Team Event: Schedule a Meeting Slot That Covers the Maximum Number of Attendees

Question

## Problem

Given a list of employees and their busy intervals, find a time slot of exactly `duration` minutes that accommodates the maximum number of employees (i.e., they are free during the entire slot). All times are in minutes from midnight.

```python
def best_meeting_slot(
    schedules: list[list[tuple[int, int]]],
    duration: int,
    day_start: int,
    day_end: int
) -> tuple[int, int]:
    # schedules[i] = list of (busy_start, busy_end) for employee i
    # return (start, end) of the best slot
    pass
```

**Example:**
```
schedules = [[(60,120),(180,240)], [(90,150)], [(200,300)]]
duration = 60, day_start=0, day_end=480
Output: (0, 60)  # all 3 employees free from 0 to 60
```

## Follow-ups

1. What is your time complexity? How do you handle thousands of employees?
2. If you must find the earliest slot where at least N out of M employees are free, how do you approach it?
3. How would you extend this to recurring weekly schedules across time zones?
4. If meetings have a preferred time window (e.g., 9am-12pm), how do you incorporate that constraint?

Team Event: Schedule a Meeting Slot That Covers the Maximum Number of Attendees

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