Airbnb Coding: Max Candies From Boxes (BFS/Greedy)

You are given a set of numbered boxes, some unlocked and some locked, plus initialBoxes you start with. Each box grants candies, may contain keys for other boxes, and may contain additional boxes. Your job is to simulate opening boxes in an order that yields the maximum total candies — you can open a box only if it is unlocked or you have a key for it, and each box is opened at most once.

This problem is typically solved with a BFS-like simulation and greedy exploration. You maintain:

• a queue (or list) of boxes you currently have access to,
• a set of keys you possess,
• a visited/opened set so you don't double-count boxes.

Flow/stages you should follow in an interview:

1. Confirm the function signature and types (status, candies, keys, containedBoxes, initialBoxes → int).
2. Initialize data structures: queue for available boxes, sets for owned keys and opened boxes.
3. Repeatedly try to open accessible boxes: when you open one, add its candies to the total, add any new keys and contained boxes to your pool, and mark it opened. Loop until no new opens are possible.

Skill signals the interviewer looks for: correct simulation logic, handling duplicates and cycles, careful use of sets/queues, edge-case reasoning (no initial unlocked boxes, keys for already-opened boxes, nested containment), and time/space complexity analysis. Expect follow-ups about optimality, complexity, and variant constraints (e.g., limited key uses, streaming boxes).