Intervals - Non-overlapping Intervals (Max Non-Overlap)
What is the time complexity of the optimal greedy algorithm that finds the maximum number of non-overlapping intervals by sorting intervals and iterating through them once?
What is the time complexity of the optimal greedy algorithm that finds the maximum number of non-overlapping intervals by sorting intervals and iterating through them once?
medium🪤 Complexity Trap Q13 of Q15
Step-by-Step Solution
Step 1: Identify sorting cost
Sorting intervals by start or end time takes O(n log n) time.Step 2: Identify iteration cost
Iterating through the sorted intervals to select non-overlapping ones takes O(n) time.Final Answer:
Option A -> Option AQuick Check:
Sorting dominates, total complexity is O(n log n) [OK]
Quick Trick: Sorting dominates time complexity in interval scheduling [OK]
Common Mistakes:
MISTAKES- Assuming iteration alone is O(n) and ignoring sorting
- Mistaking nested loops causing O(n^2)
- Confusing sorting and iteration costs
Trap Explanation:
PITFALL- Option B looks correct but is incomplete; sorting plus iteration is O(n log n), not just sorting alone.
Interviewer Note:
CONTEXT- Checks if candidate understands sorting cost dominates greedy interval scheduling.
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