"""
Solution By: Reniz Shah
Topic: Deterministic Finite Automaton (DFA)
Given a string s, return whether s is a valid number or not
Input: s = -90E3
Output: True
Leetcode link: https://leetcode.com/problems/valid-number/description/
"""
from enum import Enum
from typing import Dict

class CharType(Enum):
    NUMERIC = 'NUMERIC'
    SIGN = 'SIGN'
    EXPONENT = 'EXPONENT'
    DECIMAL = 'DECIMAL'

class State(Enum):
    INITIAL = 'INITIAL'
    SIGNED = 'SIGNED'
    WHOLE = 'WHOLE'
    FRACTIONAL = 'FRACTIONAL'
    FRACTION = 'FRACTION'
    EXPONENTIAL = 'EXPONENTIAL'
    EXP_SIGN = 'EXP_SIGN'
    EXP_NUMBER = 'EXP_NUMBER'

state_machine : Dict[State, Dict[CharType, State]] = {
    State.INITIAL: {CharType.NUMERIC: State.WHOLE, CharType.SIGN: State.SIGNED, CharType.DECIMAL: State.FRACTIONAL},
    State.SIGNED: {CharType.NUMERIC: State.WHOLE, CharType.DECIMAL: State.FRACTIONAL},
    State.WHOLE: {CharType.NUMERIC: State.WHOLE, CharType.DECIMAL: State.FRACTION, CharType.EXPONENT: State.EXPONENTIAL},
    State.FRACTIONAL: {CharType.NUMERIC: State.FRACTION},
    State.FRACTION: {CharType.NUMERIC: State.FRACTION, CharType.EXPONENT: State.EXPONENTIAL},
    State.EXPONENTIAL: {CharType.NUMERIC: State.EXP_NUMBER, CharType.SIGN: State.EXP_SIGN},
    State.EXP_SIGN: {CharType.NUMERIC: State.EXP_NUMBER},
    State.EXP_NUMBER: {CharType.NUMERIC: State.EXP_NUMBER},
}


def classify_char(char: str) -> CharType | None:
    """
    Classifies a character into one of the following categories:

    - 'CharType.NUMERIC': if the character is a digit (0-9)
    - 'CharType.SIGN': if the character is a plus sign (+) or a minus sign (-)
    - 'CharType.EXPONENT': if the character is an 'e' or 'E' (used in exponential notation)
    - 'CharType.DECIMAL': if the character is a decimal point (.)
    - None: if the character does not fit into any of the above categories or size of char is not 1

    Parameters:
    char (str): The character to be classified

    Returns:
    CharType: The classification of the character

    >>> classify_char('2')
    <CharType.NUMERIC: 'NUMERIC'>
    >>> classify_char('-')
    <CharType.SIGN: 'SIGN'>
    >>> classify_char('e')
    <CharType.EXPONENT: 'EXPONENT'>
    >>> classify_char('.')
    <CharType.DECIMAL: 'DECIMAL'>
    >>> classify_char('')
    
    >>> classify_char('0')
    <CharType.NUMERIC: 'NUMERIC'>
    >>> classify_char('01')

    """
    if len(char) != 1:
        return None
    if char.isdigit():
        return CharType.NUMERIC
    if char in "+-":
        return CharType.SIGN
    if char in "eE":
        return CharType.EXPONENT
    if char == ".":
        return CharType.DECIMAL
    return None


def is_valid_number(s: str) -> bool:
    """
    This function checks if the input string represents a valid number.

    It uses a finite state machine to parse the input string,
    transitioning between states based on the character type.
    The function returns True if the input string represents a valid number,
    and False otherwise.

    A valid number is defined as a string that can be parsed into an
    integer, decimal, or exponent.

    >>> is_valid_number("2")
    True
    >>> is_valid_number("0089")
    True
    >>> is_valid_number("-0.1")
    True
    >>> is_valid_number("+3.14")
    True
    >>> is_valid_number("4.")
    True
    >>> is_valid_number("-.9")
    True
    >>> is_valid_number("2e10")
    True
    >>> is_valid_number("-90E3")
    True
    >>> is_valid_number("3e+7")
    True
    >>> is_valid_number("+6e-1")
    True
    >>> is_valid_number("53.5e93")
    True
    >>> is_valid_number("-123.456e789")
    True


    >>> is_valid_number("abc")
    False
    >>> is_valid_number("1a")
    False
    >>> is_valid_number("1e")
    False
    >>> is_valid_number("e3")
    False
    >>> is_valid_number("99e2.5")
    False
    >>> is_valid_number("--6")
    False
    >>> is_valid_number("-+3")
    False
    >>> is_valid_number("95a54e53")
    False
    >>> is_valid_number(".")
    False
    """

    valid_final_states = {State.WHOLE, State.FRACTION, State.EXP_NUMBER}
    current_state = State.INITIAL

    for char in s:
        char_type = classify_char(char)
        if char_type is None or char_type not in state_machine[current_state]:
            return False
        current_state = state_machine[current_state][char_type]

    return current_state in valid_final_states


if __name__ == "__main__":
    import doctest

    doctest.testmod()