Took me a minute to even parse the constraint about adjacent digits.
Clarify the definition of 'Perfect Wake Number' and confirm edge cases (e.g., single-digit numbers). Then, propose an efficient algorithm that checks the three conditions in a single pass over the digits, using a set to detect repeats and comparing each digit with its neighbors to ensure no digit is a local minimum. Discuss time and space complexity, and consider optimizations or alternative approaches.
Pro tip: Demonstrate thoroughness by discussing edge cases upfront (e.g., numbers with 1 or 2 digits) and how your solution handles them, as interviewers at Google value attention to detail and robustness.
Restate the problem in your own words and ask clarifying questions about edge cases, such as single-digit numbers or numbers with leading zeros (though input is a positive integer, so no leading zeros).
Outline a step-by-step approach: convert the integer to a string or extract digits, check for zeros and repeated digits using a set, and then iterate through the digits to ensure no digit is strictly smaller than both neighbors.
State the time complexity (O(d) where d is the number of digits) and space complexity (O(1) if using a fixed-size boolean array for digits, or O(d) for a set). Discuss potential optimizations, such as early termination.
Write clean code (in a language of your choice) and walk through test cases, including valid and invalid numbers, to verify correctness.
Mention any alternative methods, such as generating all valid numbers up to a certain length, and compare trade-offs.
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