Valid number: decide whether a string is a decimal number

Return whether a string is a valid decimal number. Write down the exact rules first, then implement them cleanly.

Interface

Unless you agree on a different interface with the interviewer, assume:

• is_number(s: str) -> bool — after trimming leading and trailing spaces, the whole string must match:
  • number := sign? (digits '.' digits? | '.' digits | digits) exponent?
  • exponent := ('e' | 'E') sign? digits
  • sign := '+' | '-'; digits := one or more of 0-9

Example

valid:    "0"  "-3.14"  "+.8"  "2e10"  "-1.2E-3"  "4."  "3e+7"
invalid:  "abc"  "1a"  "e9"  "."  "+"  "1e"  "--6"  "1e2.5"

Constraints

• 1 <= len(s) <= 20; letters, digits, +, -, ., spaces.

Clarifying questions

• Are leading and trailing spaces allowed? Spaces inside?
• Is "4." valid? ".5"? "."?
• Can the exponent be fractional or signed?
• Are hexadecimal, "inf" or "NaN" in scope?

What a strong answer covers

• The grammar stated before any code, agreed with the interviewer.
• A single pass with flags (seen_digit, seen_dot, seen_exp, digit_after_exp): a sign only at the start or right after e; a dot only before any e and only once; e only once and only after a digit; at least one digit after e.
• Or an explicit finite-state machine with named states, which is easier to extend and test.
• Why a library call or a regular expression may not be acceptable, and how to test the parser against a table of cases.
• Tests: each rule's boundary, such as ".", "e", "+e1", "1e+", " 1 ".

Follow-ups

• Return the parsed value as well, without using the language's float parser.
• Add thousands separators or hexadecimal literals.
• Report the position of the first invalid character.