I'm dealing with a time-complexity problem in which I know the running time of an algorithm:
$t = 1000 \mathrm{ms} .$
I also know that the algorithm is upper bounded by $O(n!)$.
I want to know the approximate size of the input $n$ based on this:
$ f(n) = n! = t $ $ f^{-1}(t) = n = ? $