Bit Manipulation - Single Number II (Three Copies)
In an array where every element appears exactly three times except one unique element appearing once, which technique efficiently identifies the unique element using bitwise operations?
In an array where every element appears exactly three times except one unique element appearing once, which technique efficiently identifies the unique element using bitwise operations?
easy💻 Programming Q1 of Q15
Step-by-Step Solution
Solution:
Step 1: Count bits at each position
For each bit position (0 to 31), count how many numbers have that bit set.Step 2: Take modulo 3 of each bit count
Since all numbers except one appear thrice, bits set in multiples of 3 will vanish modulo 3.Step 3: Reconstruct unique number
Bits with remainder 1 after modulo 3 belong to the unique element.Final Answer:
Option C -> Option CQuick Check:
Bitwise counting isolates unique bits correctly [OK]
Quick Trick: Count bits mod 3 to find unique element [OK]
Common Mistakes:
MISTAKES- Assuming sorting helps in O(n) time
- Using hash maps increases space complexity
- Applying binary search requires sorted unique pattern
Trap Explanation:
PITFALL- Sorting or hash maps seem intuitive but don't meet O(1) space or O(n) time constraints.
Interviewer Note:
CONTEXT- Tests understanding of bitwise counting and modulo operation for unique element detection.
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