Bit Manipulation - Gray Code
What is the time complexity of generating an n-bit Gray code sequence using the list comprehension
[i ^ (i >> 1) for i in range(1 << n)]?What is the time complexity of generating an n-bit Gray code sequence using the list comprehension [i ^ (i >> 1) for i in range(1 ?
medium📊 Complexity Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Understand the range
The range is from 0 to 2^n - 1, so 2^n iterations.Step 2: Operation per iteration
Each iteration computesi ^ (i >> 1), which is O(1) bitwise operations.Step 3: Total complexity
Total time is number of iterations times O(1) = O(2^n).Final Answer:
Option B -> Option BQuick Check:
Each element computed independently in constant time. [OK]
Quick Trick: Bitwise XOR per element is constant time, total 2^n elements [OK]
Common Mistakes:
MISTAKES- Assuming bitwise operations take O(n) time
- Confusing with recursive approach complexity
- Ignoring the size of the output sequence
Trap Explanation:
PITFALL- Option A confuses bitwise operation cost with number of bits n.
Interviewer Note:
CONTEXT- Tests knowledge of time complexity for bitwise Gray code generation.
Master "Gray Code" in Bit Manipulation
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