// Sample class for string an integer with an arbitrary number of digits.  This
// version includes a member function to get the number of digits and an
// overloaded [] operator for accessing/changing individual digits of the
// number

#include <iostream>
#include <string>
#include <vector>
#include <sstream>
#include <climits>
#include <algorithm>

using namespace std;

class big_integer {
public:
    big_integer(int n = 0) {
        negative = n < 0;
        n = abs(n);
        digits.push_back(n % 10);
        n /= 10;
        while (n != 0) {
            digits.push_back(n % 10);
            n /= 10;
        }
    }

    big_integer(string s) {
        negative = s[0] == '-';
        if (negative) {
            s = s.substr(1);
        }
        for (int i = s.size() - 1; i >= 0; i--) {
            digits.push_back(s[i] - '0');
        }
    }

    string to_string() const {
        ostringstream out;
        if (negative) {
            out << "-";
        }
        for (int i = digits.size() - 1; i >= 0; i--) {
            out << digits[i];
        }
        return out.str();
    }

    // pre : n < INT_MAX / 10 (to avoid integer overflow)
    big_integer & operator*=(int n) {
        if (n >= INT_MAX / 10) {
            throw runtime_error("int is too big");
        }
        if (n < 0) {
            n = abs(n);
            negative = !negative;
        }
        int carry = 0;
        for (int & digit : digits) {
            digit = digit * n + carry;
            carry = digit / 10;
            digit = digit % 10;
        }
        while (carry > 0) {
            digits.push_back(carry % 10);
            carry /= 10;
        }
        return *this;
    }

    bool is_negative() const {
        return negative;
    }

    int number_of_digits() const {
        return digits.size();
    }

    int & operator[](int index) {
        if (index >= digits.size() || index < 0) {
            throw out_of_range("index for [] is out of range");
        }
        return digits[digits.size() - index];
    }

private:
    vector<int> digits;
    bool negative;
};

bool operator==(const big_integer & lhs, const big_integer & rhs) {
    return lhs.to_string() == rhs.to_string();
}

bool operator!=(const big_integer & lhs, const big_integer & rhs) {
    return !(lhs == rhs);
}

ostream & operator<<(ostream & out, const big_integer & big) {
    out << big.to_string();
    return out;
}

istream & operator>>(istream & in, big_integer & big) {
    string s;
    in >> s;
    big = big_integer(s);
    return in;
}

bool operator<(const big_integer & lhs, const big_integer & rhs) {
    if (lhs.is_negative() != rhs.is_negative()) {
        return lhs.is_negative();
    } else {
        string left_string = lhs.to_string();
        string right_string = rhs.to_string();
        bool result;
        if (left_string.size() != right_string.size()) {
            result = left_string.size() < right_string.size();
        } else {
            result = left_string < right_string;
        }
        if (lhs.is_negative()) {
            result = !result;
        }
        return result;
    }
}

int main() {
    big_integer x(1234);
    big_integer y(49);
    big_integer z("657894365382796543289");
    big_integer a("1234");
    cout << "give me a big int: ";
    big_integer b;
    cin >> b;

    cout << "x = " << x << endl;
    cout << "y = " << y << endl;
    cout << "z = " << z << endl;
    cout << "a = " << a << endl;
    cout << "b = " << b << endl;
    cout << endl;

    cout << "x == y returns " << (x == y) << endl;
    cout << "x == a returns " << (x == a) << endl;
    cout << "x == x returns " << (x == x) << endl;
    cout << "x == z returns " << (x == z) << endl;
    cout << "x == 1234 returns " << (x == 1234) << endl;
    cout << "1234 == x returns " << (1234 == x) << endl;
    cout << endl;

    big_integer fact(1);
    for (int i = 1; i <= 30; i++) {
        fact *= i;
        cout << i << "! = " << fact << endl;
    }
    cout << endl;

    big_integer c(-12345);
    big_integer d("-345");
    cout << "c = " << c << ", d = " << d << endl;
    cout << endl;

    c *= -2;
    d *= -3;
    cout << "c = " << c << ", d = " << d << endl;
    cout << endl;

    d = c *= 2;
    cout << "c = " << c << ", d = " << d << endl;
    cout << endl;

    vector<big_integer> numbers;
    numbers.push_back(3089);
    numbers.push_back(42);
    numbers.push_back(308);
    numbers.push_back(63234);
    numbers.push_back(-15);
    numbers.push_back(0);
    numbers.push_back(-6823);
    numbers.push_back(-6822);
    numbers.push_back(299);
    numbers.push_back(-308);
    sort(numbers.begin(), numbers.end());
    cout << "sorted list:";
    for (const big_integer & n : numbers) {
        cout << " " << n;
    }
    cout << endl;
    cout << endl;

    big_integer n("12345678");
    cout << "# of digits in " << n << " = " << n.number_of_digits() << endl;
    cout << "n[2] = " << n[2] << endl;
    n[2] = 0;
    n[6] = 0;
    cout << "after resetting n[2] and n[6], n = " << n << endl;

    return 0;
}