No65.cc

/**
 * Created by Xiaozhong on 2020/7/22.
 * Copyright (c) 2020/7/22 Xiaozhong. All rights reserved.
 */
#include <iostream>
#include <string>
#include <vector>

using namespace std;

/*
 * 该解题方法需要参考 编译原理的 DFA（有限状态机）
 */
class Solution {
public:
    bool isNumber(string s) {
        if (s.empty()) return false;
        int n = s.size();

        int state = 0;
        vector<int> finals({0, 0, 0, 1, 0, 1, 1, 0, 1}); // 合法的终止状态
        // 该状态转换矩阵需要依据 DFA 来理解
        vector<vector<int>> transfer({
                                             {0,  1,  6,  2,  -1, -1},
                                             {-1, -1, 6,  2,  -1, -1},
                                             {-1, -1, 3,  -1, -1, -1},
                                             {8,  -1, 3,  -1, 4,  -1},
                                             {-1, 7,  5,  -1, -1, -1},
                                             {8,  -1, 5,  -1, -1, -1},
                                             {8,  -1, 6,  3,  4,  -1},
                                             {-1, -1, 5,  -1, -1, -1},
                                             {8,  -1, -1, -1, -1, -1},
                                     });

        for (int i = 0; i < n; ++i) {
            state = transfer[state][_make(s[i])];
            if (state < 0) return false;
        }
        return finals[state];
    }

private:
    int _make(const char &c) {
        switch (c) {
            case ' ':
                return 0;
            case '+':
                return 1;
            case '-':
                return 1;
            case '.':
                return 3;
            case 'e':
                return 4;
            default:
                return _number(c);
        }
    }

    int _number(const char &c) {
        if (c >= '0' && c <= '9')
            return 2;
        else
            return 5;
    }
};

int main() {
    Solution s;
    cout << s.isNumber("0") << endl;
}