Valid Number

Intuition

Instead of writing an intricate regular expression, notice that each character type has simple local rules: a sign is only legal at the very start or right after an exponent marker, a dot cannot repeat and cannot appear after an exponent, and an exponent needs a digit before it and a digit after it. By resetting the digit flag when an exponent appears we force the mantissa-and-exponent structure, and a final check that a digit was seen guarantees the number is complete.

Algorithm walkthrough

1. 1Keep three booleans: seenDigit, seenDot, and seenExp, all starting false.
2. 2For a digit, mark seenDigit true.
3. 3For a sign, allow it only at index 0 or immediately after an 'e'/'E'; otherwise reject.
4. 4For a dot, reject if a dot or an exponent was already seen, else mark seenDot; for 'e'/'E', reject if an exponent was already seen or no digit came before, then mark seenExp and clear seenDigit to demand digits after it.
5. 5Reject any other character, and after the loop return seenDigit so that trailing 'e' or a bare sign fails.

Implementation

class Solution:
    def isNumber(self, s: str) -> bool:
        seen_digit = seen_dot = seen_exp = False
        for i, c in enumerate(s):
            if c.isdigit():
                seen_digit = True
            elif c in '+-':
                if i > 0 and s[i - 1] not in 'eE':
                    return False
            elif c == '.':
                if seen_dot or seen_exp:
                    return False
                seen_dot = True
            elif c in 'eE':
                if seen_exp or not seen_digit:
                    return False
                seen_exp = True
                seen_digit = False
            else:
                return False
        return seen_digit