Inherited permissions across teams, folders and files

Design a permission system for a workspace organized as a hierarchy of teams, folders, and files.

• A team is a root. It can contain folders and files.
• A folder sits inside a team or another folder. It can contain folders and files.
• A file is a leaf. It lives inside a team or a folder and has no children.

Every entity has a unique string uuid and a list of user IDs who were given access to it directly. Access is inherited: a user who has direct access to an entity can access every entity below it, at any depth. Access never flows upward.

Implement a class PermissionSystem with:

• add_team(uuid, user_ids)
• add_folder(uuid, parent_uuid, user_ids)
• add_file(uuid, parent_uuid, user_ids)
• has_access(user_id, uuid) -> bool: can this user open this entity?
• accessible_files(user_id) -> list[str]: the IDs of all files the user can open, sorted, each listed once.

Raise an error for a duplicate ID, an unknown parent, or a file used as a parent. Assume up to 10^5 entities and trees that can be deep.

Example

Team studio (users: mia) contains folder brand (users: raj) and file budget (no users). Folder brand contains file palette (users: lee).

• has_access("mia", "palette") -> True (inherited from studio)
• has_access("raj", "budget") -> False (budget is not under brand)
• has_access("lee", "brand") -> False (access does not flow upward)
• accessible_files("mia") -> ["budget", "palette"]
• accessible_files("raj") -> ["palette"]

Reconstructed from the reported question; details may differ from what interviewers ask.