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Given the final output of the XOR partitioning function is [3, 5] for n=6, arr=[1, 2, 4, 6], which of the following could be the original input array?

hard🔄 Reverse Engineer Q9 of Q15
Bit Manipulation - Find Two Missing Numbers
Given the final output of the XOR partitioning function is [3, 5] for n=6, arr=[1, 2, 4, 6], which of the following could be the original input array?
A[1, 2, 4, 6]
B[1, 2, 3, 4]
C[2, 4, 5, 6]
D[1, 3, 4, 6]
Step-by-Step Solution
Solution:
  1. Step 1: Understand missing numbers

    Output [3, 5] means these two numbers are missing from the input array.
  2. Step 2: Identify array missing 3 and 5

    Among options, only [1, 2, 4, 6] excludes 3 and 5.
  3. Final Answer:

    Option A -> Option A
  4. Quick Check:

    Input missing 3 and 5 matches output [OK]
Quick Trick: Missing numbers are those not in input array [OK]
Common Mistakes:
MISTAKES
  • Confusing missing numbers with present ones
  • Not verifying all elements
Trap Explanation:
PITFALL
  • Candidates may pick arrays containing missing numbers, invalidating output.
Interviewer Note:
CONTEXT
  • Tests candidate's ability to reason backwards from output to input
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