The idea is just to perform the addition from right to left as usual :-)

Note that the result may be longer than the original digits by 1 number (the carry).

1 class Solution { 2 public: 3     vector
     
       plusOne(vector
      
        &digits) { 4         int c = 1, n = digits.size(); 5         vector
       
         sum(n, 0); 6         for(int i = n - 1; i >= 0; i--) { 7             int val = digits[i] + c;  8             sum[i] = val % 10; 9             c = val / 10;10         }11         if(c) sum.insert(sum.begin(), c);12         return sum;13     }14 };