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?
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 Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Count total events as 2N (start and end for each interval)
Each interval contributes two endpoints, so total events = 2N.Step 2: Sorting these 2N events dominates complexity at O(N log N)
Sorting 2N events is O(N log N). The sweep line then processes events in O(N) time.Final Answer:
Option B -> Option BQuick Check:
Sorting endpoints is the bottleneck, so O(N log N) [OK]
Quick Trick: Sorting endpoints dominates time complexity [OK]
Common Mistakes:
MISTAKES- Confusing N with timeline length or quadratic complexity
Trap Explanation:
PITFALL- Candidates often think nested loops cause O(N²), but sorting dominates.
Interviewer Note:
CONTEXT- Tests understanding of time complexity in sweep line algorithms.
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