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Clarify the exact grammar rules (e.g., unary operators, decimal points) and then propose a linear-time parser using a state machine or stack to track parentheses and operator placement. Discuss trade-offs between regex, recursive descent, and iterative parsing, emphasizing efficiency and edge-case handling.
Pro tip: Mention that a stack-based approach can validate parentheses and operator placement in one pass, but be prepared to discuss how to extend it for unary operators or implicit multiplication. Also, explicitly state assumptions about the input format to avoid ambiguity.
Ask about allowed characters, unary operators (e.g., negative numbers), decimal points, and whether empty strings or spaces-only are valid. Confirm that the expression must be fully parsed with no leftover characters.
Outline a formal grammar or state transitions (e.g., expecting operand, operator, or parenthesis) to systematically validate the string. This helps in explaining the logic clearly.
Select an approach: stack for parentheses and operator tracking, or a simple state variable for linear scan. Discuss time and space complexity (O(n) time, O(1) or O(n) space).
Test the algorithm on cases like '1+2*3', '(1+2)*3', '1++2', '()', '1+', and '((1+2)'. Explain how each is handled to demonstrate correctness.
Mention how to extend for unary minus, decimals, or variables, and compare with alternative approaches like regex or recursive descent. Highlight why your chosen method is optimal for the given constraints.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is basically the classic stack-based calculator problem and I knew it, which helped.
Clarify the problem constraints (e.g., integer division, whitespace, unary minus) and then propose a two-stack or shunting-yard algorithm to handle operator precedence and parentheses. Walk through the algorithm step-by-step, emphasizing how to manage negative numbers and edge cases, and analyze time/space complexity.
Pro tip: Mention that you would first convert the expression to Reverse Polish Notation (RPN) using the shunting-yard algorithm, then evaluate it with a stack—this cleanly separates parsing from evaluation and handles precedence and parentheses elegantly. Also, proactively discuss how to handle unary minus (e.g., by treating it as part of the number or using a special operator) to show attention to detail.
Ask about input format (spaces, valid characters), integer vs floating-point division, handling of unary minus, and expected output type. Confirm that the expression is always valid.
Select a two-stack approach (operators and operands) or the shunting-yard algorithm to convert to RPN and then evaluate. Explain why this handles precedence and parentheses.
Describe how to distinguish unary minus from binary subtraction (e.g., based on context: start of expression, after '(' or another operator). Propose a strategy such as treating '-5' as a single token or using a special marker.
Trace the algorithm on a sample expression like '3 - 4 * (2 + (-5))' to demonstrate correctness, showing stack operations and operator precedence handling.
State time and space complexity (O(n) for both). Discuss edge cases: nested parentheses, division by zero, large numbers, and multiple unary operators.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.