【算法题】65. 有效数字

题目

有效数字（按顺序）可以分成以下几个部分：

一个 小数 或者 整数
（可选）一个 'e' 或 'E' ，后面跟着一个 整数
小数（按顺序）可以分成以下几个部分：

（可选）一个符号字符（'+' 或 '-'）
下述格式之一：
至少一位数字，后面跟着一个点 '.'
至少一位数字，后面跟着一个点 '.' ，后面再跟着至少一位数字
一个点 '.' ，后面跟着至少一位数字
整数（按顺序）可以分成以下几个部分：

（可选）一个符号字符（'+' 或 '-'）
至少一位数字
部分有效数字列举如下：["2", "0089", "-0.1", "+3.14", "4.", "-.9", "2e10", "-90E3", "3e+7", "+6e-1", "53.5e93", "-123.456e789"]

部分无效数字列举如下：["abc", "1a", "1e", "e3", "99e2.5", "--6", "-+3", "95a54e53"]

给你一个字符串 s ，如果 s 是一个 有效数字 ，请返回 true 。

示例 1：

输入：s = "0"
输出：true
示例 2：

输入：s = "e"
输出：false
示例 3：

输入：s = "."
输出：false

提示：

1 <= s.length <= 20
s 仅含英文字母（大写和小写），数字（0-9），加号 '+' ，减号 '-' ，或者点 '.' 。

class Solution {
    public boolean isNumber(String s) {
        Map<State, Map<CharType, State>> transfer = new HashMap<State, Map<CharType, State>>();
        Map<CharType, State> initialMap = new HashMap<CharType, State>() {{
            put(CharType.CHAR_NUMBER, State.STATE_INTEGER);
            put(CharType.CHAR_POINT, State.STATE_POINT_WITHOUT_INT);
            put(CharType.CHAR_SIGN, State.STATE_INT_SIGN);
        }};
        transfer.put(State.STATE_INITIAL, initialMap);
        Map<CharType, State> intSignMap = new HashMap<CharType, State>() {{
            put(CharType.CHAR_NUMBER, State.STATE_INTEGER);
            put(CharType.CHAR_POINT, State.STATE_POINT_WITHOUT_INT);
        }};
        transfer.put(State.STATE_INT_SIGN, intSignMap);
        Map<CharType, State> integerMap = new HashMap<CharType, State>() {{
            put(CharType.CHAR_NUMBER, State.STATE_INTEGER);
            put(CharType.CHAR_EXP, State.STATE_EXP);
            put(CharType.CHAR_POINT, State.STATE_POINT);
        }};
        transfer.put(State.STATE_INTEGER, integerMap);
        Map<CharType, State> pointMap = new HashMap<CharType, State>() {{
            put(CharType.CHAR_NUMBER, State.STATE_FRACTION);
            put(CharType.CHAR_EXP, State.STATE_EXP);
        }};
        transfer.put(State.STATE_POINT, pointMap);
        Map<CharType, State> pointWithoutIntMap = new HashMap<CharType, State>() {{
            put(CharType.CHAR_NUMBER, State.STATE_FRACTION);
        }};
        transfer.put(State.STATE_POINT_WITHOUT_INT, pointWithoutIntMap);
        Map<CharType, State> fractionMap = new HashMap<CharType, State>() {{
            put(CharType.CHAR_NUMBER, State.STATE_FRACTION);
            put(CharType.CHAR_EXP, State.STATE_EXP);
        }};
        transfer.put(State.STATE_FRACTION, fractionMap);
        Map<CharType, State> expMap = new HashMap<CharType, State>() {{
            put(CharType.CHAR_NUMBER, State.STATE_EXP_NUMBER);
            put(CharType.CHAR_SIGN, State.STATE_EXP_SIGN);
        }};
        transfer.put(State.STATE_EXP, expMap);
        Map<CharType, State> expSignMap = new HashMap<CharType, State>() {{
            put(CharType.CHAR_NUMBER, State.STATE_EXP_NUMBER);
        }};
        transfer.put(State.STATE_EXP_SIGN, expSignMap);
        Map<CharType, State> expNumberMap = new HashMap<CharType, State>() {{
            put(CharType.CHAR_NUMBER, State.STATE_EXP_NUMBER);
        }};
        transfer.put(State.STATE_EXP_NUMBER, expNumberMap);

        int length = s.length();
        State state = State.STATE_INITIAL;

        for (int i = 0; i < length; i++) {
            CharType type = toCharType(s.charAt(i));
            if (!transfer.get(state).containsKey(type)) {
                return false;
            } else {
                state = transfer.get(state).get(type);
            }
        }
        return state == State.STATE_INTEGER || state == State.STATE_POINT || state == State.STATE_FRACTION || state == State.STATE_EXP_NUMBER || state == State.STATE_END;
    }

    public CharType toCharType(char ch) {
        if (ch >= '0' && ch <= '9') {
            return CharType.CHAR_NUMBER;
        } else if (ch == 'e' || ch == 'E') {
            return CharType.CHAR_EXP;
        } else if (ch == '.') {
            return CharType.CHAR_POINT;
        } else if (ch == '+' || ch == '-') {
            return CharType.CHAR_SIGN;
        } else {
            return CharType.CHAR_ILLEGAL;
        }
    }

    enum State {
        STATE_INITIAL,
        STATE_INT_SIGN,
        STATE_INTEGER,
        STATE_POINT,
        STATE_POINT_WITHOUT_INT,
        STATE_FRACTION,
        STATE_EXP,
        STATE_EXP_SIGN,
        STATE_EXP_NUMBER,
        STATE_END
    }

    enum CharType {
        CHAR_NUMBER,
        CHAR_EXP,
        CHAR_POINT,
        CHAR_SIGN,
        CHAR_ILLEGAL
    }
}

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