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SQL/Hive: Finding total number of users in a room when a user first joins a room

Data preview:

user room start_time leave_time 
  a1    A     07:44      08:02   
  b2    A     07:45      07:50
  c3    A     07:49      08:05 
  d4    A     08:03      08:05

Is there a way to add a column called 'total_num_user' counting total number of users in a room when each person first joined the room?

Desired output:

user room start_time leave_time total_num_user 
  a1    A     07:44      08:02         1
  b2    A     07:45      07:50         2
  c3    A     07:49      08:05         3
  d4    A     08:03      08:05         2 

I tried writing a pseudocode that count when start_time of other user < start_time of user and end_time of other user > end_time of user group by room, but stuck on how to actually implement this in SQL.

This is a little more than you wanted

create table timeTable (username varchar(10), room varchar(10),start_time time, leave_time time, chek_total_num_user int);
insert into timeTable values
 ('a1','A','07:44','08:02',1)
,('b2','A','07:45','07:50',2)
,('c3','A','07:49','08:05',3)
,('d4','A','08:03','08:05',2)
;
with t1 as(
select  username,room,start_time as event_time, 1 InOut
from timeTable
union all
select  username,room,leave_time as event_time, -1 InOut
from timeTable
)
select  * 
  ,sum(InOut)over(partition by room order by event_time) total_num_user_at_event
from t1
order by event_time
username room event_time InOut total_num_user_at_event
a1 A 07:44:00.0000000 1 1
b2 A 07:45:00.0000000 1 2
c3 A 07:49:00.0000000 1 3
b2 A 07:50:00.0000000 -1 2
a1 A 08:02:00.0000000 -1 1
d4 A 08:03:00.0000000 1 2
c3 A 08:05:00.0000000 -1 0
d4 A 08:05:00.0000000 -1 0

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