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I started with the obvious stuff, a hash map from player id to current room, and that covers the O(1) movement and lookup parts no problem.
Start by clarifying requirements: player movement and room lookups must be O(1), and the leaderboard must return top-k sorted by position descending with entry time as tiebreaker in O(N + k). Then propose a hash map for player-to-room mapping and a room-to-player-set mapping, and for the leaderboard, use a bucket sort approach where buckets represent positions, and within each bucket, players are sorted by entry time. Finally, discuss trade-offs and potential optimizations.
Pro tip: Mention that the leaderboard can be maintained incrementally if updates are frequent, but for O(N + k) retrieval, a bucket-based approach is ideal. Also, clarify whether 'position' refers to room number or a score, as it affects the sorting.
Ask about the range of positions, frequency of updates vs. queries, and whether players can be in the same room. Confirm that O(1) for movement and lookup means using hash maps.
Use a hash map to map player ID to current room (for O(1) lookup and movement). Use another hash map to map room to a set of players (for O(1) room lookup). For the leaderboard, consider a bucket array where index is position, and each bucket contains players sorted by entry time.
To get top-k, iterate positions from highest to lowest, and within each position, iterate players in entry time order until k players are collected. This yields O(N + k) where N is number of distinct positions or total players? Actually, if we iterate all positions and all players, it's O(N + k) if N is number of players? Clarify: N is number of players, but we only need to scan positions that have players. Use a sorted list of positions or iterate from max position down to min, skipping empty buckets.
Explain that movement and lookup are O(1) due to hash maps. Leaderboard retrieval is O(P + k) where P is number of distinct positions (or O(N + k) if N is number of players, but we can achieve O(N + k) by scanning all players? Actually, bucket sort gives O(N + k) if we iterate all buckets and players. Discuss space complexity and potential optimizations like maintaining a sorted list of positions.
Consider concurrent updates, dynamic positions, and memory constraints. Mention how to handle ties (entry time) and whether entry time is unique. Also, discuss if k is large or if we need to support pagination.
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