Bit Manipulation - Single Number III (Two Singles)
Given an array where exactly two elements appear once and all others appear twice, which method efficiently identifies these two unique elements using bitwise operations?
Given an array where exactly two elements appear once and all others appear twice, which method efficiently identifies these two unique elements using bitwise operations?
easy💻 Programming Q1 of Q15
Step-by-Step Solution
Solution:
Step 1: XOR all elements
XORing all elements cancels out duplicates, leaving XOR of the two unique numbers.Step 2: Find a set bit in the XOR result
This bit differentiates the two unique numbers.Step 3: Partition elements based on this bit and XOR within each group
This isolates each unique number.Final Answer:
Option A -> Option AQuick Check:
Bitwise XOR cancels duplicates efficiently [OK]
Quick Trick: XOR all, find set bit, partition, XOR groups [OK]
Common Mistakes:
MISTAKES- Sorting increases time complexity unnecessarily
- Hash map uses extra space, violating O(1) space constraint
- Nested loops lead to O(n²) time complexity
Trap Explanation:
PITFALL- Sorting or hash map approaches seem straightforward but are less efficient or use extra space.
Interviewer Note:
CONTEXT- Tests understanding of XOR properties and bit manipulation for optimal solution.
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