I started confident and immediately regretted it.
Clarify the exact grammar rules and edge cases, then propose a deterministic finite automaton (DFA) that processes the string character by character, tracking state (sign, integer part, fraction, exponent). Implement the DFA with clear state transitions and validate the final state, ensuring all edge cases like missing digits are handled.
Pro tip: Mention that a DFA solution runs in O(n) time and O(1) space, and that it avoids the pitfalls of regex backtracking or multiple passes. Also, proactively discuss how you would test it with a comprehensive set of valid and invalid inputs.
Restate the rules: optional sign, mantissa with at most one decimal point and at least one digit, optional exponent with optional sign and at least one digit, no whitespace or special characters. List examples of valid and invalid inputs to confirm understanding.
Define states: start, sign, integer, dot, fraction, exponent, exponent sign, exponent digits. Specify transitions for digits, signs, dot, and 'e'/'E', ensuring no invalid transitions (e.g., multiple dots, missing digits).
Write code that iterates through each character, updates the state based on the transition table, and returns false immediately on an invalid character or transition. After the loop, return true only if the state is an accepting state (integer, fraction, or exponent digits).
Run through provided examples and additional cases like '0', '-0.1e-2', '.5', '5.', '1e', 'e1', '+', '-.', '1.2.3', '--6', '6e', '6e-', ' 1', '1 ', '1e+2.3'. Verify the function returns correct results.
State that the DFA approach is O(n) time and O(1) space. Compare with regex (which may be less efficient or harder to debug) and with built-in parsing (which may accept invalid formats). Highlight the clarity and control of the DFA.
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