#include <string>
#include <vector>
class Solution {
private:
    int i = 0;
    std::string s;
    std::vector<char> digits = {'0', '1', '2', '3', '4', '5', '6', '7', '8', '9'};

    bool atEnd() {
        return this->i == s.length();
    }

    bool test(char c) {
        if (atEnd()) {
            return false;
        }
        return s.at(i) == c;
    }
    bool test(std::vector<char> chars) {
        for (char c : chars) {
            if (test(c)) {
                return true;
            }
        }
        return false;
    }
    bool match(char c) {
        if (test(c)) {
            i++;
            return true;
        }
        return false;
    }
    bool match(std::vector<char> chars) {
        if (test(chars)) {
            i++;
            return true;
        }
        return false;
    }
    bool many(std::vector<char> chars) {    
        bool matched = false;
        while (match(chars)) {
            matched = true;
        }
        return matched;
    }
    bool digitString() {
        return many(digits);
    }

    bool integer() {
        match({'+', '-'});
        return digitString();
    }
    
    bool decimal() {
        if (!integer()) {
            return match('.') && digitString();
        } else {
            match('.');
            digitString();
            return true;
        }
    }

    bool exponent() {
        if (match({'e', 'E'})) {
            return integer();
        }
        return true;
    }

    bool number() {
        bool success = decimal();
        return success && exponent();
    }

public:
    bool isNumber(std::string s) {
        this->s = s;
        return number() && this->atEnd();
    }
};