What is the asymptotic complexity of the brute-force algorithm for all options?

The brute force algorithm, which exhaustively checks all options, usually has exponential or factorial asymptotic complexity depending on the problem.

• In general, if all possible combinations of n elements need to be checked, the complexity will be on the order of O(k^n), where k is the number of options for each element.
• If the problem involves permutations, the complexity can be O(n!).

This means that the execution time grows very rapidly with increasing input size, making this approach inefficient for large problems.

Example: enumerating all subsets of a set of n elements — O(2^n).