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What is the auxiliary space complexity of the sweep line Employee Free Time algorithm given N total intervals?

medium🪤 Complexity Trap Q6 of Q15
Intervals - Employee Free Time
What is the auxiliary space complexity of the sweep line Employee Free Time algorithm given N total intervals?
AO(1) constant space since only counters are used
BO(N²) due to storing all merged intervals
CO(N) for storing all event points and output intervals
DO(log N) for recursion stack during sorting
Step-by-Step Solution
Solution:

  1. Step 1: Identify space for events and output is O(N)

    Storing 2N events and output intervals requires O(N) space.

  2. Step 2: Recognize sorting uses recursion stack of O(log N)

    Sorting typically uses O(log N) auxiliary space for recursion stack in quicksort or mergesort.

  3. Final Answer:

    Option D -> Option D

  4. Quick Check:

    Auxiliary space excludes input/output; recursion stack is O(log N) [OK]
Quick Trick: Sorting recursion stack uses O(log N) space [OK]
Common Mistakes:
MISTAKES
  • Ignoring recursion stack space or confusing output space with auxiliary space
Trap Explanation:
PITFALL
  • Candidates often forget recursion stack space in sorting algorithms.
Interviewer Note:
CONTEXT
  • Tests understanding of auxiliary space beyond input and output storage.
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