Start by checking if the number is positive and a power of two, since all powers of four are powers of two. Then use bit manipulation to ensure the single set bit is in the correct position for a power of four. Recursive or mathematical verification can also confirm validity, making the solution concise and interview-ready for this math plus bit manipulation pattern.
Problem Statement
Given an integer n, return true if n is a power of four, and false otherwise. A power of four is defined as n equal to 4 raised to some integer exponent x.
You must implement an efficient solution leveraging both mathematical checks and bit manipulation. Example scenarios include n = 16 returning true, n = 5 returning false, and n = 1 returning true. Constraints: -231 <= n <= 231 - 1.
Examples
Example 1
Input: n = 16
Output: true
Example details omitted.
Example 2
Input: n = 5
Output: false
Example details omitted.
Example 3
Input: n = 1
Output: true
Example details omitted.
Constraints
- -231 <= n <= 231 - 1
Solution Approach
Bit Masking Verification
Check if n > 0 and n is a power of two using n & (n - 1) == 0. Then ensure the set bit is at an even position, which confirms it is a power of four. This approach directly ties the bit pattern to the mathematical property of powers of four.
Mathematical Division
Repeatedly divide n by 4 while it is divisible. If the final result is 1, then n is a power of four. This method emphasizes the math pattern and avoids unnecessary bit-level operations, highlighting the simplicity of division-based verification.
Recursive Check
Use recursion to divide n by 4 and verify each step until reaching 1. Return false if any division step leaves a remainder. This approach combines the mathematical understanding of powers with the recursive pattern, reflecting a common interview exploration of this problem.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity ranges from O(1) for bit manipulation to O(log n) for division or recursion. Space complexity is O(1) for iterative solutions and O(log n) for recursion due to call stack usage.
What Interviewers Usually Probe
- Ask about distinguishing power of two versus power of four with bit operations.
- Probe candidate understanding of position of the set bit in powers of four.
- Expect efficient solutions rather than brute force iterations or floating-point checks.
Common Pitfalls or Variants
Common pitfalls
- Checking only n > 0 or n & (n - 1) without verifying bit position can misidentify powers of two as powers of four.
- Using floating-point logarithms may introduce precision errors in edge cases.
- Failing to handle n = 1 correctly, which is a valid power of four (4^0).
Follow-up variants
- Power of Two check without enforcing power of four constraints.
- Power of Eight verification requiring similar bit and math insights.
- Recursive-only solution without bit manipulation optimizations.
How GhostInterview Helps
- Automatically identifies correct bit manipulation patterns for powers of four, reducing trial-and-error debugging.
- Provides step-by-step verification of recursive or division approaches for interview clarity.
- Highlights edge cases like n = 1 or negative numbers to ensure robust solution before submission.
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
How can I quickly check if a number is a power of four?
Use bit manipulation: confirm n > 0, n & (n - 1) == 0, and the set bit is at an even position.
Can recursion be used efficiently for Power of Four?
Yes, recursively divide by 4 until reaching 1 or encountering a remainder, reflecting the math pattern.
What common mistakes occur in Power of Four checks?
Misidentifying powers of two as powers of four or relying on floating-point logarithms can cause incorrect results.
Is there a purely mathematical approach without bit operations?
Repeatedly divide n by 4 and check if the final result is 1. This avoids bit manipulation entirely.
Why is bit position important in the Power of Four problem?
Because only powers of four have their single set bit at even positions, ensuring correct distinction from other powers of two.
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Determine if a given integer is a power of two using efficient math and bit manipulation techniques with optional recursion support.
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