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Which modification to the XOR partitioning approach correctly finds the two missing numbers?

hard🎤 Interviewer Follow-up Q15 of Q15
Bit Manipulation - Find Two Missing Numbers
Suppose the input array can contain duplicate numbers and missing numbers may appear multiple times (i.e., numbers can be reused). Which modification to the XOR partitioning approach correctly finds the two missing numbers?
AUse frequency counting with a hash map instead of XOR to handle duplicates.
BUse the same XOR partitioning approach since duplicates cancel out in XOR.
CModify XOR approach to XOR each number multiple times equal to its frequency.
DSort the array and scan for missing numbers instead of XOR.
Step-by-Step Solution

  1. Step 1: Understand impact of duplicates

    Duplicates break XOR approach because XOR assumes each number appears exactly once.

  2. Step 2: Choose correct approach

    Frequency counting with a hash map correctly tracks counts and identifies missing numbers even with duplicates.

  3. Step 3: Why other options fail

    Same XOR approach fails due to duplicates; modifying XOR by frequency is not feasible; sorting is O(n log n) and less efficient.

  4. Final Answer:

    Option A -> Option A

  5. Quick Check:

    Frequency counting handles duplicates correctly [OK]
Quick Trick: XOR fails with duplicates; frequency map handles counts [OK]
Common Mistakes:
MISTAKES
  • Assuming XOR works with duplicates
  • Trying to XOR multiple times per frequency
  • Ignoring complexity of sorting
Trap Explanation:
PITFALL
  • XOR relies on unique elements; duplicates invalidate XOR cancellation property.
Interviewer Note:
CONTEXT
  • Tests candidate's understanding of XOR limitations and ability to adapt solutions.
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