I went straight to recursion and got tripped up on operator precedence.
Clarify the expression's complexity (operators, parentheses, precedence) and then implement a two-stack or shunting-yard algorithm to evaluate it. Walk through an example to validate the approach and discuss handling edge cases like division by zero and invalid input.
Pro tip: Mention that you'd use a stack-based approach to handle operator precedence and parentheses, and that you'd consider using a recursive descent parser for more complex expressions. This shows you understand both iterative and recursive solutions and can choose the right tool for the job.
Ask about the types of operators (+, -, *, /, ^), parentheses, whitespace, and whether the expression is guaranteed valid. Also discuss integer vs floating-point division and overflow concerns.
Decide between two-stack (operands and operators) or shunting-yard to convert to postfix then evaluate. Consider recursive descent for extensibility.
Describe how to handle precedence, associativity, and parentheses. For two-stack: push operands, push operators after popping higher precedence ones, and evaluate on closing parenthesis.
Trace the algorithm on a sample expression like '3+4*2/(1-5)' to demonstrate correctness and edge case handling.
State time and space complexity (O(n) for typical expressions) and discuss handling of invalid input, division by zero, and unary minus.
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