【紫书】BigInteger 高精度类型 原书上有一个bug：A+B！=B+A

存个代码

struct BigInterger {
    static const int BASE = 1e8;
    static const int WIDTH = ;
    vector<int> s;
    BigInterger(long long num = ) { *this = num; }
    BigInterger operator =(long long num) {
        s.clear();
        do {
            s.push_back(num%BASE);
            num /= BASE;
        } while (num > );//num==0
        return *this;
    }
    BigInterger operator =(const string& str) {
        s.clear();
        int x, len = (str.length() - ) / WIDTH + ;//len==width
        for (int i = ; i < len; i++) {
            int end = str.length() - i*WIDTH;
            int start = max(, end - WIDTH);
            sscanf(str.substr(start, end - start).c_str(), "%d", &x);
            s.push_back(x);
        }
        return *this;
    }

    BigInterger operator +(const BigInterger& b)const {
        BigInterger c;
        c.s.clear();
        for (int i = , g = ;; i++) {
            if (g ==  && i >= max(s.size(), b.s.size()))break;//此处bug
            int x = g;
            if (i < s.size())x += s[i];
            if (i < b.s.size()) x += b.s[i];
            c.s.push_back(x%BASE);
            g = x / BASE;
        }
        return c;
    }
    BigInterger operator +=(const BigInterger& b) {
        *this = *this + b; return *this;
    }

    bool operator<(const BigInterger& b)const {
        if (s.size() != b.s.size()) return s.size() < b.s.size();
        for (int i = s.size() - ; i >= ; i--) {
            if (s[i] != b.s[i]) return s[i] < b.s[i];//Width 个数字一起比
        }
        return false;//==
    }
    bool operator>(const BigInterger &b)const { return b < *this; }
    bool operator<=(const BigInterger &b)const { return !(b < *this); }
    bool operator>=(const BigInterger &b)const { return !(*this < b); }
    bool operator!=(const BigInterger &b)const { return b < *this || *this<b; }
    bool operator==(const BigInterger &b)const { return!(b < *this) && !(*this<b); }
};
ostream& operator <<(ostream &out, const BigInterger& x) {
    out << x.s.back();
    for (int i = x.s.size() - ; i >= ; i--) {
        char buf[];
        sprintf(buf, "%08d", x.s[i]);
        for (int j = ; j < strlen(buf); j++)cout << buf[j];
    }
    return out;
}
istream&operator>>(istream &in, BigInterger&x) {
    string s;
    if (!(in >> s))return in;
    x = s;
    return in;
}