Addition string to avoid number limitation - c++

Question

I want to add two numbers by adding number by number like when you are child.
In order to calculate very long numbers (more than the C++ limitation).
My first step is to try an example 2 numbers having a sum < 10:
string valeur1 = "135";
string valeur2 = "844";
string result;
for (int i = 0; i < valeur1.length(); i++)
{
std::ostringstream ss;
int value;
int value3;
int value2;
//string to int
valeur1[i] >> value;
valeur2[i] >> value2;
value3 = (value + value2);
// int to string
ss << value3;
result = result + ss.str();
}
cout << result;
Am I headed in the right direction?

Answer 1

I think you are headed in the right direction. Three things you can improve:
You have to take into account when value3 is larger than 10 (You seem aware of that)
Be careful when the two numbers don't have the same number of digits. Now your code will fail in that case.
You are using an array of characters. Why not use an array of integers instead? If you only want to avoid the size limitation of an integer I think it would be a much better option as you wouldn't need all the string<->integer conversions.

Answer 2

Your first step is very simple:
#include <string>
#include <iostream>
int main()
{
std::string s1 = "135";
std::string s2 = "844";
std::string result;
for(size_t i=0;i<std::min(s1.size(),s2.size());i++)
result+= std::to_string(s1[i]-'0'+s2[i]-'0');
std::cout<<result<<std::endl;
return 0;
}
Edit:
As noted Gerard Abello , you should take into account the different size of strings and case when sum is greater than 3. However,I believe that the string representation is a good option. One of the options for adding the numbers as strings.
# include <string>
# include <iostream>
std::pair<int,std::string> simpleConvert(const std::string &str);
std::string add(const std::string &first,const std::string &second);
int main()
{
std::string s1 = "128";
std::string s2 = "9999";
std::string result = add(s1,s2);
std::cout<<result<<std::endl;
return 0;
}
std::pair<int,std::string> simpleConvert(const std::string &str)
{
if(str.size()==1)
return std::make_pair(0,str);
else if(str.size()==2)
return std::make_pair(str[0]-'0',std::string(str.begin()+1,str.end()));
}
std::string add(const std::string &first,const std::string &second)
{
std::string s1(first.rbegin(),first.rend());
std::string s2(second.rbegin(),second.rend());
auto n = s1.size();
auto m = s2.size();
auto min = std::min(n,m);
auto max = std::max(n,m);
for(size_t j=min;j!=max;j++)
if(n<m)
s1+="0";
else
s2+="0";
std::string result;
int add=0;
for(size_t i=0;i<s1.size();i++)
{
auto temp = simpleConvert(std::to_string(s1[i]-'0'+s2[i]-'0'+add));
result+= temp.second;
add = temp.first;
}
if(add!=0)
result+=std::to_string(add);
return std::string(result.rbegin(),result.rend());
}