Hierarchical query - show parent name when all children present - postgresql

Question

The problem
I'm struggling with a hierarchical problem with Postgres.
I have multi-level hierarchical structure (let's assume 3 for purpose of the question)
-> category
--> subcategory
---> item
Those are different tables but I can simply convert it into one child-parent table / CTE. Each of the parent category can have multiple children.
And I have another table, let's say UserPreferences, where there is a relation between User and Items (which Items user selected as preferences).
What I need to do is create a query that will return all user preferences BUT there is a requirement that if all nodes under the parent are selected, then parent name should be presented instead of the list of children.
Example
if we have following situation:
-> category 1
--> subcategory 1
---> item 1 (selected by user)
---> item 2 (selected by user)
--> subcategory 2
---> item 3 (selected by user)
---> item 4
-> category 2
--> subcategory 3
---> item 5 (selected by user)
Then the desired output for user is:
subcategory 1, item 3, category 2
Note that the query should allow to query for multiple users at once so function is not an option.
Attempts
I had multiple attemps on writing such query using:
recursive CTE - I had problems with writing the proper condition though :/ I'm also a bit worried about the performance - if it will be good enough
group by ROLLUP + some left lateral joins to get counts within categories - but here I had problems in a situation presented with "category 2" - so that in my case "category 2" and "subcategory 2" would be presented instead of only "category 2"
Does anyone have any suggestions what would be the best approach for this?

Answer 1

You should have a database design that represent this hierachy with intervals instead of nested set. Then the query will be simple...
I wrote some papers about that:
https://sqlpro.developpez.com/cours/arborescence/#LII
But it is in french...
The query to find the upper level when all subitems are checked is :
SELECT *
FROM INTERVAL_TREE AS IT
WHERE (RIGHT_BOUND - LEFT_BOUND) / 2 =
(SELECT COUNT(*)
FROM INTERVAL_TREE
WHERE CHECKED = 1
AND RIGHT_BOUND > IT.RIGHT_BOUND
AND LEFT_BOUND < IT.LEFT_BOUND)
Off course the predicate "CHECKED = 1" can be a subquery...