43. Multiply Strings

class Solution {
public:
    string multiply(string num1, string num2) {
        reverse(num1.begin(), num1.end());
        reverse(num2.begin(), num2.end());
        int carry = 0;
        string result;
        int len1 = num1.length();
        int len2 = num2.length();
        int resLen = len1+len2-1;
        for(int resPos = 0; resPos<resLen;++resPos) //indicate the pos of the result
        {
            int sum = 0;
            for(int i = max(0,resPos-len2+1); i < len1; ++i) //traverse the digit of num1
            {
                int j = resPos-i; //indicate the pos of num2
                if(j < 0) break;
                sum += (num1[i]-‘0‘)*(num2[j]-‘0‘);
            }
            sum += carry;
            result.push_back(sum % 10+‘0‘);
            carry = sum/10;
        }
        
        while(carry > 0)
        {
            result.push_back(carry % 10+‘0‘);
            carry /= 10;
        }
        reverse(result.begin(), result.end());
        if(result.find_first_not_of(‘0‘) == string::npos) return "0";//排除全0的情况
        else return result;
    }
};