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The basic case felt fine until I realized I needed to actually handle precedence correctly, not just left-to-right.
Clarify the requirements and edge cases first, then implement a two-stack (operands and operators) algorithm that respects precedence and parentheses. Walk through the code with a sample expression, and discuss trade-offs like time/space complexity and potential extensions.
Pro tip: Explicitly handle integer division truncating toward zero, especially for negative numbers, as many languages' default division rounds toward negative infinity. Mention that you can use a helper function like truncate(a / b) to ensure correctness.
Ask about input format (spaces, unary operators, parentheses), integer division behavior for negatives, and error handling. Confirm expected output type and constraints.
Decide between two-stack (operators and operands) or recursive descent parsing. Explain why two-stack is simpler for precedence and parentheses.
Iterate through tokens, push numbers to operand stack, and for operators, pop and apply while precedence allows. Handle parentheses by evaluating sub-expressions.
Walk through expressions like '3+2*2', '10/3', '-7/2', and '(1+2)*3' to verify correctness, especially integer division truncation.
State O(n) time and O(n) space. Mention alternative approaches (e.g., shunting-yard, recursive descent) and their pros/cons.
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