Apenas para evitar trabalho duplo, aqui estão os dados (substituí o compartimento de limite superior inclusivo por um exclusivo, que é mais comum, IMHO):
-- CREATE SCHEMA tmp;
DROP TABLE tmp.gaps CASCADE;
CREATE TABLE tmp.gaps
( id INTEGER NOT NULL PRIMARY KEY -- surrogate key
, ztype CHAR(1) NOT NULL
, start_datetime TIMESTAMP NOT NULL -- lower boundary := inclusive
, end_datetime TIMESTAMP NOT NULL -- upper boundary := exclusive
);
CREATE UNIQUE INDEX gaps_forward ON tmp.gaps(ztype,start_datetime);
CREATE UNIQUE INDEX gaps_backward ON tmp.gaps(ztype,end_datetime);
INSERT INTO tmp.gaps(id,ztype,start_datetime,end_datetime) VALUES
(1,'a', '2012-01-11 00:00:00', '2012-01-15 00:00:00' )
,(2,'a', '2012-01-18 00:00:00', '2012-01-21 00:00:00' )
,(3,'b', '2012-01-14 00:00:00', '2012-01-20 00:00:00' )
,(4,'c', '2012-01-10 00:00:00', '2012-01-16 00:00:00' )
,(5,'d', '2012-01-11 00:00:00', '2012-01-21 00:00:00' )
,(6,'e', '2012-01-11 00:00:00', '2012-01-15 00:00:00' ) -- added this
,(7,'e', '2012-01-15 00:00:00', '2012-01-21 00:00:00' ) -- and this
;
-- SELECT * FROM tmp.gaps;
UPDATE:aqui vem o CTE. Na primeira UNION, adiciono dois intervalos falsos à esquerda e à direita do intervalo desejado (12-Jan - 19-Jan).
Por ztype eu conto o número total de intervalos. Este deve ser um se não houver buracos, dois se houver um buraco, etc. Isso também encontrará lacunas para ztypes que não possuem nenhum registro no intervalo desejado.
-- EXPLAIN ANALYZE
WITH RECURSIVE meuk(ztype,start_datetime,end_datetime) AS (
-- For every possible "ztype" add two dummie records
-- just before and just after our wanted interval.
WITH plus2 AS (
SELECT g0.ztype,g0.start_datetime,g0.end_datetime FROM tmp.gaps g0
WHERE (g0.start_datetime <= '2012-01-12 00:00:00' AND g0.end_datetime >= '2012-01-12 00:00:00')
OR (g0.start_datetime >= '2012-01-12 00:00:00' AND g0.end_datetime <= '2012-01-19 00:00:00')
OR (g0.start_datetime <= '2012-01-19 00:00:00' AND g0.end_datetime >= '2012-01-19 00:00:00')
UNION ALL SELECT DISTINCT g1.ztype, '1900-01-01 00:00:00'::timestamp, '2012-01-12 00:00:00'::timestamp FROM tmp.gaps g1
UNION ALL SELECT DISTINCT g2.ztype, '2012-01-19 00:00:00'::timestamp, '2100-01-01 00:00:00'::timestamp FROM tmp.gaps g2
)
SELECT p0.ztype,p0.start_datetime,p0.end_datetime
FROM plus2 p0
-- the start of a stretch: there is no older overlapping
-- (or touching) interval
WHERE NOT EXISTS (SELECT *
FROM plus2 nx
WHERE nx.ztype = p0.ztype
AND nx.start_datetime < p0.start_datetime -- older
AND nx.end_datetime >= p0.start_datetime -- touching or overlapping
)
UNION
SELECT mk.ztype
, LEAST(mk.start_datetime,p1.start_datetime)
, GREATEST(mk.end_datetime,p1.end_datetime)
FROM plus2 p1
, meuk mk
WHERE p1.ztype = mk.ztype
AND (p1.start_datetime >= mk.start_datetime AND p1.start_datetime <= mk.end_datetime AND p1.end_datetime > mk.end_datetime)
)
SELECT ztype, COUNT(*)-1 AS ngap
FROM meuk mk
WHERE NOT EXISTS (SELECT *
FROM meuk nx
WHERE nx.ztype = mk.ztype
AND (nx.start_datetime,nx.end_datetime) OVERLAPS( mk.start_datetime,mk.end_datetime)
AND (nx.end_datetime - nx.start_datetime) > (mk.end_datetime - mk.start_datetime)
)
GROUP BY ztype
ORDER BY ztype
;
A criação da soma final fica como exercício para o leitor;-)
RESULTADOS:
ztype | ngap
-------+------
a | 1
b | 1
c | 1
d | 0
e | 0
(5 rows)
