This problem can be solved easily once you find the regularities :-) has done it for you. You may refer to its Python version. I rewrite it in C++ below.

1 class Solution { 2 public: 3     vector
     
       findStrobogrammatic(int n) {  4         vector
      
        strobos; 5         if (n & 1) strobos = {
   "0", "1", "8"}; 6         else strobos = {
   ""}; 7         vector
       
         bases = {
   "00", "11", "88", "69", "96"}; 8         int m = bases.size();  9         while (n > 1) {10             n -= 2;11             vector
        
          temp;12             for (string strobo : strobos)13                 for (int i = (n < 2 ? 1 : 0); i < m; i++)14                     temp.push_back(bases[i].substr(0, 1) + strobo + bases[i].substr(1));15             swap(temp, strobos);16         }17         return strobos;18     }19 };