Bit Manipulation - Find the Missing Number
If the input array may contain duplicate numbers but the missing number is still from 0 to n, which modification to the XOR approach ensures correct identification of the missing number?
If the input array may contain duplicate numbers but the missing number is still from 0 to n, which modification to the XOR approach ensures correct identification of the missing number?
hard🔁 Follow Up Q10 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand XOR limitations
XOR works correctly only if all numbers are distinct except the missing one.Step 2: Handle duplicates
Duplicates cause XOR to cancel out incorrectly, so XOR alone fails.Step 3: Use frequency map
Counting occurrences ensures duplicates are accounted for and missing number can be found reliably.Final Answer:
Option D -> Option DQuick Check:
XOR fails with duplicates; frequency map works [OK]
Quick Trick: XOR fails with duplicates; use counting instead [OK]
Common Mistakes:
MISTAKES- Assuming XOR works with duplicates
- Trying to fix XOR by double application
- Sorting does not fix duplicate XOR issues
Trap Explanation:
PITFALL- XOR cancels duplicates, hiding missing number if duplicates exist.
Interviewer Note:
CONTEXT- Tests understanding of XOR limitations and alternative approaches.
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