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Which approach fundamentally changes compared to the original problem?

hard🎤 Interviewer Follow-up Q10 of Q15
Intervals - Count of Intervals Containing Each Point
Suppose intervals can be reused infinitely many times, and you want to count how many intervals cover each point considering unlimited reuse. Which approach fundamentally changes compared to the original problem?
AUse binary search on sorted intervals ignoring reuse
BBrute force nested loops with repeated counting
CModel problem as counting multisets of intervals covering points, requiring combinatorial DP
DUse line sweep with event counts multiplied by reuse factor
Step-by-Step Solution
Solution:

  1. Step 1: Understand reuse effect

    Infinite reuse means intervals can cover points multiple times, changing counting semantics.

  2. Step 2: Impact on approaches

    Line sweep and binary search count intervals once; infinite reuse requires counting multisets or repeated coverage, which naive brute force can simulate but is inefficient.

  3. Step 3: Fundamental change

    Counting multisets requires combinatorial DP or different modeling; naive brute force is the fallback but inefficient.

  4. Final Answer:

    Option B -> Option B

  5. Quick Check:

    Infinite reuse breaks original counting assumptions, requiring different approach [OK]
Quick Trick: Infinite reuse breaks original counting assumptions [OK]
Common Mistakes:
MISTAKES
  • Assuming line sweep can handle infinite reuse directly
  • Ignoring combinatorial explosion from reuse
  • Thinking binary search suffices without modification
Trap Explanation:
PITFALL
  • Candidates often try to apply original algorithms without adapting for infinite reuse, missing complexity change.
Interviewer Note:
CONTEXT
  • Tests candidate's ability to adapt problem understanding and algorithm choice for variants.
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