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What is the auxiliary space complexity of the optimal insert interval approach that appends, sorts, then merges intervals?

medium🪤 Complexity Trap Q6 of Q15
Intervals - Insert Interval
What is the auxiliary space complexity of the optimal insert interval approach that appends, sorts, then merges intervals?
AO(n^2)
BO(1)
CO(n)
DO(log n)
Step-by-Step Solution
Solution:

  1. Step 1: Consider space for sorting

    Sorting typically requires O(log n) auxiliary space for recursive stack in quicksort.

  2. Step 2: Consider space for merged list

    Merged list can be up to O(n) size, but since input is modified in place, no extra list needed.

  3. Step 3: Consider input modification

    Appending new interval and creating merged list requires O(n) space.

  4. Final Answer:

    Option A -> Option A

  5. Quick Check:

    Auxiliary space dominated by merged list storage -> O(n) [OK]
Quick Trick: Merged list requires O(n) space auxiliary to input [OK]
Common Mistakes:
MISTAKES
  • Forgetting merged list space, assuming O(1) space
Trap Explanation:
PITFALL
  • Candidates often ignore auxiliary space for merged output list, underestimating space complexity.
Interviewer Note:
CONTEXT
  • Tests understanding of auxiliary space including output storage.
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