Performance Analytics - Compute Athlete Stats from Event Data

Question

## Problem

You are given a list of performance events for athletes in a competition. Each event has `{athlete_id, event_type, value, timestamp}`. Implement:

- `top_k(event_type, k) -> List[Athlete]`: athletes with the highest aggregate value for that event type.
- `personal_best(athlete_id, event_type) -> float`: the single best value recorded.
- `trend(athlete_id, event_type) -> str`: `"improving"`, `"declining"`, or `"stable"` based on the last 5 events.

```python
class PerformanceAnalytics:
    def __init__(self, events: List[dict]): ...
    def top_k(self, event_type: str, k: int) -> List[str]: ...
    def personal_best(self, athlete_id: str, event_type: str) -> float: ...
    def trend(self, athlete_id: str, event_type: str) -> str: ...
```

**Example:**
```
events = [
  {"athlete_id": "a1", "event_type": "sprint", "value": 10.5, "timestamp": 1},
  {"athlete_id": "a1", "event_type": "sprint", "value": 10.2, "timestamp": 2},
  {"athlete_id": "a2", "event_type": "sprint", "value": 10.8, "timestamp": 1}
]
top_k("sprint", 1) -> ["a1"]   # lowest sprint time = best
personal_best("a1", "sprint") -> 10.2
trend("a1", "sprint") -> "improving"
```

## Follow-ups

1. How do you define "improving" vs "stable" - linear regression slope, or simple delta?
2. How would you update analytics incrementally as new events stream in?
3. How do you handle athletes with fewer than 5 recorded events for `trend`?
4. What index structures would you use to make `top_k` O(log n)?

Performance Analytics - Compute Athlete Stats from Event Data

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