Bit Manipulation - Gray Code
You need to generate a sequence of 2ⁿ binary numbers where each consecutive pair differs in exactly one bit. Which algorithmic pattern best fits this problem?
You need to generate a sequence of 2ⁿ binary numbers where each consecutive pair differs in exactly one bit. Which algorithmic pattern best fits this problem?
easy🔍 Pattern Recognition Q1 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand the problem constraints
The problem requires a sequence where each consecutive number differs by exactly one bit, covering all 2ⁿ numbers.Step 2: Identify the pattern that guarantees one-bit difference
Gray code generation using the XOR formula i ^ (i >> 1) produces such a sequence efficiently.Final Answer:
Option B -> Option BQuick Check:
Gray code ensures one-bit difference between consecutive numbers [OK]
Quick Trick: Gray code uses XOR with shifted index [OK]
Common Mistakes:
MISTAKES- Thinking sorting decimal values ensures one-bit difference
- Using brute force backtracking for large n
Trap Explanation:
PITFALL- Candidates often confuse sorting or DP with Gray code, missing the bitwise XOR pattern.
Interviewer Note:
CONTEXT- Tests candidate's ability to recognize bit manipulation patterns from problem description.
Master "Gray Code" in Bit Manipulation
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