方法一

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
string a, b;
int main(){
    cin >> a >> b;
    int cnt = 0;
    string res = "";
    int i;
    reverse(a.begin(), a.end());
    reverse(b.begin(), b.end());
    for(i = 0; i < a.size() && i < b.size(); i ++ ){
        int num = cnt + a[i] + b[i] - 2 * '0';
        if(num >= 10){
            cnt = 1;
            res += (num - 10 + '0');
        }else{
            cnt = 0;
            res += (num + '0');
        }
    }
    while(i < a.size()){
        int num = a[i] - '0' + cnt;
        if(num >= 10){
            cnt = 1;
            res += (num - 10 + '0');
        }else{
            cnt = 0;
            res += (num + '0');
        }
        i ++ ;
    }
    while(i < b.size()){
        int num = b[i] - '0' + cnt;
        if(num >= 10){
            cnt = 1;
            res += (num - 10 + '0');
        }else{
            cnt = 0;
            res += (num + '0');
        }
        i ++ ;
    }
    if(cnt != 0)    res += '1';
    reverse(res.begin(), res.end());
    cout << res << endl;
    return 0;
}

方法二（精简版）

#include <iostream>
#include <vector>
using namespace std;
vector<int> add(vector<int> &A, vector<int> &B){
    vector<int> C;
    int t = 0;
    for(int i = 0; i < A.size() || i < B.size(); i ++ ){
        if(i < A.size())    t += A[i];
        if(i < B.size())    t += B[i];
        C.push_back(t % 10);
        t /= 10;
    }
    if(t)   C.push_back(1);
    return C;
}
int main(){
    string a, b;    cin >> a >> b;
    vector<int> A, B;
    for(int i = a.size() - 1; i >= 0; i -- )    A.push_back(a[i] - '0');
    for(int i = b.size() - 1; i >= 0; i -- )    B.push_back(b[i] - '0');
    vector<int> C = add(A, B);
    for(int i = C.size() - 1; i >= 0; i -- )    cout << C[i];
    return 0;
}