I went with the three-flag scan approach (tracking whether I'd seen a digit, a dot, an exponent) instead of a full state machine, which felt cleaner to code quickly.
Clarify the exact grammar rules and edge cases before coding, then choose between a deterministic finite automaton (DFA) or a regex-based solution. Walk through the DFA states and transitions, and discuss trade-offs like time/space complexity and maintainability.
Pro tip: Mention that a DFA is essentially a state machine that can be implemented with a few boolean flags, and that this approach runs in O(n) time with O(1) space, which is optimal. Also, note that using built-in parsing functions (like Double.parseDouble in Java) is often discouraged in interviews because it may accept invalid formats or be too permissive.
Ask about the exact definition of a valid number: allowed signs, decimal points, exponents, and whether leading/trailing whitespace or empty strings are considered. List edge cases like '.', 'e', '+', '1e', 'e1', '1e+', '1.2.3', etc.
Define states such as start, sign, integer, dot, fraction, exponent, exponent sign, and exponent integer. Specify transitions for digits, signs, dot, and exponent characters, and identify accepting states.
Code the DFA using a loop over characters and a switch or if-else statements to update the current state. Use flags or an enum for states and ensure all transitions are covered.
Run through the edge cases identified in step 1 to verify correctness. Also test typical valid and invalid numbers to ensure the DFA behaves as expected.
State that the solution runs in O(n) time and O(1) space. Mention alternative approaches like regex or using built-in parsers, and explain why the DFA is preferable in an interview setting.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.