Grouping SQL rows based on overlapping active time intervals, valid from and valid to

I’m working in bigquery with this mock data:

create schema if not exists dbo;
create table if not exists dbo.player_history(team_id INT, player_id INT, active_from TIMESTAMP, active_to TIMESTAMP);
truncate table dbo.player_history;
INSERT INTO dbo.player_history VALUES(1,1,'2020-01-01', '2020-01-08');
INSERT INTO dbo.player_history VALUES(1,2,'2020-06-01', '2020-09-08');
INSERT INTO dbo.player_history VALUES(1,3,'2020-06-10', '2020-10-01');
INSERT INTO dbo.player_history VALUES(1,4,'2020-02-01', '2020-02-15');
INSERT INTO dbo.player_history VALUES(1,5,'2021-01-01', '2021-01-08');
INSERT INTO dbo.player_history VALUES(1,6,'2021-01-02', '2021-06-08');
INSERT INTO dbo.player_history VALUES(1,7,'2021-01-03', '2021-06-08');
INSERT INTO dbo.player_history VALUES(1,8,'2021-01-04', '2021-06-08');
INSERT INTO dbo.player_history VALUES(1,9,'2020-01-02', '2021-02-05');
INSERT INTO dbo.player_history VALUES(1,10,'2020-10-01', '2021-04-08');
INSERT INTO dbo.player_history VALUES(1,11,'2020-11-01', '2021-05-08');


select *
 from dbo.player_history
order by 3, 4

and what I want to get out is the active lineups. The output would look like so:

With the logic behind it being:

I’ve almost cracked it using some sort of lead(valid_from) between valid_to and valid_from and, doing a case when to make it 1 if its a new lineup 0 otherwise, and then doing some sort of cumulative sum on that to get the ID but I’m not able to solve it 100%… I’m very desperate, don’t know where to look anymore.

**correction: lineup 4 & 5 should actually just be one lineup.

Answer

Given that a player can belong to multiple line up as we discussed in the comment section, you might try the approach below using JOIN:

WITH LINEUPS AS 
    (SELECT a.*,b.player_id as b_player_id
    FROM `dbo.player_history` a
    INNER JOIN  `dbo.player_history` b on b.active_from BETWEEN a.active_from AND a.active_to
    ORDER BY 3, 4)
SELECT 
    team_id,
    ROW_NUMBER () OVER (PARTITION BY team_id ORDER BY  active_from, active_to) AS lineup_id,
    active_from, 
    active_to, 
    ARRAY_AGG(DISTINCT b_player_id) as player_ids
FROM LINEUPS 
GROUP BY team_id, active_from, active_to
ORDER BY active_from, active_to

Since the output is too long for me to show you via screenshot in Bigquery console, I extracted the results to Google sheets. See below screenshot of output: