Bogosort

Bogosort (also permutation sort, and rather succinctly stupid sort) is a sorting algorithm that successively randomises (i.e., it generates permutations) a set until it finds one that is sorted.

For obvious reasons this isn’t useful. In its worst-case performance, we get a time complexity of $O(n\cdot n!)$ and a best-case of $\Omega (n)$. The extra $n$ terms come from the permuting itself. If we ignore the permutation operation, the algorithm reduces down to $O(n!)$ and $\Omega (1)$, respectively.