有效数字

该题解使用了有限状态自动机（Finite State Machine, FSM）的方法来解决问题。首先，定义了不同的状态（State）和字符类型（CharType）。然后，根据题目给出的有效数字的定义，构建了状态转移图，其中包含了各个状态下对应字符类型的下一个状态。最后，遍历输入字符串，根据当前字符的类型和当前状态，进行状态转移，如果遇到非法字符或者无法转移的状态，则返回false。最终，如果字符串遍历完成后，状态机处于接受状态（即整数、小数、指数部分的数字、或者末尾空格状态），则返回true，表示字符串是一个有效数字。

时间复杂度: O(n)

空间复杂度: O(1)

from enum import Enum, auto


class Solution:
    def isNumber(self, s: str) -> bool:
        class State(Enum):
            STATE_INITIAL = auto()
            STATE_INT_SIGN = auto()
            STATE_INTEGER = auto()
            STATE_POINT = auto()
            STATE_POINT_WITHOUT_INT = auto()
            STATE_FRACTION = auto()
            STATE_EXP = auto()
            STATE_EXP_SIGN = auto()
            STATE_EXP_NUMBER = auto()
            STATE_END = auto()

        class CharType(Enum):
            CHAR_NUMBER = auto()
            CHAR_EXP = auto()
            CHAR_POINT = auto()
            CHAR_SIGN = auto()
            CHAR_SPACE = auto()
            CHAR_ILLEGAL = auto()

        def toCharType(ch):
            if ch.isdigit():
                return CharType.CHAR_NUMBER
            elif ch.lower() == 'e':
                return CharType.CHAR_EXP
            elif ch == '.':
                return CharType.CHAR_POINT
            elif ch == '+' or ch == '-':
                return CharType.CHAR_SIGN
            elif ch == ' ':
                return CharType.CHAR_SPACE
            else:
                return CharType.CHAR_ILLEGAL

        transfer = {
            State.STATE_INITIAL: {
                CharType.CHAR_SPACE: State.STATE_INITIAL,
                CharType.CHAR_NUMBER: State.STATE_INTEGER,
                CharType.CHAR_POINT: State.STATE_POINT_WITHOUT_INT,
                CharType.CHAR_SIGN: State.STATE_INT_SIGN,
            },
            State.STATE_INT_SIGN: {
                CharType.CHAR_NUMBER: State.STATE_INTEGER,
                CharType.CHAR_POINT: State.STATE_POINT_WITHOUT_INT,
            },
            State.STATE_INTEGER: {
                CharType.CHAR_NUMBER: State.STATE_INTEGER,
                CharType.CHAR_EXP: State.STATE_EXP,
                CharType.CHAR_POINT: State.STATE_POINT,
                CharType.CHAR_SPACE: State.STATE_END,
            },
            State.STATE_POINT: {
                CharType.CHAR_NUMBER: State.STATE_FRACTION,
                CharType.CHAR_EXP: State.STATE_EXP,
                CharType.CHAR_SPACE: State.STATE_END,
            },
            State.STATE_POINT_WITHOUT_INT: {
                CharType.CHAR_NUMBER: State.STATE_FRACTION,
            },
            State.STATE_FRACTION: {
                CharType.CHAR_NUMBER: State.STATE_FRACTION,
                CharType.CHAR_EXP: State.STATE_EXP,
                CharType.CHAR_SPACE: State.STATE_END,
            },
            State.STATE_EXP: {
                CharType.CHAR_NUMBER: State.STATE_EXP_NUMBER,
                CharType.CHAR_SIGN: State.STATE_EXP_SIGN,
            },
            State.STATE_EXP_SIGN: {
                CharType.CHAR_NUMBER: State.STATE_EXP_NUMBER,
            },
            State.STATE_EXP_NUMBER: {
                CharType.CHAR_NUMBER: State.STATE_EXP_NUMBER,
                CharType.CHAR_SPACE: State.STATE_END,
            },
            State.STATE_END: {
                CharType.CHAR_SPACE: State.STATE_END,
            },
        }

        st = State.STATE_INITIAL
        for ch in s:
            char_type = toCharType(ch)
            if char_type not in transfer[st]:
                return False
            st = transfer[st][char_type]

        return st in [State.STATE_INTEGER, State.STATE_POINT, State.STATE_FRACTION, 
                      State.STATE_EXP_NUMBER, State.STATE_END]