Bit Manipulation - Gray Code
Suppose you want to generate a Gray code sequence where each number can be repeated multiple times (i.e., reuse allowed). Which modification to the optimal bitwise formula approach correctly handles this variant?
Which modification to the optimal bitwise formula approach correctly handles this variant?
hard🎤 Interviewer Follow-up Q15 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand the reuse constraint
Allowing repeated numbers breaks the Gray code uniqueness property, so the original formula which generates unique numbers won't work.Step 2: Identify suitable approach
Brute force backtracking can explore sequences with repeated numbers and enforce the one-bit difference condition without uniqueness constraints.Step 3: Why other options fail
Original formula always generates unique numbers; simply allowing duplicates in output breaks Gray code definition; generating fewer numbers misses full coverage.Final Answer:
Option A -> Option AQuick Check:
Backtracking is flexible enough to handle reuse constraints [OK]
Quick Trick: Original formula assumes unique numbers; reuse needs backtracking [OK]
Common Mistakes:
MISTAKES- Assuming original formula can be tweaked trivially for reuse
- Thinking fewer numbers still form valid Gray code
- Ignoring uniqueness property of Gray code
Trap Explanation:
PITFALL- Options A, B, and D look plausible but violate Gray code uniqueness or coverage; only backtracking can handle reuse properly.
Interviewer Note:
CONTEXT- Tests if candidate understands Gray code uniqueness and can adapt approach for relaxed constraints.
Master "Gray Code" in Bit Manipulation
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