Bit Manipulation - Gray Code
You need to generate a sequence of numbers where each consecutive pair differs in exactly one bit, covering all 2^n numbers. Which approach guarantees an optimal and correct solution for this problem?
You need to generate a sequence of numbers where each consecutive pair differs in exactly one bit, covering all 2^n numbers. Which approach guarantees an optimal and correct solution for this problem?
easy🔍 Pattern Recognition Q11 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand the problem constraints
The problem requires a sequence of 2^n numbers where each consecutive number differs by exactly one bit.Step 2: Identify the approach that guarantees correctness and efficiency
The reflected Gray code construction recursively builds the sequence by reflecting and prefixing bits, ensuring the one-bit difference property and covering all numbers exactly once.Final Answer:
Option B -> Option BQuick Check:
Reflected Gray code is the classic, proven method for this problem [OK]
Quick Trick: Reflected Gray code ensures one-bit difference and full coverage [OK]
Common Mistakes:
MISTAKES- Greedy flipping bits can miss valid sequences or repeat numbers
- Brute force is correct but impractical for large n
- DP is not suitable as this is not a subproblem overlapping problem
Trap Explanation:
PITFALL- Greedy and brute force seem plausible but either fail correctness or efficiency; DP is a common misconception for sequence generation problems.
Interviewer Note:
CONTEXT- Tests if candidate recognizes the classic Gray code pattern and avoids naive or incorrect approaches.
Master "Gray Code" in Bit Manipulation
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