Bit Manipulation - Single Number III (Two Singles)
If an array contains exactly two unique numbers but all other numbers appear an odd number of times (not necessarily twice), which approach is required to find the unique numbers efficiently?
If an array contains exactly two unique numbers but all other numbers appear an odd number of times (not necessarily twice), which approach is required to find the unique numbers efficiently?
hard🔁 Follow Up Q10 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand problem constraints
Duplicates appear an odd number of times, not necessarily twice.Step 2: XOR approach limitation
XOR cancels pairs but fails with odd counts other than two.Step 3: Use frequency map
Counting occurrences identifies elements appearing once regardless of odd counts.Final Answer:
Option D -> Option DQuick Check:
XOR fails with odd counts other than two [OK]
Quick Trick: XOR only works if duplicates appear exactly twice [OK]
Common Mistakes:
MISTAKES- Applying XOR approach blindly with odd duplicates
- Assuming XOR cancels all duplicates regardless of count
- Ignoring extra space needed for frequency counting
Trap Explanation:
PITFALL- XOR approach looks elegant but fails with odd duplicates other than two.
Interviewer Note:
CONTEXT- Tests understanding of XOR limitations and alternative approaches.
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