0

What is the time complexity of the binary search + preprocessing approach for the Minimum Interval to Include Each Query problem, given n intervals and m queries?

medium🪤 Complexity Trap Q13 of Q15

Intervals - Minimum Interval to Include Each Query

What is the time complexity of the binary search + preprocessing approach for the Minimum Interval to Include Each Query problem, given n intervals and m queries?

AO(n log n + m n log n)

BO(n log n + m log n * n)

CO((n + m) log n)

DO(n * m)

Step-by-Step Solution

Solution:

Step 1: Analyze preprocessing
Sorting intervals by length takes O(n log n).
Step 2: Analyze per query cost
For each query, binary search over lengths is O(log n), but coverage check scans up to O(n) intervals, so O(n log n) per query.
Final Answer:
Option A -> Option A
Quick Check:
Overall complexity is O(n log n + m n log n) due to coverage scanning [OK]

Quick Trick: Coverage check inside binary search causes O(n) scan per query [OK]

Common Mistakes:

MISTAKES

Assuming coverage check is O(log n) ignoring linear scan
Confusing n and m in complexity
Forgetting sorting cost

Trap Explanation:

PITFALL

Option B looks similar but misses the linear scan inside coverage check, making it incorrect.

Interviewer Note:

CONTEXT

Tests understanding of nested loops and binary search combined complexity.

Master "Minimum Interval to Include Each Query" in Intervals

3 interactive learning modes - each teaches the same concept differently

Try It Solution Trace

Want More Practice?

15+ quiz questions · All difficulty levels · Free

Free Signup - Practice All Questions

More Intervals Quizzes