How can I recursively retrieve the top parent ID by querying with any of its (grand)child IDs in PostgreSQL?

I've looked at half a dozen different answers here on various scenarios that require recursive CTEs and experimented with them, but have been unable to adapt any of them to work in this situation. I just fundamentally don't understand how recursion works in PostgreSQL.

I've got a view person_v whose simplified contents look like this:

      id      | parent_id |   name
--------------+-----------+----------
         1024 |       512 |   foo
          512 |           |   bar
          900 |       600 |   huey
          600 |       300 |   louie
          300 |           |   dewey

What I need is a query that always returns me the topmost parent_id of any id, or the id itself if parent_id is NULL (i.e. empty in the above table). Not an aggregation of all parents either, just the top one.

To be explicit:

Querying for 1024, I'd get 512.
Querying for 512, I'd get 512.
Querying for 900, I'd get 300. (Not 600, so not the immediate parent, but the top parent.)
Querying for 600, I'd get 300.
Querying for 300, I'd get 300.

The parent-child relationships can be any numbers of levels deep, even though the above example only shows two levels of parentage.

I'm fairly certain that this is possible with the help of recursive CTEs instead of using custom functions, but I just can't grasp how.

Solution

We take start row (by id) as anchor of recursive query and go up to topmost parent. Topmost parent is row with higher lvl.
You can take parent_id, or coalesce(parent_id,id) where parent is null. The first, in my opinion, is preferable.

See example

with recursive r as( -- anchor part of recursive query
  select 0 lvl,id,parent_id
  from person_v
  where id=900 --  pId  -- parameter
     -- or pId is null  -- parent_id for all id  -- parameter is null
  union all
            -- recursive part
  select lvl+1,r.id,p.parent_id
  from r inner join person_v p on p.id=r.parent_id
  where p.parent_id is not null
)
select id,parent_id  -- or coalesce(parent_id,id)
from(
  select * 
    ,row_number()over(partition by id order by lvl desc) rn
  from r 
)rnt
where rn=1
;

lvl	id	parent_id	rn
1	900	300	1

demo

for example, full output of recursive query (ranged by id,lvl desc) for pId=900

lvl	id	parent_id	rn
0	900	600	2
1	900	300	1

for pId is null

lvl	id	parent_id	rn
0	24	512	1
0	300	null	1
0	512	null	1
0	600	300	1
0	900	600	2
1	900	300	1