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What is the auxiliary space complexity of the line sweep algorithm for counting intervals containing each point, given n intervals and m points?

medium🪤 Complexity Trap Q6 of Q15
Intervals - Count of Intervals Containing Each Point
What is the auxiliary space complexity of the line sweep algorithm for counting intervals containing each point, given n intervals and m points?
AO(1) auxiliary space
BO(m) for storing points only
CO(n + m) for storing events and results
DO(n) for storing intervals only
Step-by-Step Solution
Solution:

  1. Step 1: Identify data structures used

    The algorithm stores 2n + m events and a result array of size m.

  2. Step 2: Auxiliary space excludes input storage

    Auxiliary space is O(n + m) for events and O(m) for results, but input intervals are given, so extra space is O(n + m).

  3. Final Answer:

    Option B -> Option B

  4. Quick Check:

    Auxiliary space includes events and result arrays [OK]
Quick Trick: Auxiliary space includes events and result arrays [OK]
Common Mistakes:
MISTAKES
  • Ignoring space for event list
  • Counting input intervals as auxiliary space
  • Assuming constant extra space
Trap Explanation:
PITFALL
  • Candidates often forget that event list and result array consume O(n + m) space.
Interviewer Note:
CONTEXT
  • Tests understanding of auxiliary space beyond input storage.
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