Bit Manipulation - Single Number III (Two Singles)
What is the overall time complexity of the XOR and partition approach to find two unique numbers in an array of size
n?What is the overall time complexity of the XOR and partition approach to find two unique numbers in an array of size n?
medium📊 Complexity Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: XOR all elements
This requires a single pass through the array, O(n).Step 2: Find a set bit
This is a constant time operation, O(1).Step 3: Partition and XOR each group
Another pass through the array, O(n).Final Answer:
Option C -> Option CQuick Check:
Two linear passes plus constant time steps [OK]
Quick Trick: Two passes over array, constant extra work [OK]
Common Mistakes:
MISTAKES- Assuming sorting is involved, leading to O(n log n)
- Mistaking nested loops for XOR approach
- Ignoring constant time bit operations
Trap Explanation:
PITFALL- Confusing XOR approach with sorting or brute force methods inflates complexity.
Interviewer Note:
CONTEXT- Tests understanding of time complexity of bitwise XOR solution.
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