I started with the easy case, addition and multiplication, and got through precedence fine using a stack.
Clarify the problem constraints (e.g., integer-only, no parentheses, operator precedence) and then propose a two-phase solution: tokenize the input string and then evaluate using a stack-based or recursive descent approach that respects precedence. Walk through an example to demonstrate correctness and discuss trade-offs between different parsing strategies.
Pro tip: Mention that exponentiation is right-associative and has higher precedence than multiplication, which is higher than addition; also note that you can handle right-associativity by adjusting the parsing order or using a stack with careful popping conditions.
Ask about input format (e.g., spaces, parentheses, negative numbers), operator precedence, associativity, and expected output type. Confirm whether the expression is guaranteed valid.
Decide between recursive descent, shunting-yard, or two-stack approach. Explain why your choice fits the constraints (e.g., recursive descent is clean for precedence, shunting-yard handles right-associativity well).
Describe tokenization, then evaluation. For recursive descent, define functions for each precedence level. For stack-based, detail how to handle operators and operands with precedence and associativity.
Trace a sample expression like '2+3*4^2' to show how the algorithm respects precedence and associativity, and produces the correct result.
Analyze time and space complexity (O(n) time, O(n) space for stacks). Compare approaches in terms of code simplicity, extensibility, and handling of edge cases.
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