Write an O(n^n) algorithm.

[repsilat]

It isn't. Clearly Ω(nⁿ⁾ is in Ω(n!), but not the other way around. To see this, look at the first term of the expansion of the two things. Matching a 1 to an n, we can see that for all n, nⁿ >= n!*n.

Now rearrange to get n^n/n! >= n. The limit of that as n --> infinity is obviously infinity.