Game Ranking: Design a Real-Time Leaderboard System with Score Updates and Rank Queries

Question

## Problem

Design a leaderboard system for a multiplayer game that supports: updating a player's score, querying a player's current rank (1-indexed, rank 1 = highest score), and fetching the top K players. Scores can only increase.

```python
class GameRanking:
    def __init__(self): ...
    def add_score(self, player_id: str, score: int) -> None: ...
    def get_rank(self, player_id: str) -> int: ...
    def top_k(self, k: int) -> list[tuple[str, int]]: ...
    # top_k returns [(player_id, score)] sorted by score desc
```

**Example:**
```
gr = GameRanking()
gr.add_score("Alice", 500)
gr.add_score("Bob",   800)
gr.add_score("Carol", 800)
gr.add_score("Alice", 300)  # Alice total = 800 (if cumulative) or 500
gr.get_rank("Alice")  -> 2 or 3 depending on design
gr.top_k(2)           -> [("Bob",800),("Carol",800)] or similar
```

**Clarify:** Does `add_score` replace the score or add to it?

## Follow-ups

1. How would you implement `get_rank` efficiently -- what data structure supports O(log n) rank queries (e.g., sorted set, order-statistics tree)?
2. How does Redis's ZSET (sorted set) solve this problem in production, and what are its rank/score query commands?
3. What is the time complexity of your top_k query, and how does it change if scores are bounded integers (e.g., 0-10000)?
4. How would you shard the leaderboard across multiple servers for 100 million players?

Game Ranking: Design a Real-Time Leaderboard System with Score Updates and Rank Queries

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