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What is the auxiliary space complexity of the optimal two pointers interval intersection algorithm for input lists of sizes m and n?

medium🪤 Complexity Trap Q6 of Q15
Intervals - Interval List Intersections
What is the auxiliary space complexity of the optimal two pointers interval intersection algorithm for input lists of sizes m and n?
AO(log(m + n)) due to recursion stack
BO(1) constant space
CO(m + n) for output storage
DO(m * n) due to nested loops
Step-by-Step Solution
Solution:

  1. Step 1: Identify space usage

    Algorithm uses no recursion, so no recursion stack space.

  2. Step 2: Output space

    Output list can be up to O(m + n) in worst case, but auxiliary space excludes output.

  3. Step 3: Auxiliary space

    Only constant variables used, so auxiliary space is O(1).

  4. Final Answer:

    Option A -> Option A

  5. Quick Check:

    Auxiliary space excludes output, so constant [OK]
Quick Trick: Auxiliary space excludes output list [OK]
Common Mistakes:
MISTAKES
  • Counting output space as auxiliary
  • Assuming recursion stack
Trap Explanation:
PITFALL
  • Candidates confuse output space with auxiliary or assume recursion stack exists.
Interviewer Note:
CONTEXT
  • Tests understanding of space complexity distinctions.
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