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Suppose the input array can contain duplicate numbers and the missing number is still from 0 to n. Which modification to the XOR approach correctly finds the missing number?

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Bit Manipulation - Find the Missing Number

Suppose the input array can contain duplicate numbers and the missing number is still from 0 to n. Which modification to the XOR approach correctly finds the missing number?

AXOR approach fails; instead use a frequency count array to find the missing number

BUse XOR as usual; duplicates cancel out so the missing number is found correctly

CSort the array and scan for the first missing number ignoring duplicates

DUse sum approach but subtract duplicates only once to avoid errors

Step-by-Step Solution

Step 1: Understand XOR behavior with duplicates
Duplicates XORed twice cancel out, but duplicates in input break the assumption of unique elements, causing incorrect missing number.
Step 2: Identify correct approach for duplicates
Frequency counting tracks occurrences accurately, allowing detection of missing number despite duplicates.
Final Answer:
Option A -> Option A
Quick Check:
XOR fails with duplicates; frequency count handles duplicates correctly [OK]

Quick Trick: XOR assumes unique elements; duplicates break cancellation [OK]

Common Mistakes:

MISTAKES

Assuming XOR works with duplicates
Trying to fix sum approach without frequency
Ignoring duplicates impact on XOR

Trap Explanation:

PITFALL

XOR approach is optimal only if elements are unique; duplicates invalidate XOR cancellation logic.

Interviewer Note:

CONTEXT

Tests candidate's understanding of XOR assumptions and ability to adapt to relaxed constraints

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