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Given multiple employees' schedules with intervals representing their busy times, which algorithmic approach guarantees finding all common free time intervals where no employee is busy?

easy🔍 Pattern Recognition Q11 of Q15
Intervals - Employee Free Time
Given multiple employees' schedules with intervals representing their busy times, which algorithmic approach guarantees finding all common free time intervals where no employee is busy?
AGreedy interval scheduling that picks earliest finishing intervals
BDynamic programming to find maximum non-overlapping intervals
CSweep line / event processing that tracks interval start and end events
DBrute force checking every time point across all intervals
Step-by-Step Solution

  1. Step 1: Understand problem requires identifying gaps where no intervals overlap

    Greedy scheduling or DP focus on selecting intervals, not gaps between them.

  2. Step 2: Sweep line processes all start/end events in order, tracking active intervals to find free gaps

    This approach efficiently detects when no employee is busy, yielding correct free times.

  3. Final Answer:

    Option C -> Option C

  4. Quick Check:

    Sweep line tracks active intervals and finds free gaps [OK]
Quick Trick: Sweep line tracks interval endpoints to find free gaps [OK]
Common Mistakes:
MISTAKES
  • Assuming greedy or DP can find free gaps directly
Trap Explanation:
PITFALL
  • Greedy and DP focus on selecting intervals, not detecting free time gaps, making them incorrect here.
Interviewer Note:
CONTEXT
  • Tests if candidate can identify the correct pattern beyond textbook interval algorithms.
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