I went with recursive descent because two-stack shunting-yard always trips me up when I try to code it live.
Clarify requirements and edge cases, then design a solution using a stack-based or recursive descent parser that respects operator precedence and right-associativity. Implement the algorithm, test with examples, and discuss trade-offs between approaches.
Pro tip: Demonstrate strong communication by walking through a concrete example step-by-step before coding, and explicitly state how you handle spaces and multi-digit numbers.
Ask about input constraints (e.g., maximum expression length, integer overflow), expected output format, and handling of invalid expressions. Confirm that spaces can be ignored and that only non-negative integers and the operators +, *, ^ are allowed.
Decide between a stack-based two-pass algorithm (first handle ^, then * and +) or a recursive descent parser. Consider trade-offs: stack-based is simpler for this specific operator set, while recursive descent is more extensible.
For stack-based: tokenize the expression, then process ^ right-associatively using a stack, followed by * and + with standard precedence. For recursive descent: define grammar with ^ highest precedence and right-associative, then implement parsing functions.
Write clean code with helper functions for tokenization and evaluation. Test with examples like '2^3^2' (should be 512), '2+3*4' (14), and expressions with spaces. Handle edge cases like single number, leading/trailing spaces.
State time and space complexity (O(n) time, O(n) space for stack). Discuss potential optimizations, such as evaluating on the fly or using two stacks for operators and operands. Mention how to extend to other operators or parentheses.
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