大整数简单四则运算模板（c++）

常用于计算大的正整数之间的四则运算。
在王道机试指南基础上，有修改其中存在的bug

#include<iostream>
using namespace std;
const int MAXN = 1000;
struct BitInteger {
	int digit[MAXN];
	int length;
	BitInteger() {
		memset(digit, 0, sizeof(digit));
		length = 0;
	}
	BitInteger(int x) {
		memset(digit, 0, sizeof(digit)); 
		length = 0;
		if (x == 0) 
			digit[length++] = x;
		while (x != 0) {
			digit[length++] = x % 10;
			x /= 10;
		}
	}
	BitInteger(string str) {
		memset(digit, 0, sizeof(digit));
		length = str.size();
		for (int i = 0; i < length; ++i)
			digit[i] = str[length - i - 1] - '0';
	}
	BitInteger operator=(int x) {
		memset(digit, 0, sizeof(digit));
		length = 0;
		if (x == 0)
			digit[length++] = x;
		while (x != 0) {
			digit[length++] = x % 10;
			x /= 10;
		}
		return *this;
	}
	BitInteger operator=(string str) {
		memset(digit, 0, sizeof(digit));
		length = str.size();
		for (int i = 0; i < length; ++i)
			digit[i] = str[length - i - 1] - '0';
		return *this;
	}
	bool operator<=(const BitInteger& b) {
		if (length < b.length)
			return true;
		else if (b.length < length)
			return false;
		else {
			for (int i = length - 1; i >= 0; --i) {
				if (digit[i] != b.digit[i])
					return digit[i] < b.digit[i];
			}
		}
		return true;
	}
	bool operator>(const BitInteger b) {
		if (length > b.length)
			return true;
		else if (length < b.length)
			return false;
		else {
			for (int i = length - 1; i >= 0; --i) {
				if (digit[i] != b.digit[i])
					return digit[i] > b.digit[i];
			}
		}
		return true;
	}
	bool operator<(const BitInteger b) {
		if (length < b.length)
			return true;
		else if (length > b.length)
			return false;
		else {
			for (int i = length - 1; i >= 0; --i) {
				if (digit[i] != b.digit[i])
					return digit[i] < b.digit[i];
			}
		}
		return true;
	}
	BitInteger operator+(const BitInteger b) {
		int carry = 0;
		BitInteger ans;
		for (int i = 0; i < length || i < b.length; ++i) {
			int cur = digit[i] + b.digit[i] + carry;
			carry = cur / 10;
			ans.digit[ans.length++] = cur % 10;
		}
		if (carry != 0) 
			ans.digit[ans.length++] = carry;
		return ans;
	}
	BitInteger operator-(BitInteger &b) {
		int remain = 0,temp;
		bool minus = false;
		BitInteger ans;
		if (*this < b) {
			for (int i = max(length, b.length) - 1; i >= 0; --i) {
				temp = digit[i];
				digit[i] = b.digit[i];
				b.digit[i] = temp;
			}
			temp = length;
			length = b.length;
			b.length = temp;
			minus = true;
		}
		for (int i = 0; i < length; ++i) {
			int cur = digit[i] - b.digit[i] - remain;
			if (cur < 0) {
				cur += 10;
				remain = 1;
			}
			else
				remain = 0;
			ans.digit[ans.length++] = cur;
		}
		while (ans.digit[ans.length - 1] == 0 && ans.length > 1)
			ans.length--;
		if(minus)
			ans.digit[ans.length - 1] *= -1;
		return ans;
	}
	BitInteger operator*(const BitInteger& b) {
		
		//* 简便方法一，借助加法进行运算
		/*BitInteger ans;
		int cnt;
		for (int j = 0; j < b.length; ++j) {
			cnt = b.digit[j] * int(pow(10,j));
			while (cnt--)
				ans = ans + *this;
		}
		return ans;*/
		//* 方法二，借助加法进行运算
		BitInteger ans;
		ans.length = length + b.length;
		for (int i = 0; i < length; ++i) {
			for (int j = 0; j < b.length; ++j) {
				ans.digit[i + j] = digit[i] * b.digit[j];
			}
		}
		//最多向前进一位数值
		for (int i = 0; i < ans.length; ++i) {
			ans.digit[i + 1] += ans.digit[i] / 10;
			ans.digit[i] = ans.digit[i] % 10;
		}
		//除去多余的前导数字0
		while (ans.length > 1 && ans.digit[ans.length - 1] == 0)
			ans.length--;
		return ans;
	}
	BitInteger operator/(const BitInteger& b) {
		BitInteger ans;
		ans.length = length;
		BitInteger remainder = 0;
		BitInteger temp = b;
		for (int i = length - 1; i >= 0; --i) {
			if (!(remainder.length == 1 && remainder.digit[0] == 0)) {
				for (int j = remainder.length - 1; j >= 0; --j)
					remainder.digit[j + 1] = remainder.digit[j];
				remainder.length++;
			}
			remainder.digit[0] = digit[i];
			while (temp <= remainder) {
				remainder = remainder - temp;
				ans.digit[i]++;
			}
		}
		while (ans.length > 1 && ans.digit[ans.length - 1] == 0)
			ans.length--;
		return ans;
	}
	BitInteger operator%(const BitInteger b) {
		BitInteger remainder = 0;
		BitInteger temp = b;
		for (int i = length - 1; i >= 0; --i) {
			if (!(remainder.length == 1 && remainder.digit[0] == 0)) {
				for (int j = remainder.length - 1; j >= 0; --j)
					remainder.digit[j + 1] = remainder.digit[j];
				remainder.length++;
			}
			remainder.digit[0] = digit[i];
			while (temp <= remainder)
				remainder = remainder - temp;
		}
		return remainder;
	}
	friend istream& operator>>(istream& in, BitInteger& x) {
		string str;
		cin >> str;
		x = str;
		return in;
	}
	friend ostream& operator<<(ostream& out, const BitInteger& x) {
		for (int i = x.length - 1; i >= 0; --i)
			out << x.digit[i];
		return out;
	}
};
int main()
{
	BitInteger a,b;
	cin >> a;
	cin >> b;
	cout << "a = " << a << endl;
	cout << "b = " << b << endl;
	cout << "a + b = " << a + b << endl;
	cout << "a - b = " << a - b << endl;
	cout << "a * b = " << a * b << endl;
	cout << "a / b = " << a / b << endl;
	cout << "a % b = " << a % b << endl;
}

运行示例：