Intervals - Merge Intervals
What is the time complexity of the optimal in-place merge intervals algorithm that first sorts the intervals and then merges them in one pass?
What is the time complexity of the optimal in-place merge intervals algorithm that first sorts the intervals and then merges them in one pass?
medium🪤 Complexity Trap Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze sorting step
Sorting intervals by start time takes O(n log n) time.Step 2: Analyze merging step
Merging intervals in one pass is O(n) time.Step 3: Combine complexities
Total time is dominated by sorting: O(n log n) + O(n) -> O(n log n).Final Answer:
Option B -> Option BQuick Check:
Sorting dominates time complexity [OK]
Quick Trick: Sorting dominates time complexity -> O(n log n) [OK]
Common Mistakes:
MISTAKES- Choosing O(n) ignoring sorting
- Confusing with quadratic due to nested loops
Trap Explanation:
PITFALL- Candidates often forget sorting cost and assume linear time due to single pass merge.
Interviewer Note:
CONTEXT- Tests understanding of time complexity combining sorting and linear merge.
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