SQL: Use value from previous row to populate current row

Question

I have two tables table1 and table2 like so. You can see the times have gaps

table1
date      item time amount
----------------------------
1/1/2000  a    1    100
1/1/2000  a    2    100
1/1/2000  a    3    200
1/1/2000  a    6    300
1/1/2000  b    1    100
1/1/2000  b    2    100
1/1/2000  b    5    200
2/1/2000  a    1    500
2/1/2000  a    3    500
2/1/2000  a    4    550

I also have table2 where I fill the gaps

table2
date      item time amount new
-------------------------------------------
1/1/2000  a    1    100    N
1/1/2000  a    2    100    N
1/1/2000  a    3    200    N
1/1/2000  a    4           Y  <-- added amount should be 200
1/1/2000  a    5           Y  <-- added amount should be 200
1/1/2000  a    6    300    N
1/1/2000  b    1    100    N
1/1/2000  b    2    100    N
1/1/2000  b    3           Y  <-- added amount should be 100 
1/1/2000  b    4           Y  <-- added amount should be 100
1/1/2000  b    5    200    N
2/1/2000  a    1    500    N
2/1/2000  a    2    500    N
2/1/2000  a    3           Y  <-- added amount should be 500
2/1/2000  a    4    550    N

The gap row for amount should take the value of the last/previous time. I was able to identify the missing rows and add the gap rows but I tried copying the amounts to the gap rows but was not successful. I looked at what I thought were similar questions in stackoverflow and tried the solutions but it did not work such as:

update t2
set t2.amount = t1.amount
from table2 t2
inner join table1 t1 on t2.date = t1.date and t1.item = t2.item
where t2.new = 'Y'
and t2.time > (select t2.time 
              from table1 t3
              where max(t3.time) < t2.time)


update t2
set t2.amount = t1.amount
from table1 t1
inner join table2 t2 on t1.date = t2.date and t1.item = t2.item
where t2.new = 'Y' and max(t1.time) < t2.time     

Does anyone know how to access the amount for the previous row? A cursor works but that is a last resort solution. Thank you for taking the time from your busy day to help.

adding my create table code

create table #table1  (or #table2)
(
   date smalldatetime,
   item char(1),
   [time] int,
   amount int
   ,new char(1) -- for new row flag 
)

Answer 1

You need to find the previous non null value of amount:

update t
set amount = (
  select amount from table2 
  where
  date = t.date and item = t.item and time = (
    select max(time) from table2
    where 
    date = t.date and item = t.item 
    and time < t.time and amount is not null and new = 'N'
  ) 
)
from table2 t
where t.amount is null and t.new = 'Y'

See the demo.