leetcode-43 Multiply Strings

Input: num1 = "2", num2 = "3"
Output: "6"

class Solution {
public:
    string multiply(string num1, string num2) {
        string sum(num1.size()+num2.size(), '0');
        
        for(int i = num1.size() - 1; 0 <= i; --i){
            int carry = 0;    
            for(int j = num2.size()-1; 0 <= j; --j){
                int tmp = (sum[i+j+1]-'0') + (num1[i]-'0')*(num2[j]-'0') + carry;
                sum[i+j+1] = tmp % 10 + '0';
                carry = tmp / 10;
            }
            sum[i] += carry;
        }
        
        size_t start = sum.find_first_not_of('0');
        if(string::npos != start){
            return sum.substr(start);
        }
        return "0";
    }
};