#include <iostream>
using namespace std;

string add(string s,string st) {
 string res;
 int nho = 0, tmp;
 
 while (s.length() > st.length()) st = '0' + st;
    while (s.length() < st.length()) s = '0' + s;
  
 for (int i = s.length() - 1;i >= 0;i--) {
  tmp = s[i] + st[i] - 2 * '0' + nho;
  nho = tmp/10;
  tmp %= 10;
  res = char(tmp + '0') + res;
 }
 if (nho == 1) res = '1' + res;
 return res;
}
int main()
{
 string s, st;
 cin >> s >> st;
 cout << add(s, st);
}

Dạng này dùng Bignum.

#include <iostream>
#include <string>
#include <vector>
#include <cmath>
#include <stack>
#include <queue>
#include <deque>
#include <algorithm>
#include <map>
#include <cstring>
#include <cstdlib>
#include <cstdio>
#include <set>
#include <bitset>
#include <iomanip>
#include <sstream>
#define ll long long
#define ull unsigned long long
#define pa for(int i = 0; i < n; ++i) cout << a[i] << " ";
#define pi atan(1) * 4
using namespace std;

string add(string a, string b) {
    string c;
    int carry = 0;
    
    while(a.size() < b.size()) a = '0' + a;
    while(b.size() < a.size()) b = '0' + b;
        
    for(int i = a.size() - 1; i >= 0; --i) {
        int sum = (int)a[i] - 48 + (int)b[i] - 48;
        carry = sum / 10;
        c = (char)(sum % 10 + 48) + c;
    }
    
    if(carry > 0) c = '1' + c;
    return c;
}

int main() {
    ios::sync_with_stdio(0);
    cin.tie(0);cout.tie(0);
    
    string a, b; cin >> a >> b;
    cout << add(a,b);
}