Are there any real O(n^n) algorithms?

Question

Is there any real Algorithm with a time complexity O(n^n), that isn\'t just a gimmick?

I can create such an Algorithm, like computing n^n in O(n^n) / Θ(n^n):

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Answer 1

There are many optimization problems that are essentially O(n!), i.e in data compression. The common algorithms for this all need to cheat one way or another (many rely on heuristics) but can't make sure that they have found the perfect result this way. I.e. choosing the optimal line filters during compression of a PNG image is such a problem that is comparatively easy to understand.

Another example are algorithms to break encryption which can potentially be even worse than O(n!).