How do you find the element that appears exactly once in an array?
This classic problem tests bitwise manipulation skills and the ability to optimize space complexity. It is a favorite for assessing low-level programming intuition.
Why Interviewers Ask This
Interviewers use this to check if candidates know the XOR property where a ^ a = 0 and a ^ 0 = a. It demonstrates whether they can solve a problem in O(n) time with O(1) space instead of using hash maps or sorting. This shows efficiency in resource usage and familiarity with fundamental bitwise operators which are crucial for systems programming.
How to Answer This Question
Explain the properties of the XOR operation clearly. Propose iterating through the array and applying XOR to all elements. Explain why duplicates cancel out leaving only the unique element. Compare this with alternative methods like using a hash map or sorting, highlighting why XOR is superior in terms of space. Ensure the code snippet is concise and handles empty arrays or negative numbers correctly.
Key Points to Cover
- Leverage XOR properties: a^a=0, a^0=a
- Achieve O(n) time and O(1) space
- Avoid extra data structures like Hash Maps
- Handle edge cases like single element arrays
Sample Answer
The most efficient way to find the single non-duplicate element is using the XOR operation. Since XORing a number with itself results in zero, and XORing with zero returns the number, all duplicate pairs will cancel each…
Common Mistakes to Avoid
- Using a hash map leading to O(n) space complexity
- Sorting the array resulting in O(n log n) time
- Not explaining why XOR works mathematically
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