My first instinct was to reach for a parser library but obviously that's not happening in an interview.
Clarify the grammar and constraints, then propose a recursive descent parser that evaluates the expression on the fly. Walk through a simple example to validate the logic, and discuss iterative alternatives and edge cases.
Pro tip: Mention that you can evaluate during parsing to avoid building an AST, and that an explicit stack can prevent recursion depth issues for deeply nested expressions.
Ask about the exact syntax (e.g., 'add(x, y)', 'sub(x, y)'), allowed whitespace, integer ranges, and maximum nesting depth. Confirm that the input is always valid.
Propose a recursive descent parser that reads the function name, then recursively parses the arguments, and computes the result. Alternatively, suggest an iterative approach using a stack.
Outline the recursive function: parse the function name, expect '(', parse the first argument (which may be a nested call or an integer), expect ',', parse the second argument, expect ')', then apply the operation. Handle integers by parsing digits.
State that time complexity is O(n) where n is the length of the string, and space is O(d) for recursion depth d. Discuss edge cases: negative numbers, large integers, deeply nested expressions, and malformed input (if not guaranteed valid).
Walk through a simple example like 'add(1, sub(5, 3))' to show the recursion and result. Mention testing with nested calls, negative results, and single integer input if allowed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.