MySQL 8.0

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select version();


version()


8.0.22


create table t(household_id int, tv_set_id int, start_time int, end_time int)
insert into t
select '111',1,500 ,550 union all
select '111',1,550 ,570 union all
select '111',1,590 ,620 union all
select '111',1,650 ,670 union all
select '111',2,660 ,680 union all
select '111',2,680 ,700 union all
select '111',2,700 ,750 union all
select '111',2,750 ,770 union all
select '112',2,1050,1060 union all
select '113',1,1060,1080 union all
select '113',1,1080,1100 union all
select '113',1,1100,1120 union all
select '113',1,1500,1520 
    with data
      as (
    select *
          ,case when lag(end_time) over(partition by household_id,tv_set_id order by end_time)
                    <> start_time then 
                sum(1) over(partition by household_id,tv_set_id order by end_time)
                else 
                sum(0) over(partition by household_id,tv_set_id order by end_time)
            end as group_number
      from t
          )
    select household_id
           ,tv_set_id
           ,min(start_time) as start_time
           ,max(end_time) as end_time
      from data
    group by household_id,tv_set_id,group_number


household_id
tv_set_id
start_time
end_time


111
1
500
570

111
1
590
620

111
1
650
670

111
2
660
770

112
2
1050
1060

113
1
1060
1120

113
1
1500
1520

household_id	tv_set_id	start_time	end_time
111	1	500	570
111	1	590	620
111	1	650	670
111	2	660	770
112	2	1050	1060
113	1	1060	1120
113	1	1500	1520