Postgres 12

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with data
  as (
    select 'A' as client_id,'cart'     as event_type   , 1  as count1, cast('AM 12:00:00' as time) as time1 union all 
    select 'A' as client_id,'view'     as event_type   , 4  as count1, cast('AM 12:01:00' as time) as time1 union all
    select 'A' as client_id,'purchase' as event_type   , 2  as count1, cast('AM 12:05:00' as time) as time1 union all
    select 'A' as client_id,'view'     as event_type   , 2  as count1, cast('AM 12:10:00' as time) as time1 union all
    select 'B' as client_id,'view'     as event_type   , 3  as count1, cast('AM 12:03:00' as time) as time1 union all
    select 'B' as client_id,'purchase' as event_type   , 1  as count1, cast('AM 12:05:00' as time) as time1 union all
    select 'B' as client_id,'view' as event_type   , 2  as count1, cast('AM 12:10:00' as time) as time1 
     )
   ,grp_split
   as(
select case when lag(event_type) over(partition by client_id order by time1)='purchase' 
              or lag(event_type) over(partition by client_id order by time1) is null 
             then
                 row_number() over(partition by client_id order by time1)
        end as grp
      ,*
  from data
      )
 select x.client_id
       ,max(case when event_type='view' then count1 else 0 end) as view
       ,max(case when event_type='cart' then count1 else 0 end) as cart
       ,max(case when event_type='purchase' then count1 else 0 end) as purchase
  from (
  select *
        ,max(grp) over(partition by client_id order by time1) as grp2
    from grp_split
       )x
  group by client_id
           ,grp2 
  order by client_id

client_id	view	cart	purchase
A	4	1	2
A	2	0	0
B	3	0	1
B	2	0	0