Create range of ID without cursor - sql

Question

Not sure if this or similar question is asked already but i could not find one.
The Requirement to create range of IDs while the Value is not changed. This schema can be used:
declare #mytable as table(ID int, Val int)
insert into #mytable values
(1, 1),
(2, 1),
(3, 1),
(4, 2),
(5, 2),
(6, 2),
(7, 2),
(8, 1),
(9, 1),
(10, 1),
(11, 4),
(12, 4),
(13, 4),
(14, 4),
(15, 4),
(16, 5);
And the expected result would be
StartID EndID Val
1 3 1
4 7 2
8 10 1
11 15 4
16 16 5
Now I can achieve this by running cursor and If n case the number of records will be millions, I think, cursor will be slower. I hope it can be written using some compound query but could not figure-out how.
So I need help in writing that kind of query and needless to mention yet, it is not a school/collage project/assignment.

Answer 1

This is a gaps-and-islands scenario where you're trying to group records together based on the change in Val.
This is using window functions to determine when the Val changes, and assign the island_nbr.
Answer:
select min(b.ID) as StartID
, max(b.ID) as EndID
, max(b.Val) as Val
from (
select a.ID
, a.Val
, sum(a.is_chng_flg) over (order by a.ID asc) as island_nbr
from (
select m.ID
, m.Val
, case lag(m.Val, 1, m.Val) over (order by m.ID asc) when m.Val then 0 else 1 end is_chng_flg
from #mytable as m
) as a
) as b
group by b.island_nbr --forces the right records to show up
order by 1

Answer 2

This is a gaps-and-islands problem. But the simplest method is the difference of row numbers:
select min(id) as startId, max(id) as endId, val
from (select t.*,
row_number() over (order by id) as seqnum,
row_number() over (partition by val order by id) as seqnum_v
from #mytable t
) t
group by (seqnum - seqnum_v), val
order by startId;