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What is the time complexity of the optimal insert interval approach that appends, sorts, then merges intervals?

medium🪤 Complexity Trap Q5 of Q15
Intervals - Insert Interval
What is the time complexity of the optimal insert interval approach that appends, sorts, then merges intervals?
AO(n)
BO(n^2)
CO(log n)
DO(n log n)
Step-by-Step Solution
Solution:

  1. Step 1: Analyze sorting step

    Sorting intervals takes O(n log n) time.

  2. Step 2: Analyze merging step

    Merging intervals is O(n) after sorting.

  3. Final Answer:

    Option D -> Option D

  4. Quick Check:

    Sorting dominates time complexity -> O(n log n) [OK]
Quick Trick: Sorting dominates time complexity -> O(n log n) [OK]
Common Mistakes:
MISTAKES
  • Assuming linear time ignoring sorting cost
Trap Explanation:
PITFALL
  • Candidates often forget sorting cost and claim O(n) time incorrectly.
Interviewer Note:
CONTEXT
  • Tests understanding of time complexity including sorting overhead.
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