用字符串实现大数相乘

? ? 题目：用字符串实现整数的大数相乘。输入不合法则返回空字符串。

? ?

string Multiplication_of_large_Numbers(string s1,string s2)
{
	if (s1.empty() || s2.empty())
		return "";
	int sign1=1,sign2=1,sign;
	if (s1[0] == '+')
	{
		sign1 = 1;
		s1 = s1.substr(1,s1.size() - 1);
	}
	else if (s1[0] == '-')
	{
		sign1 = -1;
		s1 = s1.substr(1,s1.size() - 1);
	}
	if (s2[0] == '+')
	{
		sign2 = 1;
		s2 = s2.substr(1,s2.size() - 1);
	}
	else if (s2[0] == '-')
	{
		sign2 = -1;
		s2 = s2.substr(1,s2.size() - 1);
	}

	//判断输入是否合法
	
	if (s1.empty() || s2.empty())
		return "";
	for (int i = 0; i < s1.size(); i++)
	{
		if (s1[i]>'9' || s1[i] < '0')
			return "";
	}
	for (int i = 0; i < s2.size(); i++)
	{
		if (s2[i]>'9' || s2[i] < '0')
			return "";
	}	

	//记录最终结果的正负号
	sign = sign1*sign2;
	string result(s1.size() + s2.size(),'0');
	
	int pos_start = result.size() - 1;//标记一次运算中，result的起点
	//开始运算
	for (int i2 = s2.size() - 1; i2 >= 0; i2--)
	{
		if (s2[i2] == '0')
		{
			pos_start--;//不要忘了
			continue;
		}
		int index = pos_start;//对应于result相应的下标
		int carry = 0;
		for (int i1 = s1.size() - 1; i1 >= 0; i1--)
		{			
			int tmp= (s1[i1] - '0')*(s2[i2] - '0') + carry + result[index]-'0';
			result[index] = tmp%10 + '0';
			carry = tmp / 10;
			index--;
		}
	    //消除进位
		while (carry)
		{
			result[index] = (result[index] - '0' + carry )%10+'0';
			carry = (result[index] - '0' + carry ) / 10;
			index--;
		}			
		pos_start--;//不要忘了
	}
	//消除开头的“0”
	int i;
	for (i = 0; result[i] == '0'; i++);
	result = result.substr(i,result.size() - 1 - i + 1);
	//结果是0的时候
	if (result.empty())
		return "0";
	//加上负号
	if (sign < 0)
		result = "-" + result;
	return result;
}