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What is the time complexity of the optimal sweep line algorithm for Employee Free Time, given N total intervals across all employees?

medium🪤 Complexity Trap Q13 of Q15
Intervals - Employee Free Time
What is the time complexity of the optimal sweep line algorithm for Employee Free Time, given N total intervals across all employees?
AO(N log N) due to sorting all interval endpoints
BO(N log M) where M is number of employees
CO(N) because each interval is processed once
DO(N²) due to nested iteration over intervals
Step-by-Step Solution

  1. Step 1: Identify main operations

    We create 2N events (start and end per interval) and sort them.

  2. Step 2: Sorting events dominates complexity

    Sorting 2N events takes O(N log N). The sweep through events is O(N).

  3. Final Answer:

    Option A -> Option A

  4. Quick Check:

    Sorting dominates, so O(N log N) [OK]
Quick Trick: Sorting interval endpoints dominates time complexity [OK]
Common Mistakes:
MISTAKES
  • Assuming linear time because each interval processed once
Trap Explanation:
PITFALL
  • Confusing linear iteration with sorting cost leads to underestimating complexity.
Interviewer Note:
CONTEXT
  • Checks understanding of sorting impact on interval sweep line algorithms.
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