MySQL 8.0

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CREATE TABLE timeslots (
  time_start TIME,
  time_end TIME,
  CHECK ('00:00:00' <= time_start),
  CHECK (time_start < time_end),
  CHECK (time_end <= '24:00:00')
);
INSERT INTO timeslots VALUES 
('19:00', '19:40'), ('20:30', '21:00');
SELECT * FROM timeslots;

Records: 2  Duplicates: 0  Warnings: 0




time_start
time_end


19:00:00
19:40:00

20:30:00
21:00:00


WITH
cte1 AS (
  SELECT '00:00:00' slot, 1 weight
  UNION ALL
  SELECT '24:00:00', -1
  UNION ALL
  SELECT time_start, -1 FROM timeslots
  UNION ALL
  SELECT time_end, 1 FROM timeslots
  )
SELECT * FROM cte1


slot
weight


00:00:00
1

24:00:00
-1

19:00:00
-1

20:30:00
-1

19:40:00
1

21:00:00
1


WITH
cte1 AS (
  SELECT '00:00:00' slot, 1 weight
  UNION ALL
  SELECT '24:00:00', -1
  UNION ALL
  SELECT time_start, -1 FROM timeslots
  UNION ALL
  SELECT time_end, 1 FROM timeslots
  ),
cte2 AS (
  SELECT slot, SUM(weight) OVER (ORDER BY slot) cum_sum
  FROM cte1
  )
SELECT * FROM cte2


slot
cum_sum


00:00:00
1

19:00:00
0

19:40:00
1

20:30:00
0

21:00:00
1

24:00:00
0


WITH
cte1 AS (
  SELECT '00:00:00' slot, 1 weight
  UNION ALL
  SELECT '24:00:00', -1
  UNION ALL
  SELECT time_start, -1 FROM timeslots
  UNION ALL
  SELECT time_end, 1 FROM timeslots
  ),
cte2 AS (
  SELECT slot, SUM(weight) OVER (ORDER BY slot) cum_sum
  FROM cte1
  ),
cte3 AS (
  SELECT slot, SUM(cum_sum) OVER (ORDER BY slot) cum_sum
  FROM cte2
  )
SELECT * FROM cte3


slot
cum_sum


00:00:00
1

19:00:00
1

19:40:00
2

20:30:00
2

21:00:00
3

24:00:00
3


WITH
cte1 AS (
  SELECT '00:00:00' slot, 1 weight
  UNION ALL
  SELECT '24:00:00', -1
  UNION ALL
  SELECT time_start, -1 FROM timeslots
  UNION ALL
  SELECT time_end, 1 FROM timeslots
  ),
cte2 AS (
  SELECT slot, SUM(weight) OVER (ORDER BY slot) cum_sum
  FROM cte1
  ),
cte3 AS (
  SELECT slot, SUM(cum_sum) OVER (ORDER BY slot) cum_sum
  FROM cte2
  )
SELECT MIN(slot) free_time_start,
       MAX(slot) free_time_end 
FROM cte3 
GROUP BY cum_sum;


free_time_start
free_time_end


00:00:00
19:00:00

19:40:00
20:30:00

21:00:00
24:00:00