# Does Poly Exponential Time complexity exist?

Poly-Exponential time complexity. Where $f(x) = n^n$

Are there any algorithms which have this time complexity.

Please list them if they exist. I coined the term myself, and a Google search turned nothing.

• "Are there any algorithms that have this time complexity". Yes - one can construct generic algorithms. For instance, the algorithm that counts the number of strings formed from $n$ distinct symbols by enumerating them works in time $n^n$. You shouldn't expect useful algorithms with complexity $n^n$ to be well-studied, as it's too slow. – davidlowryduda Nov 17 '16 at 16:26
• So $\sum{^n_{i=0} nPi} = n^n$ ? Can I please get a proof of this? – Tobi Alafin Nov 18 '16 at 8:55

The number of permutations of $n$ distinct items is $n! \sim \sqrt{2\pi} n^{n+1/2} e^{-n}$, so consider an algorithm that enumerates all these permutations and spends at most $e^n/\sqrt{n}$ time on each one.