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What is the time complexity of the optimal algorithm that determines if a person can attend all meetings given n intervals?

medium🪤 Complexity Trap Q5 of Q15
Intervals - Meeting Rooms I
What is the time complexity of the optimal algorithm that determines if a person can attend all meetings given n intervals?
AO(n log n)
BO(n^2)
CO(n)
DO(log n)
Step-by-Step Solution
Solution:

  1. Step 1: Analyze sorting step

    Sorting n intervals by start time takes O(n log n) time.

  2. Step 2: Analyze single pass check

    Checking overlaps in one pass is O(n), dominated by sorting.

  3. Final Answer:

    Option A -> Option A

  4. Quick Check:

    Sorting dominates time complexity [OK]
Quick Trick: Sorting dominates complexity -> O(n log n) [OK]
Common Mistakes:
MISTAKES
  • Assuming O(n) without sorting
  • Confusing with quadratic brute force O(n^2)
Trap Explanation:
PITFALL
  • Candidates often forget sorting cost and pick O(n) or O(n^2) incorrectly.
Interviewer Note:
CONTEXT
  • Tests understanding of time complexity in interval sorting algorithms.
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