C++大数类实现加减功能

以下是一个基本的 C++ 大数类实现，包括加和减的功能。该实现使用了字符串来存储大数，通过重载运算符来实现加减运算。

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

using namespace std;

class BigInteger {
private:
    string num;
    bool sign;

public:
    BigInteger() : num(""), sign(false) {}

    BigInteger(string s) {
        if (isdigit(s[0])) {
            setNumber(s);
            sign = false;
        } else {
            setNumber(s.substr(1));
            sign = (s[0] == '-');
        }
    }

    void setNumber(string s) {
        num = s;
        reverse(num.begin(), num.end());
    }

    string toString() const {
        string res = num;
        reverse(res.begin(), res.end());
        if (sign) res = '-' + res;
        return res;
    }

    BigInteger operator + (const BigInteger& b) const {
        if (sign != b.sign) return *this - (-b);
        BigInteger res;
        res.sign = sign;
        int carry = 0;
        for (int i = 0; i < (int)max(num.length(), b.num.length()) || carry; i++) {
            int x = carry;
            if (i < (int)num.length()) x += num[i] - '0';
            if (i < (int)b.num.length()) x += b.num[i] - '0';
            res.num += (x % 10) + '0';
            carry = x / 10;
        }
        return res;
    }

    BigInteger operator - (const BigInteger& b) const {
        if (sign != b.sign) return *this + (-b);
        if (abs(*this) < abs(b)) return -(b - *this);
        BigInteger res;
        res.sign = (sign == false && b.sign == true);
        int borrow = 0;
        for (int i = 0; i < (int)num.length(); i++) {
            int x = num[i] - '0' - borrow;
            if (i < (int)b.num.length()) x -= b.num[i] - '0';
            borrow = 0;
            if (x < 0) {
                x += 10;
                borrow = 1;
            }
            res.num += x + '0';
        }
        res.removeLeadingZeros();
        return res;
    }

    BigInteger operator - () const {
        BigInteger res = *this;
        res.sign = !sign;
        return res;
    }

    bool operator < (const BigInteger& b) const {
        if (sign != b.sign) return sign;
        if (num.length() != b.num.length()) return num.length() < b.num.length();
        for (int i = (int)num.length() - 1; i >= 0; i--)
            if (num[i] != b.num[i]) return sign ? num[i] > b.num[i] : num[i] < b.num[i];
        return false;
    }

    bool operator > (const BigInteger& b) const {
        return b < *this;
    }

    bool operator <= (const BigInteger& b) const {
        return !(b < *this);
    }

    bool operator >= (const BigInteger& b) const {
        return !(*this < b);
    }

    bool operator == (const BigInteger& b) const {
        return !(*this < b) && !(b < *this);
    }

    bool operator != (const BigInteger& b) const {
        return *this < b || b < *this;
    }

    void removeLeadingZeros() {
        while (num.length() > 1 && num.back() == '0')
            num.pop_back();
        if (num.length() == 1 && num[0] == '0') sign = false;
    }

    BigInteger abs() const {
        BigInteger res = *this;
        res.sign = false;
        return res;
    }
};

int main() {
    BigInteger a("123456789012345678901234567890");
    BigInteger b("-987654321098765432109876543210");
    cout << a + b << endl;
    cout << a - b << endl;
    return 0;
}

在上面的代码中，我们将大数类定义为一个 `BigInteger` 类，它包含一个字符串类型的 `num` 成员变量和一个布尔类型的 `sign` 成员变量，分别表示大数的绝对值和符号。实现了构造函数、设置数值、转换为字符串、加、减、取反、比较、移除前导零等操作。其中加、减操作使用了类似小学竖式计算的方法，从个位到高位逐位相加或相减，并处理进位、借位等情况。