Merge Overlapping Intervals and Track Maximum Value in BigQuery SQL

Question

I am trying to solve a problem where i want to merge overlapping intervals for a given column id, but i also want to track the maximum value for each overlapped interval. I have start_time and stop_time for each interval and each interval has a hierarchy/priority associated with it.

These are the following columns in the table: id, start_time, stop_time, some_value

example input:

example output:

Answer 1

Below is for BigQuery Standard SQL and I assume you stll working on the same use-case as in previous question, so I wanted to keep it inline with that solution - and you can extend it for when you also want to account for priorities for example

So, anyway:

#standardSQL
WITH check_times AS (
  SELECT id, start_time AS TIME FROM `project.dataset.table` UNION DISTINCT
  SELECT id, stop_time AS TIME FROM `project.dataset.table` 
), distinct_intervals AS (
  SELECT id, TIME AS start_time, LEAD(TIME) OVER(PARTITION BY id ORDER BY TIME) stop_time
  FROM check_times
), deduped_intervals AS (
  SELECT a.id, a.start_time, a.stop_time, MAX(some_value) some_value 
  FROM distinct_intervals a
  JOIN `project.dataset.table` b
  ON a.id = b.id 
  AND a.start_time BETWEEN b.start_time AND b.stop_time 
  AND a.stop_time BETWEEN b.start_time AND b.stop_time
  GROUP BY a.id, a.start_time, a.stop_time
), combined_intervals AS (
  SELECT id, MIN(start_time) start_time, MAX(stop_time) stop_time, MAX(some_value) some_value 
  FROM (
    SELECT id, start_time, stop_time, some_value, COUNTIF(flag) OVER(PARTITION BY id ORDER BY start_time) grp
    FROM (
      SELECT id, start_time, stop_time, some_value,
        start_time != IFNULL(LAG(stop_time) OVER(PARTITION BY id ORDER BY start_time), start_time) flag
      FROM deduped_intervals
    )
  )
  GROUP BY id, grp
)
SELECT *
FROM combined_intervals
-- ORDER BY id, start_time

If to apply to your sample data - result is

Row id  start_time  stop_time   some_value   
1   1   0           36          50   
2   1   41          47          23    

Is it possible to add one more column to the result which will show number of events during that time period

#standardSQL
WITH check_times AS (
  SELECT id, start_time AS TIME FROM `project.dataset.table` UNION DISTINCT
  SELECT id, stop_time AS TIME FROM `project.dataset.table` 
), distinct_intervals AS (
  SELECT id, TIME AS start_time, LEAD(TIME) OVER(PARTITION BY id ORDER BY TIME) stop_time
  FROM check_times
), deduped_intervals AS (
  SELECT a.id, a.start_time, a.stop_time, MAX(some_value) some_value, ANY_VALUE(To_JSON_STRING(b)) event_hash
  FROM distinct_intervals a
  JOIN `project.dataset.table` b
  ON a.id = b.id 
  AND a.start_time BETWEEN b.start_time AND b.stop_time 
  AND a.stop_time BETWEEN b.start_time AND b.stop_time
  GROUP BY a.id, a.start_time, a.stop_time
), combined_intervals AS (
  SELECT id, MIN(start_time) start_time, MAX(stop_time) stop_time, MAX(some_value) some_value, COUNT(DISTINCT event_hash) events
  FROM (
    SELECT *, COUNTIF(flag) OVER(PARTITION BY id ORDER BY start_time) grp
    FROM (
      SELECT *,
        start_time != IFNULL(LAG(stop_time) OVER(PARTITION BY id ORDER BY start_time), start_time) flag
      FROM deduped_intervals
    )
  )
  GROUP BY id, grp
)
SELECT *
FROM combined_intervals
-- ORDER BY id, start_time

with result

Row id  start_time  stop_time   some_value  events   
1   1   0           36          50          8    
2   1   41          47          23          1    

Answer 2

You can determine when a new grouping starts using a cumulative max(). Then a cumulative conditional count() to identify the groups . . . and finally aggregation:

select min(start_time), max(stop_time), max(some_value)
from (select t.*,
             countif(prev_stop_time is null or prev_stop_time < start_time) over (partition by id order by start_time) as grp
      from (select t.*,
                   max(stop_time) over (partition by id order by start_time rows between unbounded preceding and 1 preceding) as prev_stop_time
            from t
           ) t
     ) t
group by item_id, grp;