The problem itself isn't too bad once you wrap your head around the recursive structure, boxes inside boxes with keys scattered around.
Model the boxes as a graph where edges represent containment and keys unlock boxes. Use a traversal (BFS/DFS) to explore all reachable boxes, tracking keys and candies, and sum candies from all opened boxes. If boxes can be opened without keys, treat them as initially accessible.
Pro tip: Clarify constraints upfront (e.g., can keys open multiple boxes? Are there cycles?) and discuss trade-offs between BFS and DFS for this problem. Mention that this is similar to a graph traversal with dependencies, and consider edge cases like locked boxes with no keys.
Ask questions to understand the rules: Are keys reusable? Can a box contain multiple keys? Are there cycles? What is the input format? This ensures you address the correct problem.
Represent each box as a node. Directed edges from a box to its sub-boxes. Keys are attributes that unlock specific boxes. Initially, only boxes without locks are accessible.
Use BFS or DFS to explore all reachable boxes. Maintain a set of collected keys and a set of opened boxes. When a key is found, check if it unlocks any previously inaccessible boxes and add them to the queue/stack.
As you open each box, add its candies to a running total. Ensure you don't double-count if a box is reached multiple times (use a visited set).
Discuss time and space complexity (O(N) where N is number of boxes). Consider edge cases: no keys, all boxes locked, cycles, multiple keys for same box.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.