This was a follow-up to an earlier problem and I just fell apart.
First, clarify the definition of 'Perfect Wake Numbers' and any constraints (e.g., n up to 10^9). Then, derive a mathematical characterization or efficient algorithm (e.g., digit DP, precomputation, or formula) to count them up to n, and analyze time/space complexity.
Pro tip: Always ask clarifying questions about the definition and constraints before diving into a solution; this shows you think about edge cases and scalability, which is crucial at Google.
Ask the interviewer to precisely define 'Perfect Wake Numbers' and provide examples. Also, inquire about the range of n and expected time/space complexity.
Manually compute or write a brute-force check for small n to understand the properties of these numbers. Look for patterns or mathematical relationships.
Based on the pattern, design an algorithm (e.g., digit DP, combinatorial counting, or precomputation) that can count up to n without iterating over all numbers if n is large.
Determine the time and space complexity of your approach. If needed, optimize further by reducing states or using mathematical shortcuts.
Validate your solution with edge cases (n=0, n=1, large n) and explain how you would test it. Be ready to discuss trade-offs.
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