Start by converting the integer to a string and count the frequency of each digit. Precompute all powers of two within the allowed range and store their digit counts in a hash set. Then, check if any precomputed pattern matches the digit frequency of the input, which ensures correctness without brute-force permutations.
Problem Statement
Given an integer n, reorder its digits in any possible arrangement such that no number begins with zero. Return true if the reordered number can be a power of two.
For example, n = 1 returns true since 1 itself is a power of two, while n = 10 returns false because no rearrangement forms a power of two. Implement a solution that efficiently checks possible digit combinations without generating all permutations.
Examples
Example 1
Input: n = 1
Output: true
Example details omitted.
Example 2
Input: n = 10
Output: false
Example details omitted.
Constraints
- 1 <= n <= 109
Solution Approach
Digit Counting with Hash
Convert n to a string and create a frequency map of its digits. For all powers of two within range, precompute their digit counts and store them in a hash set for O(1) comparison.
Compare Patterns Efficiently
Instead of generating all permutations of n, compare the digit count map of n with precomputed digit count maps of powers of two. If a match exists, return true.
Optimization by Range
Only consider powers of two that have the same number of digits as n to reduce unnecessary checks. This avoids mismatches caused by differing lengths and ensures faster execution.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity depends on the number of powers of two up to 10^9 and comparing digit counts, roughly O(log n). Space complexity is O(log n) for storing precomputed hash sets of digit counts.
What Interviewers Usually Probe
- Ask if brute-force permutations are required or if a counting method is possible.
- Check if candidate optimizations use digit frequency maps rather than full sorting or permutation generation.
- Probe understanding of why hashing digit counts improves performance over naive checking.
Common Pitfalls or Variants
Common pitfalls
- Failing to precompute powers of two and checking all permutations leads to timeouts.
- Ignoring leading zero constraints results in incorrect matches.
- Not comparing digit counts properly can cause false negatives even if a valid rearrangement exists.
Follow-up variants
- Determine if digits can form any perfect square instead of a power of two.
- Return all powers of two that can be formed by rearranging the digits of n.
- Check the same property for numbers with a fixed number of digits rather than the input's length.
How GhostInterview Helps
- Automatically generates precomputed digit count maps of powers of two for instant comparison.
- Highlights the failure modes of naive permutation approaches and guides toward hash-based counting.
- Provides quick feedback on whether the candidate's approach correctly handles leading zeros and digit constraints.
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 main idea behind Reordered Power of 2?
The key is to use a digit frequency hash to check if a number's digits can match a precomputed power of two, avoiding permutations.
Why is hashing digit counts faster than generating permutations?
Because comparing frequency maps avoids factorial time complexity, reducing checks to O(log n) with precomputed powers.
Does Reordered Power of 2 allow numbers with leading zeros?
No, any rearranged number must have a non-zero leading digit to be considered valid.
How many powers of two need to be precomputed?
All powers of two with digit lengths up to the number of digits in n, which is roughly up to 2^30 for n <= 10^9.
Can GhostInterview handle different patterns like Hash Table plus Math?
Yes, it specifically guides the candidate to apply counting, hashing, and mathematical checks tailored to this problem's pattern.
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