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What is the auxiliary space complexity of the optimal greedy algorithm that sorts balloons by their end coordinate and iterates through them to find the minimum number of arrows?

medium🪤 Complexity Trap Q6 of Q15
Intervals - Minimum Number of Arrows to Burst Balloons
What is the auxiliary space complexity of the optimal greedy algorithm that sorts balloons by their end coordinate and iterates through them to find the minimum number of arrows?
AO(n) due to recursion stack
BO(n) due to auxiliary arrays
CO(log n) due to sorting stack space
DO(1) ignoring input storage
Step-by-Step Solution
Solution:

  1. Step 1: Consider input storage

    Input array is given, not counted as auxiliary space.

  2. Step 2: Analyze sorting space

    Typical sorting algorithms use O(log n) stack space for recursion or merges.

  3. Final Answer:

    Option C -> Option C

  4. Quick Check:

    Auxiliary space is O(log n) due to sorting, no extra arrays used [OK]
Quick Trick: Sorting recursion stack causes O(log n) space [OK]
Common Mistakes:
MISTAKES
  • Forgetting sorting stack space or assuming O(n) extra arrays
Trap Explanation:
PITFALL
  • Candidates often forget sorting uses recursion stack space.
Interviewer Note:
CONTEXT
  • Tests understanding of auxiliary space beyond input storage.
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