Multiply Strings

Given two numbers represented as strings, return multiplication of the numbers as a string.

Note: The numbers can be arbitrarily large and are non-negative.

class Solution {
public:
    void multiply(string &num1,char digit,string &res,int pos)
    {
        int num1Size = num1.size();
        int c = 0;
        for(int i=num1Size-1;i>=0;i--){
            char tmp  = ((num1[i]-'0')*(digit-'0') + (res[pos]-'0') + c) % 10  + '0' ;
            c =  ((num1[i]-'0')*(digit-'0') + res[pos]-'0' +c ) / 10;
            res[pos] = tmp;
            pos--;
        }
        if(c!=0){
            res[pos] = c + '0';
        }
    }
    string multiply(string num1, string num2) {
        int num1Size = num1.size();
        int num2Size = num2.size();
        int len = num1Size+num2Size;
        string res(len,'0');
        int pos = len;
        for(int i=num2Size-1;i>=0;i--){
            multiply(num1,num2[i],res,--pos);
        }
        int i=0,k=0;
        while(i<len && res[i]=='0'){
            i++;
        }
        if(i==len){
            res="0";
        }else{
            res.erase(res.begin(),res.begin()+i);
        }
        return res;
    }
};