First, clarify the problem statement and constraints, especially the variable bases and what is being counted. Then, model the problem as counting numbers in a mixed-radix system, derive a formula or recurrence, and validate with small examples before coding.
Pro tip: Demonstrate strong communication by thinking aloud and asking clarifying questions; Google values problem-solving process over just the final answer. Also, consider edge cases like zero and empty representations to show thoroughness.
Ask questions to fully understand the problem: what are the bases, what is the range of numbers, and what exactly needs to be computed? Confirm input/output format and constraints.
Recognize that variable-base representations are mixed-radix numbers. Map the problem to counting or converting in this system, identifying the place values and digit ranges.
Develop a mathematical formula or recurrence relation to solve the problem efficiently. Consider dynamic programming if counting is involved, or direct conversion if it's a single number.
Test your approach on small, hand-computable cases to ensure correctness. Check edge cases like zero, maximum values, and empty inputs.
Write clean code, then analyze time and space complexity. Discuss potential optimizations and trade-offs.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.