Bit Manipulation - Reverse Bits
What is the time complexity of the optimal bit reversal algorithm using divide and conquer masks on a fixed 32-bit integer?
What is the time complexity of the optimal bit reversal algorithm using divide and conquer masks on a fixed 32-bit integer?
medium🪤 Complexity Trap Q13 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze algorithm steps
The algorithm performs a sequence of bitwise operations that swap bits in stages, each stage halving the problem size.Step 2: Determine complexity
Since the algorithm performs log n stages (where n=32 bits), the time complexity is O(log n).Final Answer:
Option C -> Option CQuick Check:
Number of steps proportional to log n due to divide and conquer swaps [OK]
Quick Trick: Divide and conquer bit swaps perform O(log n) steps [OK]
Common Mistakes:
MISTAKES- Assuming fixed bit width means O(1) for arbitrary n
- Confusing bit count with input size
- Thinking each bit is processed individually in a loop
Trap Explanation:
PITFALL- While fixed 32-bit width means constant time, the algorithm conceptually performs O(log n) steps for n-bit inputs.
Interviewer Note:
CONTEXT- Checks understanding of complexity in divide and conquer bit manipulation algorithms.
Master "Reverse Bits" in Bit Manipulation
Want More Practice?
15+ quiz questions · All difficulty levels · Free
Free Signup - Practice All QuestionsMore Bit Manipulation Quizzes