The idea is just to add the elements in the spiral order. First the up-most row (u), then the right-most column (r), then the down-most row (d), and finally the left-most column (l). After finishing a row or a column, update the corresponding variable to continue the process.

The code is as follows.

1 class Solution { 2 public: 3     vector
     
       spiralOrder(vector
      
       
        >& matrix) { 4         if (matrix.empty()) return {}; 5         int m = matrix.size(), n = matrix[0].size(); 6         vector
        
          spiral(m * n); 7         int u = 0, d = m - 1, l = 0, r = n - 1, k = 0; 8         while (true) { 9             // up10             for (int col = l; col <= r; col++) spiral[k++] = matrix[u][col];11             if (++u > d) break;12             // right13             for (int row = u; row <= d; row++) spiral[k++] = matrix[row][r];14             if (--r < l) break;15             // down16             for (int col = r; col >= l; col--) spiral[k++] = matrix[d][col];17             if (--d < u) break;18             // left19             for (int row = d; row >= u; row--) spiral[k++] = matrix[row][l];20             if (++l > r) break;21         }22         return spiral;23     }24 };