Design room progression with leaderboard

Design a data structure to simulate a sequence of rooms where players solve tasks and can move only to the next room once finished. Support the following operations with high throughput: addPlayer(id); recordTask(playerId, roomId, points); moveToNextRoom(playerId); getPlayerState(playerId) -> {room, score}; and topK(k) -> the k players with highest total scores across all rooms at query time. Implement efficient updates to the leaderboard and explain how you will prevent duplicate entries when using a heap (e.g., lazy deletion, versioning, or indexed heaps). Analyze the time and space complexity of each operation and justify your design choices.