

SELECT *,string_to_array(mycolumn,',')
FROM t
WHERE string_to_array(mycolumn,',') <@ ARRAY['A'] 

id
mycolumn
string_to_array

1
A
{A}

SELECT 1

-- Inserting 100000 data sets with the value 'D,E,F'
INSERT INTO t SELECT j.id,'D,E,F' FROM generate_series(1,100000) j(id);

-- Query Time without Index
EXPLAIN (ANALYSE,COSTS OFF)
SELECT *,string_to_array(mycolumn,',')
FROM t
WHERE string_to_array(mycolumn,',') <@ ARRAY['A','B','C']

INSERT 0 100000

QUERY PLAN

Seq Scan on t (actual time=0.025..65.670 rows=3 loops=1)

  Filter: (string_to_array(mycolumn, ','::text) <@ '{A,B,C}'::text[])

  Rows Removed by Filter: 100000

Planning Time: 0.074 ms

Execution Time: 65.712 ms

EXPLAIN

-- Creating GIN index
CREATE INDEX t_mycolumn_array_gist ON t USING gin (string_to_array(mycolumn,','));

-- Query time with index
EXPLAIN (ANALYSE,COSTS OFF)
SELECT *,string_to_array(mycolumn,',')
FROM t
WHERE string_to_array(mycolumn,',') <@ ARRAY['A','B','C']

CREATE INDEX

QUERY PLAN

Bitmap Heap Scan on t (actual time=0.550..0.555 rows=3 loops=1)

  Recheck Cond: (string_to_array(mycolumn, ','::text) <@ '{A,B,C}'::text[])

  Heap Blocks: exact=1

  ->  Bitmap Index Scan on t_mycolumn_array_gist (actual time=0.395..0.395 rows=3 loops=1)

        Index Cond: (string_to_array(mycolumn, ','::text) <@ '{A,B,C}'::text[])

Planning Time: 0.758 ms

Execution Time: 0.593 ms

EXPLAIN