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What is the auxiliary space complexity of the XOR partitioning approach for finding two missing numbers?

medium🪤 Complexity Trap Q6 of Q15
Bit Manipulation - Find Two Missing Numbers
What is the auxiliary space complexity of the XOR partitioning approach for finding two missing numbers?
AO(n)
BO(log n)
CO(1)
DO(n^2)
Step-by-Step Solution
Solution:

  1. Step 1: Identify extra space usage

    The XOR approach uses only a few integer variables and no additional data structures proportional to n.

  2. Step 2: Confirm constant space

    All variables are scalars; no recursion or auxiliary arrays are used, so space is O(1).

  3. Final Answer:

    Option C -> Option C

  4. Quick Check:

    Only constant extra variables used [OK]
Quick Trick: XOR approach uses constant extra variables only [OK]
Common Mistakes:
MISTAKES
  • Assuming auxiliary arrays or recursion stack
  • Confusing input space with auxiliary space
Trap Explanation:
PITFALL
  • Candidates often confuse input storage with auxiliary space or forget recursion stack in other approaches.
Interviewer Note:
CONTEXT
  • Tests candidate's understanding of space complexity in bit manipulation
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