The multi-digit number part is where I almost slipped up.
Clarify the problem constraints (e.g., integer division, operator precedence, parentheses) and then propose a two-stack or recursive descent parser solution. Walk through the algorithm step-by-step, emphasizing how to handle precedence and parentheses, and analyze time/space complexity.
Pro tip: Mention that you would use a stack-based approach to handle operator precedence and parentheses, and that you would test edge cases like negative numbers, division by zero, and multi-digit numbers. This shows attention to detail and robustness.
Ask about input format, integer division behavior, handling of spaces, and whether unary operators or negative numbers are allowed. Confirm that division truncates toward zero.
Decide between two-stack (operators and operands) or recursive descent parsing. Explain why one is more suitable given the constraints.
Describe how to process the string: handle digits, operators, and parentheses. For two-stack, detail when to push/pop operators based on precedence.
State time and space complexity (O(n) time, O(n) space). Discuss edge cases like division by zero, large numbers, and nested parentheses.
Walk through a sample expression like '3+2*2' and '(1+(4+5+2)-3)+(6+8)' to verify the algorithm and demonstrate correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by acknowledging that the current solution likely uses a stack-based or recursive descent parser, and that adding new operators requires updating the precedence and associativity rules. Then, propose a flexible design such as a precedence table or configurable operator definitions, and walk through how you would extend the parser and evaluator to handle exponentiation (right-associative) and custom operators. Finally, discuss testing and edge cases.
Pro tip: Mention that exponentiation is right-associative (e.g., 2^3^2 = 2^(3^2)), unlike most binary operators, and that custom operators may require dynamic precedence handling. This shows attention to detail and adaptability.
Ask the interviewer about the expected behavior of the new operators: precedence, associativity, and whether custom operators can be defined at runtime. Confirm if the solution should be extensible without modifying core code.
Briefly explain how your current calculator parses and evaluates expressions (e.g., shunting-yard, recursive descent). Identify where precedence and associativity are handled.
Propose a data-driven approach: a precedence table mapping operators to precedence levels and associativity. For custom operators, allow registration of new operators with specified precedence and associativity.
Modify the parser to consult the precedence table when deciding operator order. For exponentiation, ensure right-associativity by adjusting the parsing logic (e.g., in shunting-yard, treat right-associative operators differently when popping).
Write test cases covering new operators, mixed precedence, associativity, and custom operator definitions. Discuss potential pitfalls like unary minus vs. exponentiation precedence.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.