Bit Manipulation - Find the Missing Number
What is the overall time complexity of using the XOR method to find the missing number in an array of size n containing numbers from 0 to n?
What is the overall time complexity of using the XOR method to find the missing number in an array of size n containing numbers from 0 to n?
medium🧠 Conceptual Test Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand the XOR approach
The XOR method involves iterating through the array once and XORing all elements with numbers from 0 to n.Step 2: Analyze the loops
Both loops run linearly over n elements, so the total operations are proportional to n.Final Answer:
Option C -> Option CQuick Check:
Single pass through array and range [0..n] [OK]
Quick Trick: XOR approach requires just one linear pass [OK]
Common Mistakes:
MISTAKES- Confusing XOR with sorting leading to O(n log n)
- Assuming nested loops cause O(n²)
- Thinking XOR operations are logarithmic
Trap Explanation:
PITFALL- Incorrect answers often assume sorting or nested loops are involved.
Interviewer Note:
CONTEXT- Tests understanding of time complexity in bit manipulation algorithms.
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