SQL Server 2019

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drop table if exists #a;

create table #a
(pass        int
,category    varchar(5)
,rangebegin  int
,rangeend    int)
;

insert #a
values 
  (0, 'a', 1, 19)
, (0, 'a', 1, 27)
, (0, 'a', 9, 37)
, (0, 'a', 14, 42)
, (0, 'a', 45, 65)
, (0, 'a', 47, 70)
, (0, 'a', 52, 62)
, (0, 'a', 65, 65)
, (0, 'a', 81, 83)
, (0, 'a', 95, 95)

, (0, 'b', 3, 33)
, (0, 'b', 17, 22)
, (0, 'b', 21, 44)

, (0, 'c', 30, 35)
, (0, 'c', 33, 40)
, (0, 'c', 39, 42)
;

select *
from #a
order by 1,2,3
;

declare @pass           int,
        @prevcount      int,
        @currcount      int

select  @pass = 0,
        @prevcount = (select count(*) from #a where pass = 0),
        @currcount = 0

while   @currcount != @prevcount
begin
        insert  #a
                (pass, category, rangebegin, rangeend)
        select  distinct
                @pass + 1,
                a1.category,
                (select min(a2.rangebegin)
                 from   #a a2
                 where  a2.category     = a1.category
                 and    a2.pass         = @pass
                 and    (       a1.rangebegin   between  a2.rangebegin and a2.rangeend
                         or     a1.rangeend     between  a2.rangebegin and a2.rangeend)),
                (select max(a3.rangeend)
                 from   #a a3
                 where  a3.category     = a1.category
                 and    a3.pass         = @pass
                 and    (       a1.rangebegin   between  a3.rangebegin and a3.rangeend
                         or     a1.rangeend     between  a3.rangebegin and a3.rangeend))
        from    #a a1
        where   a1.pass = @pass

select  @pass      = @pass + 1,
                @prevcount = @currcount,
                @currcount = (select count(*) from #a where pass = @pass+1)

--      print '############# %1!', @pass
--      select  * from #a where pass = @pass order by 2,3,4
end

select  category,
        rangebegin,
        rangeend
from    #a
where   pass = @pass
order by 1,2,3
;

category	rangebegin	rangeend
a	1	19
a	1	27
a	9	37
a	14	42
a	45	65
a	47	70
a	52	62
a	65	65
a	81	83
a	95	95
b	3	33
b	17	22
b	21	44
c	30	35
c	33	40
c	39	42

category	rangebegin	rangeend
a	1	42
a	45	70
a	81	83
a	95	95
b	3	44
c	30	42

category	rangebegin	rangeend
a	1	19
a	1	27
a	9	37
a	14	42
a	45	65
a	47	70
a	52	62
a	65	65
a	81	83
a	95	95
b	3	33
b	17	22
b	21	44
c	30	35
c	33	40
c	39	42

category	rangebegin	rangeend
a	1	19
a	1	27
a	9	37
a	14	42
a	45	65
a	47	70
a	52	62
a	65	65
a	81	83
a	95	95
b	3	33
b	17	22
b	21	44
c	30	35
c	33	40
c	39	42

category	rangebegin	rangeend
a	1	19
a	1	27
a	9	37
a	14	42
a	45	65
a	47	70
a	52	62
a	65	65
a	81	83
a	95	95
b	3	33
b	17	22
b	21	44
c	30	35
c	33	40
c	39	42