Which modification to the line sweep approach correctly handles this scenario?
hard🎤 Interviewer Follow-up Q15 of Q15
Intervals - Count of Intervals Containing Each Point
Suppose the problem changes: intervals can be reused infinitely many times, and you want to count how many intervals contain each point considering unlimited reuse (e.g., intervals repeat periodically). Which modification to the line sweep approach correctly handles this scenario?
ANo change needed; line sweep already counts intervals correctly regardless of reuse.
BPreprocess intervals to merge overlapping intervals into one, then run line sweep once.
CUse a segment tree or binary indexed tree to handle repeated intervals efficiently instead of line sweep.
DModify events to include multiple copies of intervals explicitly and run line sweep on expanded events.
Step-by-Step Solution
Step 1: Understand reuse impact
Infinite reuse means intervals repeat periodically, so naive line sweep with explicit events cannot handle infinite copies.
Step 2: Recognize data structure need
Segment trees or binary indexed trees can efficiently query counts over ranges and handle repeated intervals without enumerating all copies.
Step 3: Why other options fail
No change (A) ignores infinite reuse; merging (B) loses count detail; explicit expansion (D) is infeasible for infinite repeats.
Final Answer:
Option C -> Option C
Quick Check:
Segment trees handle range queries with repeated intervals efficiently [OK]
Quick Trick:Infinite reuse requires data structures, not event enumeration [OK]
Common Mistakes:
MISTAKES
Assuming line sweep handles infinite repeats
Trying to expand events explicitly
Merging intervals loses count accuracy
Trap Explanation:
PITFALL
Line sweep looks flexible but cannot handle infinite repeated intervals without data structures.
Interviewer Note:
CONTEXT
Tests candidate's ability to adapt interval counting to advanced constraints and choose suitable data structures.
Master "Count of Intervals Containing Each Point" in Intervals
3 interactive learning modes - each teaches the same concept differently
