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What is the additional space complexity of the optimal in-place counting solution that sorts intervals and scans once?

medium🪤 Complexity Trap Q6 of Q15
Intervals - Remove Covered Intervals
What is the additional space complexity of the optimal in-place counting solution that sorts intervals and scans once?
AO(n) for auxiliary arrays
BO(log n) due to sorting stack
CO(1) additional space besides input
DO(n) recursion stack space
Step-by-Step Solution
Solution:

  1. Step 1: Analyze sorting space

    Sorting typically uses O(log n) stack space for recursive quicksort or mergesort.

  2. Step 2: Analyze scanning space

    Scanning uses O(1) additional variables.

  3. Step 3: Combine space usage

    Total additional space is O(log n) due to sorting recursion stack.

  4. Final Answer:

    Option B -> Option B

  5. Quick Check:

    Sorting recursion stack dominates auxiliary space [OK]
Quick Trick: Sorting recursion stack uses O(log n) space [OK]
Common Mistakes:
MISTAKES
  • Ignoring recursion stack space
  • Assuming O(1) total space including sorting
Trap Explanation:
PITFALL
  • Candidates forget sorting recursion stack space when claiming O(1) space.
Interviewer Note:
CONTEXT
  • Tests understanding of space complexity beyond obvious variables.
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