SQL Server 2019

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create table TimeLog (
  EmployeeId bigint not null,
  RoomId nchar(6) not null,
  Event nvarchar(6) not null,
  EventDate DateTime not null
)
insert TimeLog (EmployeeID, RoomId, Event, EventDate)
values (107733,	'05-27F',	'Login',	'2020-02-26 07:02:00')
     , (107733,	'05-27F',	'Logout',	'2020-02-26 08:38:00')
     , (107733,	'05-25F',	'Login',	'2020-02-26 08:39:00')
     , (107733,	'05-25F',	'Logout',	'2020-02-26 08:51:00')
     , (107733,	'05-25F',	'Login',	'2020-02-27 08:39:00')
     , (107733,	'05-25F',	'Logout',	'2020-02-27 08:51:00')
     , (107733,	'05-25X',	'Login',	'2020-02-27 08:39:00')
     , (107733,	'05-25Y',	'Logout',	'2020-02-27 08:51:00')
     , (107733,	'05-25F',	'Login',	'2020-02-28 08:39:00')
     , (107733,	'05-25F',	'Logout',	'2020-02-28 08:51:00')
     , (107733,	'05-25F',	'Logout',	'2020-02-20 08:51:00')
     , (107733,	'05-25F',	'Logout',	'2020-02-21 08:51:00')
     , (107733,	'05-25F',	'Logout',	'2020-02-22 08:51:00')
     , (107733,	'05-25F',	'Logout',	'2020-02-23 08:51:00')
     , (107733,	'05-25F',	'Login',	'2020-03-01 08:39:00')
15 rows affected

-- If there's no corresponding login/logout show null
with cte as (
  select row_number() over (partition by EmployeeId, RoomId order by EventDate) r
  , *
  from TimeLog
)
select i.EventDate LoginDate
, o.EventDate LogoutDate
, coalesce(i.EmployeeId, o.EmployeeId) EmployeeId_
, coalesce(i.RoomId, o.RoomId)  RoomId_
from (select * from cte where Event = 'Login') i
full outer join (select * from cte where Event = 'Logout') o
on o.EmployeeId = i.EmployeeId
and o.RoomId = i.RoomId
and o.r = i.r+1
order by coalesce(i.EventDate, o.EventDate), o.EventDate, EmployeeId_, RoomId_


LoginDate
LogoutDate
EmployeeId_
RoomId_


null
2020-02-20 08:51:00.000
107733
05-25F

null
2020-02-21 08:51:00.000
107733
05-25F

null
2020-02-22 08:51:00.000
107733
05-25F

null
2020-02-23 08:51:00.000
107733
05-25F

2020-02-26 07:02:00.000
2020-02-26 08:38:00.000
107733
05-27F

2020-02-26 08:39:00.000
2020-02-26 08:51:00.000
107733
05-25F

2020-02-27 08:39:00.000
null
107733
05-25X

2020-02-27 08:39:00.000
2020-02-27 08:51:00.000
107733
05-25F

null
2020-02-27 08:51:00.000
107733
05-25Y

2020-02-28 08:39:00.000
2020-02-28 08:51:00.000
107733
05-25F

2020-03-01 08:39:00.000
null
107733
05-25F


-- If there's no corresponding login/logout duplicate the logout/login date
with cte as (
  select row_number() over (partition by EmployeeId, RoomId order by EventDate) r
  , *
  from TimeLog
)
select coalesce(i.EventDate, o.EventDate) LoginDate
, coalesce(o.EventDate, i.EventDate) LogoutDate
, coalesce(i.EmployeeId, o.EmployeeId) EmployeeId_
, coalesce(i.RoomId, o.RoomId)  RoomId_
from (select * from cte where Event = 'Login') i
full outer join (select * from cte where Event = 'Logout') o
on o.EmployeeId = i.EmployeeId
and o.RoomId = i.RoomId
and o.r = i.r+1
order by coalesce(i.EventDate, o.EventDate), o.EventDate, EmployeeId_, RoomId_


LoginDate
LogoutDate
EmployeeId_
RoomId_


2020-02-20 08:51:00.000
2020-02-20 08:51:00.000
107733
05-25F

2020-02-21 08:51:00.000
2020-02-21 08:51:00.000
107733
05-25F

2020-02-22 08:51:00.000
2020-02-22 08:51:00.000
107733
05-25F

2020-02-23 08:51:00.000
2020-02-23 08:51:00.000
107733
05-25F

2020-02-26 07:02:00.000
2020-02-26 08:38:00.000
107733
05-27F

2020-02-26 08:39:00.000
2020-02-26 08:51:00.000
107733
05-25F

2020-02-27 08:39:00.000
2020-02-27 08:39:00.000
107733
05-25X

2020-02-27 08:39:00.000
2020-02-27 08:51:00.000
107733
05-25F

2020-02-27 08:51:00.000
2020-02-27 08:51:00.000
107733
05-25Y

2020-02-28 08:39:00.000
2020-02-28 08:51:00.000
107733
05-25F

2020-03-01 08:39:00.000
2020-03-01 08:39:00.000
107733
05-25F


SET ANSI_WARNINGS OFF -- for the `min(o.eventdate)` piece: https://blog.sqlauthority.com/2015/02/13/sql-server-warning-null-value-is-eliminated-by-an-aggregate-or-other-set-operation/
with LoginCte as (
  select row_number() over (partition by EmployeeId, RoomId order by EventDate) LoginNo
  , EmployeeId
  , RoomId
  , EventDate LoginDate
  from TimeLog
  where Event = 'Login'
)
, LogoutCte as (
  select count(icte.LoginNo) PriorLoginCount
  , octe.EmployeeId
  , octe.RoomId
  , EventDate LogoutDate
  from TimeLog octe
  left outer join LoginCte icte 
  on icte.EmployeeId = octe.EmployeeId
  and icte.RoomId = octe.RoomId
  where Event = 'Logout'
  group by octe.EmployeeId, octe.RoomId, octe.Eventdate
)
select coalesce(i.EmployeeId, o.EmployeeId) EmployeeId_
, coalesce(i.RoomId, o.RoomId) RoomId_
, LoginDate
, LogoutDate
from LoginCte i
full outer join logoutCte o
on o.EmployeeId = i.EmployeeId
and o.RoomId = i.RoomId
and o.PriorLoginCount = i.LoginNo






EmployeeId_
RoomId_
LoginDate
LogoutDate


107733
05-25F
2020-03-01 08:39:00.000
2020-02-20 08:51:00.000

107733
05-25F
2020-03-01 08:39:00.000
2020-02-21 08:51:00.000

107733
05-25F
2020-03-01 08:39:00.000
2020-02-22 08:51:00.000

107733
05-25F
2020-03-01 08:39:00.000
2020-02-23 08:51:00.000

107733
05-25F
2020-03-01 08:39:00.000
2020-02-26 08:51:00.000

107733
05-25F
2020-03-01 08:39:00.000
2020-02-27 08:51:00.000

107733
05-25F
2020-03-01 08:39:00.000
2020-02-28 08:51:00.000

107733
05-25Y
null
2020-02-27 08:51:00.000

107733
05-27F
2020-02-26 07:02:00.000
2020-02-26 08:38:00.000

107733
05-25F
2020-02-28 08:39:00.000
null

107733
05-25F
2020-02-26 08:39:00.000
null

107733
05-25F
2020-02-27 08:39:00.000
null

107733
05-25X
2020-02-27 08:39:00.000
null


-- Use the closest login/logout, even if not paired

/*
DOESN'T WORK
I've left this here for people to see another attempted approach; but this one
doesn't work exactly as required; as if you have a login record with multiple 
logouts related, only the first logout would show.
*/

select i.EventDate LoginDate
, min(o.EventDate) LogoutDate -- this will produce a warning as sometimes the value will be null
, coalesce(i.EmployeeId, o.EmployeeId) EmployeeId_
, coalesce(i.RoomId, o.RoomId)  RoomId_
from (select row_number() over (order by EventDate) dummyId, * from TimeLog where Event = 'Login') i
full outer join (select row_number() over (order by EventDate) dummyId, * from TimeLog where Event = 'Logout') o
on o.EmployeeId = i.EmployeeId
and o.RoomId = i.RoomId
and o.EventDate >= i.EventDate  
where coalesce(i.RoomId, o.RoomId) = '05-25F' -- simplify whilst testing
group by coalesce(i.EmployeeId,o.EmployeeId), coalesce(i.RoomId,o.RoomId), i.EventDate
, i.dummyId, coalesce(i.dummyId, o.dummyId)
order by LoginDate, LogoutDate


LoginDate
LogoutDate
EmployeeId_
RoomId_


null
2020-02-20 08:51:00.000
107733
05-25F

null
2020-02-21 08:51:00.000
107733
05-25F

null
2020-02-22 08:51:00.000
107733
05-25F

null
2020-02-23 08:51:00.000
107733
05-25F

2020-02-26 08:39:00.000
2020-02-26 08:51:00.000
107733
05-25F

2020-02-27 08:39:00.000
2020-02-27 08:51:00.000
107733
05-25F

2020-02-28 08:39:00.000
2020-02-28 08:51:00.000
107733
05-25F

2020-03-01 08:39:00.000
null
107733
05-25F
LoginDate	LogoutDate	EmployeeId_	RoomId_
null	2020-02-20 08:51:00.000	107733	05-25F
null	2020-02-21 08:51:00.000	107733	05-25F
null	2020-02-22 08:51:00.000	107733	05-25F
null	2020-02-23 08:51:00.000	107733	05-25F
2020-02-26 07:02:00.000	2020-02-26 08:38:00.000	107733	05-27F
2020-02-26 08:39:00.000	2020-02-26 08:51:00.000	107733	05-25F
2020-02-27 08:39:00.000	null	107733	05-25X
2020-02-27 08:39:00.000	2020-02-27 08:51:00.000	107733	05-25F
null	2020-02-27 08:51:00.000	107733	05-25Y
2020-02-28 08:39:00.000	2020-02-28 08:51:00.000	107733	05-25F
2020-03-01 08:39:00.000	null	107733	05-25F