This problem can be solved easily once you find the regularities :-) This link 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<string> findStrobogrammatic(int n) { 4 vector<string> strobos; 5 if (n & 1) strobos = {"0", "1", "8"}; 6 else strobos = {""}; 7 vector<string> bases = {"00", "11", "88", "69", "96"}; 8 int m = bases.size(); 9 while (n > 1) { 10 n -= 2; 11 vector<string> 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 };