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I have to find an example of a running time that is neither polynomial nor exponential. At first I was thinking about $n!$ but I think that this is bounded below by exponential functions for large n (which would imply exponential running time). Could someone help me out with this question? Thanks in advance

StudTW
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  • $n!$ is not bounded above by an exponential though - it grows faster than any exponential. So it seems like a good choice? – Joppy Dec 13 '20 at 12:17

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Your initial intuition is correct, factorial time is certainly not polynomial, and it is not bounded above by exponential time (if by exponential time you mean $a^n$ for some $a$). Note, however, that there is another category called the superexponential time, of the form $n^n$, which does indeed outgrow $n!$. See this question for more details.

Chubby Chef
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