This problem requires reversing all 32 bits of a given unsigned integer efficiently. Use divide and conquer to split the integer into smaller bit blocks and swap them iteratively, applying bit manipulation operations like shifts and masks. GhostInterview highlights key failure points like off-by-one shifts and ensures candidates reason through both bit-level logic and iterative recombination for correctness.
Problem Statement
Given a 32-bit unsigned integer n, reverse all its bits and return the resulting integer. The input is guaranteed to be within the range of 0 to 2^31 - 2, and n is even, ensuring predictable behavior for bit manipulation operations.
For example, if n = 43261596, the reversed bits produce 964176192. If n = 2147483644, reversing its bits yields 1073741822. Implement a solution that leverages divide and conquer plus bit manipulation to achieve the reversal efficiently and correctly.
Examples
Example 1
Input: n = 43261596
Output: 964176192
Example 2
Input: n = 2147483644
Output: 1073741822
Constraints
- 0 <= n <= 231 - 2
- n is even.
Solution Approach
Iterative Bit Swapping
Split the 32-bit integer into smaller segments, swap pairs of bits, then nibbles, bytes, and finally halves. Apply masks and shift operations at each level of the divide and conquer process to build the reversed integer progressively.
Recursive Divide and Conquer
Recursively divide the integer into left and right halves, reverse each half, then merge using bit shifts. This emphasizes understanding the hierarchical structure of bits and ensures correctness at each recursion depth.
Optimized Lookup Table
Precompute reversed values for 8-bit blocks and process the 32-bit integer in four chunks. This approach reduces repeated bitwise operations and aligns with the divide and conquer principle by handling smaller subproblems efficiently.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity depends on the chosen approach: iterative and recursive divide-and-conquer methods run in O(1) since the bit length is fixed at 32, while the lookup table method also achieves O(1) with faster constant-time operations. Space complexity varies: iterative uses O(1), recursive uses O(log32)=O(1) stack, and lookup table uses O(256) for precomputation.
What Interviewers Usually Probe
- Expect candidates to recognize bit-level patterns and swap sequences.
- Look for proper handling of masks and shifts without off-by-one errors.
- Assess whether the candidate applies divide and conquer to sub-bit blocks correctly.
Common Pitfalls or Variants
Common pitfalls
- Incorrectly swapping bits without using proper masks leading to wrong output.
- Forgetting to handle all 32 bits consistently in iterative or recursive steps.
- Misaligning left and right halves when merging, producing off-by-one bit errors.
Follow-up variants
- Reverse bits for integers of arbitrary bit lengths, not limited to 32 bits.
- Count the number of 1s after reversing bits to combine bit manipulation patterns.
- Perform in-place bit reversal for arrays of integers using the same divide and conquer principle.
How GhostInterview Helps
- Highlights exact bit manipulation steps and divide and conquer swaps to prevent common off-by-one mistakes.
- Provides targeted practice on merging bit segments efficiently, ensuring candidates can reason through iterative and recursive approaches.
- Clarifies the trade-offs of iterative versus lookup table approaches, helping candidates choose optimal methods during timed interviews.
Topic Pages
Related GhostInterview Pages
- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What is the fastest way to reverse bits for a 32-bit integer?
Use a combination of divide and conquer with masks and shifts, or precompute a lookup table for 8-bit blocks to reduce operations.
Does the input always need to be even in the Reverse Bits problem?
The problem statement guarantees even integers, which simplifies some bit shift calculations, but solutions should still handle all 32 bits.
Can recursive approaches be used without hitting stack limits?
Yes, since the recursion depth is bounded by the fixed 32-bit length, stack usage remains minimal and safe.
What common mistakes should I avoid when reversing bits?
Avoid misaligned shifts, off-by-one swaps, and forgetting to handle all bit segments consistently in iterative or recursive merges.
How does divide and conquer specifically help in Reverse Bits?
It allows breaking the integer into smaller blocks, reversing each independently, and then combining them correctly, reducing mental and operational complexity.
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