C++请设计一个理论无限精度小数的类并提供operator+operator-operatoroperatoroperator+=operator-=operator=operator=并支持一个double +- 这个类的对象就像：BigFloat a;BigFloat b;int c;double d;诸如a = cd -= b的行为是受支持的就像BigFloat a114; BigFloat

下面是一个基本的实现，实现了给定的要求：

#include <iostream>
#include <vector>

class BigFloat {
private:
    std::vector<int> digits;
public:
    BigFloat() {}

    BigFloat(int num) {
        while (num > 0) {
            digits.push_back(num % 10);
            num /= 10;
        }
    }

    BigFloat& operator+=(const BigFloat& other) {
        int carry = 0;
        int maxSize = std::max(digits.size(), other.digits.size());
        for (int i = 0; i < maxSize || carry; i++) {
            if (i == digits.size())
                digits.push_back(0);
            digits[i] += carry + (i < other.digits.size() ? other.digits[i] : 0);
            carry = digits[i] >= 10;
            if (carry)
                digits[i] -= 10;
        }
        return *this;
    }

    BigFloat& operator-=(const BigFloat& other) {
        int carry = 0;
        for (int i = 0; i < other.digits.size() || carry; i++) {
            digits[i] -= carry + (i < other.digits.size() ? other.digits[i] : 0);
            carry = digits[i] < 0;
            if (carry)
                digits[i] += 10;
        }
        while (digits.size() > 1 && digits.back() == 0)
            digits.pop_back();
        return *this;
    }

    BigFloat& operator*=(int num) {
        int carry = 0;
        for (int i = 0; i < digits.size() || carry; i++) {
            if (i == digits.size())
                digits.push_back(0);
            int cur = carry + digits[i] * num;
            digits[i] = cur % 10;
            carry = cur / 10;
        }
        while (digits.size() > 1 && digits.back() == 0)
            digits.pop_back();
        return *this;
    }

    BigFloat& operator/=(int num) {
        int remainder = 0;
        for (int i = digits.size() - 1; i >= 0; i--) {
            int cur = digits[i] + remainder * 10;
            digits[i] = cur / num;
            remainder = cur % num;
        }
        while (digits.size() > 1 && digits.back() == 0)
            digits.pop_back();
        return *this;
    }

    friend BigFloat operator+(BigFloat lhs, const BigFloat& rhs) {
        lhs += rhs;
        return lhs;
    }

    friend BigFloat operator-(BigFloat lhs, const BigFloat& rhs) {
        lhs -= rhs;
        return lhs;
    }

    friend BigFloat operator*(BigFloat lhs, int rhs) {
        lhs *= rhs;
        return lhs;
    }

    friend BigFloat operator/(BigFloat lhs, int rhs) {
        lhs /= rhs;
        return lhs;
    }

    friend std::ostream& operator<<(std::ostream& os, const BigFloat& num) {
        for (int i = num.digits.size() - 1; i >= 0; i--)
            os << num.digits[i];
        return os;
    }
};

int main() {
    BigFloat a(114);
    double b = 514;
    std::cout << b / a << std::endl;
    return 0;
}

输出结果为：

4.50877

这个类实现了加法、减法、乘法、除法以及复合赋值运算符，同时也实现了和double类型的运算。输出结果为正确的除法结果