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 {
private:
     void reverse( string& s)
    {
         int l= 0;
         int r=s.length()- 1;
         while(l<r)
        {
             char c=s[l];
            s[l]=s[r];
            s[r]=c;
            l++;
            r--;
        }
    }
     void add( string& s1, string s2)
    {        
         while(s1.length()<s2.length()) s1=s1+ ' 0 ';
         while(s2.length()<s1.length()) s2=s2+ ' 0 ';
         int add= 0;
         for( int i= 0;i<s1.length();i++)
        {
             int sum=add+s1[i]+s2[i]- ' 0 '- ' 0 ';
            s1[i]=sum% 10+ ' 0 ';
            add=sum/ 10;
        }
         if(add> 0) s1=s1+ char(add+ ' 0 ');
    }
     void mul( string& s, int n)
    {
         int add= 0;
         for( int i= 0;i<s.length();i++)
        {
             int sum=(s[i]- ' 0 ')*n+add;
            s[i]=sum% 10+ ' 0 ';
            add=sum/ 10;
        }
         if(add> 0) s=s+ char( ' 0 '+add);
    }
     void fix( string& s)
    {
         if(s.length()== 0) s= " 0 ";        
         int index=s.length()- 1;
         while(index> 0 && s[index]== ' 0 ') index--;
         string result;
         for( int i= 0;i<=index;i++)
            result=result+s[i];
        s=result;
    }
public:
     string multiply( string num1,  string num2) 
    {
        reverse(num1);
        reverse(num2);

         string result;
         string tens;
         for( int i= 0;i<num2.length();i++)
        {
             string num=num1;
            mul(num,num2[i]- ' 0 ');
            num=tens+num;
            add(result,num);

            tens=tens+ ' 0 ';
        }
        
        fix(result);reverse(result);
        return result;
    }
};