Postgres 8.4

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CREATE TABLE tmp (
   date    timestamp UNIQUE NOT NULL
 , id_type integer NOT NULL
) ;
INSERT INTO tmp (date, id_type)
VALUES
    ( '2017-01-10 07:19:21.0', 3 ),
    ( '2017-01-10 07:19:22.0', 3 ),
    ( '2017-01-10 07:19:23.1', 3 ),
    ( '2017-01-10 07:19:24.1', 3 ),
    ( '2017-01-10 07:19:25.0', 3 ),
    ( '2017-01-10 07:19:26.0', 5 ),
    ( '2017-01-10 07:19:27.1', 3 ),
    ( '2017-01-10 07:19:28.0', 5 ),
    ( '2017-01-10 07:19:29.0', 5 ),
    ( '2017-01-10 07:19:30.1', 3 ),
    ( '2017-01-10 07:19:31.0', 5 ),
    ( '2017-01-10 07:19:32.0', 3 ),
    ( '2017-01-10 07:19:33.1', 5 ),
    ( '2017-01-10 07:19:35.0', 5 ),
    ( '2017-01-10 07:19:36.1', 5 ),
    ( '2017-01-10 07:19:37.1', 5 );
16 rows affected

INSERT INTO tmp(date, id_type)
SELECT date + interval '1 day' * g, id_type
FROM   tmp, generate_series(1,8000) g;
128000 rows affected

VACUUM ANALYZE tmp;
CREATE OR REPLACE FUNCTION f_tmp_groups()
  RETURNS TABLE (id_type int, grp_begin timestamp, grp_end timestamp) AS
$func$
DECLARE
   _row  tmp;                       -- use table type for row variable
BEGIN
   FOR _row IN
      TABLE tmp ORDER BY date       -- add more columns to make order deterministic
   LOOP
      CASE _row.id_type = id_type 
      WHEN TRUE THEN                -- same group continues
         grp_end := _row.date;      -- remember last date so far
      WHEN FALSE THEN               -- next group starts
         RETURN NEXT;               -- return result for last group
         id_type   := _row.id_type;
         grp_begin := _row.date;
         grp_end   := _row.date;
      ELSE                          -- NULL for 1st row
         id_type   := _row.id_type; -- remember row data for starters
         grp_begin := _row.date;
         grp_end   := _row.date;
      END CASE;
   END LOOP;

   RETURN NEXT;                     -- return last result row      
END
$func$ LANGUAGE plpgsql;
-- 1.
EXPLAIN ANALYZE
SELECT id_type
     , min(date) AS begin
     , max(date) AS end
FROM  (
   SELECT date, id_type, count(step OR NULL) OVER (ORDER BY date) AS grp
   FROM  (
      SELECT date, id_type
           , lag(id_type) OVER (ORDER BY date) <> id_type AS step
      FROM   tmp
      ) sub1
   ) sub2
GROUP  BY id_type, grp
ORDER  BY min(date);


QUERY PLAN


Sort  (cost=26898.01..26930.01 rows=12802 width=20) (actual time=511.933..526.859 rows=64008 loops=1)

  Sort Key: (min(sub2.date))

  Sort Method:  external merge  Disk: 2632kB

  ->  GroupAggregate  (cost=24232.42..26024.65 rows=12802 width=20) (actual time=374.881..463.911 rows=64008 loops=1)

        ->  Sort  (cost=24232.42..24552.46 rows=128016 width=20) (actual time=374.870..415.777 rows=128016 loops=1)

              Sort Key: sub2.id_type, sub2.grp

              Sort Method:  external merge  Disk: 4224kB

              ->  Subquery Scan sub2  (cost=0.00..10744.34 rows=128016 width=20) (actual time=0.041..230.758 rows=128016 loops=1)

                    ->  WindowAgg  (cost=0.00..9464.18 rows=128016 width=13) (actual time=0.040..192.611 rows=128016 loops=1)

                          ->  WindowAgg  (cost=0.00..6263.78 rows=128016 width=12) (actual time=0.033..111.294 rows=128016 loops=1)

                                ->  Index Scan using tmp_date_key on tmp  (cost=0.00..4023.50 rows=128016 width=12) (actual time=0.022..38.134 rows=128016 loops=1)

Total runtime: 538.023 ms


-- 2.
EXPLAIN ANALYZE
SELECT min(date) AS begin
     , max(date) AS end
     , id_type
FROM  (
   SELECT date, id_type
        , row_number() OVER (ORDER BY date)
        - row_number() OVER (PARTITION BY id_type ORDER BY date) AS grp
   FROM   tmp
   ) sub
GROUP  BY id_type, grp
ORDER  BY min(date);


QUERY PLAN


Sort  (cost=39308.50..39340.51 rows=12802 width=20) (actual time=603.614..618.263 rows=64008 loops=1)

  Sort Key: (min(tmp.date))

  Sort Method:  external merge  Disk: 2632kB

  ->  GroupAggregate  (cost=36642.91..38435.14 rows=12802 width=20) (actual time=486.928..559.273 rows=64008 loops=1)

        ->  Sort  (cost=36642.91..36962.95 rows=128016 width=20) (actual time=486.918..511.419 rows=128016 loops=1)

              Sort Key: tmp.id_type, (((row_number() OVER (?)) - row_number() OVER (?)))

              Sort Method:  external sort  Disk: 4256kB

              ->  WindowAgg  (cost=18994.32..21874.68 rows=128016 width=12) (actual time=231.210..344.083 rows=128016 loops=1)

                    ->  Sort  (cost=18994.32..19314.36 rows=128016 width=12) (actual time=231.184..275.473 rows=128016 loops=1)

                          Sort Key: tmp.id_type, tmp.date

                          Sort Method:  external merge  Disk: 4224kB

                          ->  WindowAgg  (cost=0.00..5943.74 rows=128016 width=12) (actual time=0.012..94.416 rows=128016 loops=1)

                                ->  Index Scan using tmp_date_key on tmp  (cost=0.00..4023.50 rows=128016 width=12) (actual time=0.009..35.779 rows=128016 loops=1)

Total runtime: 629.593 ms


-- 3.
EXPLAIN ANALYZE
SELECT * FROM f_tmp_groups();


QUERY PLAN


Function Scan on f_tmp_groups  (cost=0.00..260.00 rows=1000 width=20) (actual time=171.841..183.274 rows=64008 loops=1)

Total runtime: 191.398 ms