Redshift SQL: Get date difference based on start and end dates

Whenever there is sophisticated logic, I'd suggest to use union queries and split the logic into a select query (or even table) each. Then you'd be able to calculate this in two steps. The main difference seems to be whether the 0.5 between 00:00:00 and 00:30:00 should be counted to the previous workday or whether it should stand alone. The latter seems to be determined based on whether the end_date is also a workday itself. I see three cases:

• Next day is a workday:
  1. Report all hours on start_date
• Next day is not a workday:
  2. Report hours from start_date to midnight on start_date
  3. Report hours from midnight to end_date on end_date

I used the following example data based on your description:

create temporary table _test (user varchar(20), start_date timestamp, end_date timestamp);
insert into _test values ('Alex', '7/25/2016 16:00', '7/26/2016 0:30'), ('Alex', '7/24/2016 16:00', '7/25/2016 0:30'), ('Alex', '7/21/2016 16:00', '7/22/2016 0:30'), ('Alex', '7/20/2016 16:00', '7/21/2016 0:30'), ('Alex', '7/19/2016 16:00', '7/20/2016 0:30'), ('Alex', '7/18/2016 16:00', '7/19/2016 0:30'), ('Alex', '7/17/2016 16:00', '7/18/2016 0:30'), ('Alex', '7/14/2016 16:00', '7/15/2016 0:30'), ('Alex', '7/13/2016 16:00', '7/14/2016 0:30'), ('Alex', '7/12/2016 16:00', '7/13/2016 0:30'), ('Alex', '7/11/2016 16:00', '7/12/2016 0:30'), ('Alex', '7/10/2016 16:00', '7/11/2016 0:30');

We will need to know whether the next day is a workday, so I suggest using the lead() window function (see documentation) which will give you the start_date from the next row.

create temporary table _differences as (
    select
        user_name
      , start_date::date as start_date
      , end_date::date as end_date
       /** 
        * Calculate difference in hours between start_date and end_date: */
      , round(cast(datediff(seconds, start_date, end_date) as decimal)/3600,2) as hours_start_to_end
       /** 
        * Calculate difference in hours between start_date and midnight: */
      , round(cast(datediff(seconds, start_date, dateadd(day, 1, start_date::date)) as decimal)/3600,2) as hours_start_to_midnight
       /**
        * Calculate difference between midnight on end_date and end_date: */
      , round(cast(datediff(seconds, end_date::date, end_date) as decimal)/3600,2) as hours_midnight_to_end
       /**
        * Calculate number of days from end_date until next start_date: */
      , datediff(day, end_date::date, lead(start_date::date) over(partition by user_name order by start_date::date)) as days_until_next_workday
    from
        _test
);

Then the following query:

    select
        user_name          as user_name
      , start_date         as ref_date
      , hours_start_to_end as difference
    from
        _differences
    where
        days_until_next_workday = 0 -- report all work hours on start_date
union
    select
        user_name               as user_name
      , start_date              as ref_date
      , hours_start_to_midnight as difference
    from
        _differences
    where
        days_until_next_workday > 0 -- report partial work hours on start_date
union
    select
        user_name             as user_name
      , end_date              as ref_date
      , hours_midnight_to_end as difference
    from
        _differences
    where
        days_until_next_workday > 0 -- report partial work hours on end_date
order by
    user_name
  , ref_date desc
;

Would yield the following result:

 user_name |  ref_date  | difference
-----------+------------+------------
 Alex      | 2016-07-24 |       8.50
 Alex      | 2016-07-22 |       0.50
 Alex      | 2016-07-21 |       8.00
 Alex      | 2016-07-20 |       8.50
 Alex      | 2016-07-19 |       8.50
 Alex      | 2016-07-18 |       8.50
 Alex      | 2016-07-17 |       8.50
 Alex      | 2016-07-15 |       0.50
 Alex      | 2016-07-14 |       8.00
 Alex      | 2016-07-13 |       8.50
 Alex      | 2016-07-12 |       8.50
 Alex      | 2016-07-11 |       8.50
 Alex      | 2016-07-10 |       8.50
(13 rows)

You can see that 7/25/2016 is missing because there is no start_date on or after 7/26/2016, so you'll need to figure out how to account for that special case.

here is how I have done the calc and it works perfectly

select user, trunc(start_time) as date1, 
       SUM(case when id = 1 then round(cast(datediff(seconds, start_time, st_t1) as decimal)/3600,2) end) as SCHEDULE

from
(
select user, start_time,
       case when trunc(start_time) <> trunc(end_time) then cast(to_char(start_time,'yyyy-mm-dd 23:59:59') as timestamp) else cast(to_char(end_time,'yyyy-mm-dd hh24:mi:ss') as timestamp) end as st_t1
from   table1 a
where id = 1
group by user_name, trunc(start_time)

union

select user_name, trunc(end_time) as date1,
       SUM(case when id = 1 then round(cast(datediff(seconds, st_t2, end_time) as decimal)/3600,2) end) as SCHEDULE

from
(
select user_name, end_time, 
       case when trunc(start_time) <> trunc(end_time) then cast(to_char(end_time,'yyyy-mm-dd 00:00:00') as timestamp) else cast(to_char(end_time,'yyyy-mm-dd hh24:mi:ss') as timestamp) end as st_t2
from   table1 a
where  id = 1    
)
group by user, trunc(end_time)