The table below shows the limits that can be reached in a few seconds by algorithms of different complexities. I've also added a few examples of algorithms or problems and data structures that may occur in those complexity classes.
|_. size of n |_. complexity |_. algorithms |_. data structures|

| 9-10 | n!, n^n^ | brute force, backtracking, next_permutation |   |

| 8 |  n^n^ | brute force, cartesian product |   |
| 9-10 | n! | brute force, backtracking, next_permutation |   |

| 13-17 | 3^n^ | dynamic programming with exponential states | hash_map (to store the states) |
| 15 - 20 | n^2^ 2^n^ | dynamic programming with exponential states | bitsets, hash_map |
| 15 - 25 | 2^n^ | subset enumeration, brute force, dynamic programming with exponential states |   |