Scoring Opportunities - Interval Overlap Coding Interview

Question

## Problem

A sports analytics system records "scoring opportunities" for a team as time intervals `[start, end]` (in seconds). Two opportunities are "linked" if they overlap or are within 5 seconds of each other. A "sequence" is a maximal group of linked opportunities.

Given a list of intervals, return:
1. The number of distinct sequences.
2. The total duration covered by each sequence (union of its intervals).

```python
def scoring_sequences(opportunities: list[tuple[int,int]]) -> list[dict]:
    # Each dict: {"sequence_id": int, "interval_count": int, "total_duration": int}
    ...
```

**Example:**
```
opportunities = [(0,10),(8,20),(25,35),(50,60),(54,70)]
Output: [
  {"sequence_id":1, "interval_count":2, "total_duration":20},  # [0,10],[8,20] -> union [0,20]
  {"sequence_id":2, "interval_count":1, "total_duration":10},  # [25,35]
  {"sequence_id":3, "interval_count":2, "total_duration":20}   # [50,70]
]
```

## Follow-ups
- How does sorting the intervals first simplify the merge step?
- What is the time complexity? Can you do it in O(n log n)?
- Extend to track which player was involved in each opportunity and return per-player sequence stats.

Scoring Opportunities - Interval Overlap Coding Interview

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