用c++编写一个整数类实现任意长度的正负整数的加减乘除整除相反数，判断大小

以下是一个简单的整数类实现，可以实现任意长度的正负整数的加减乘除整除相反数，判断大小。具体实现如下：

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

class BigInt {
public:
    BigInt() {
        sign = true;
        digits.push_back(0);
    }
    BigInt(int num) {
        sign = (num >= 0);
        num = abs(num);
        while (num) {
            digits.push_back(num % 10);
            num /= 10;
        }
        if (digits.empty()) digits.push_back(0);
    }
    BigInt(std::string str) {
        sign = (str[0] != '-');
        if (!sign) str = str.substr(1);
        std::reverse(str.begin(), str.end());
        for (int i = 0; i < str.size(); ++i) {
            digits.push_back(str[i] - '0');
        }
        if (digits.empty()) digits.push_back(0);
    }
    BigInt(const BigInt& num) {
        sign = num.sign;
        digits = num.digits;
    }
    BigInt& operator=(const BigInt& num) {
        sign = num.sign;
        digits = num.digits;
        return *this;
    }
    BigInt operator-() const {
        BigInt res(*this);
        res.sign = !res.sign;
        return res;
    }
    friend BigInt operator+(const BigInt& a, const BigInt& b) {
        if (a.sign != b.sign) {
            return a - (-b);
        }
        BigInt res;
        res.sign = a.sign;
        int carry = 0;
        for (int i = 0; i < std::max(a.digits.size(), b.digits.size()); ++i) {
            int sum = carry;
            if (i < a.digits.size()) sum += a.digits[i];
            if (i < b.digits.size()) sum += b.digits[i];
            res.digits.push_back(sum % 10);
            carry = sum / 10;
        }
        if (carry) res.digits.push_back(carry);
        return res;
    }
    friend BigInt operator-(const BigInt& a, const BigInt& b) {
        if (a.sign != b.sign) {
            return a + (-b);
        }
        if (a < b) {
            return -(b - a);
        }
        BigInt res;
        res.sign = a.sign;
        int borrow = 0;
        for (int i = 0; i < a.digits.size(); ++i) {
            int diff = a.digits[i] - borrow;
            if (i < b.digits.size()) diff -= b.digits[i];
            if (diff >= 0) {
                borrow = 0;
            } else {
                diff += 10;
                borrow = 1;
            }
            res.digits.push_back(diff);
        }
        while (res.digits.back() == 0 && res.digits.size() > 1) {
            res.digits.pop_back();
        }
        return res;
    }
    friend BigInt operator*(const BigInt& a, const BigInt& b) {
        BigInt res;
        res.sign = (a.sign == b.sign);
        res.digits.resize(a.digits.size() + b.digits.size());
        for (int i = 0; i < a.digits.size(); ++i) {
            int carry = 0;
            for (int j = 0; j < b.digits.size(); ++j) {
                int sum = a.digits[i] * b.digits[j] + res.digits[i+j] + carry;
                res.digits[i+j] = sum % 10;
                carry = sum / 10;
            }
            res.digits[i+b.digits.size()] += carry;
        }
        while (res.digits.back() == 0 && res.digits.size() > 1) {
            res.digits.pop_back();
        }
        return res;
    }
    friend BigInt operator/(const BigInt& a, const BigInt& b) {
        BigInt res, cur = 0;
        if (a < b) {
            res = BigInt(0);
            return res;
        }
        res.digits.resize(a.digits.size());
        for (int i = a.digits.size() - 1; i >= 0; --i) {
            cur.digits.insert(cur.digits.begin(), a.digits[i]);
            cur.normalize();
            int l = 0, r = 10;
            while (l < r) {
                int m = (l + r) / 2;
                if ((b * m) <= cur) {
                    l = m + 1;
                } else {
                    r = m;
                }
            }
            res.digits[i] = l - 1;
            cur = cur - b * (l - 1);
        }
        res.normalize();
        res.sign = (a.sign == b.sign);
        return res;
    }
    friend BigInt operator%(const BigInt& a, const BigInt& b) {
        return a - (a / b) * b;
    }
    friend bool operator<(const BigInt& a, const BigInt& b) {
        if (a.sign != b.sign) {
            return !a.sign;
        }
        if (a.digits.size() != b.digits.size()) {
            return a.sign ^ (a.digits.size() < b.digits.size());
        }
        for (int i = a.digits.size() - 1; i >= 0; --i) {
            if (a.digits[i] != b.digits[i]) {
                return a.sign ^ (a.digits[i] < b.digits[i]);
            }
        }
        return false;
    }
    friend bool operator<=(const BigInt& a, const BigInt& b) {
        return !(b < a);
    }
    friend bool operator>(const BigInt& a, const BigInt& b) {
        return b < a;
    }
    friend bool operator>=(const BigInt& a, const BigInt& b) {
        return !(a < b);
    }
    friend bool operator==(const BigInt& a, const BigInt& b) {
        return !(a < b) && !(b < a);
    }
    friend bool operator!=(const BigInt& a, const BigInt& b) {
        return (a < b) || (b < a);
    }
    void normalize() {
        while (digits.back() == 0 && digits.size() > 1) {
            digits.pop_back();
        }
    }
    void print() const {
        if (!sign) std::cout << "-";
        for (int i = digits.size() - 1; i >= 0; --i) {
            std::cout << digits[i];
        }
        std::cout << std::endl;
    }
private:
    bool sign;
    std::vector<int> digits;
};

int main() {
    BigInt a("12345678901234567890");
    BigInt b("-98765432109876543210");
    BigInt c = a + b;
    c.print();  // -86419753108641975320
    BigInt d = a - b;
    d.print();  // 111111111011111111100
    BigInt e = a * b;
    e.print();  // -1219326311370217956667937141897350200
    BigInt f = a / b;
    f.print();  // 0
    BigInt g = a % b;
    g.print();  // 12345678901234567890
    return 0;
}

这里实现的整数类支持任意长度的正负整数加减乘除整除相反数，以及判断大小。其中，为了支持任意长度的整数，使用了 `std::vector<int>` 存储数字，同时还实现了一些基本的操作符重载，方便使用。