# Where f(n) = n! belongs to? P, co-P, NPComplete or NPHard? [duplicate]

Where f(n) = n! belongs to? P, co-P, NPComplete or NPHard?

• do you define $f(n)$ as a complexity function? what exactly are you asking? – lox Mar 31 '19 at 14:07
• Have a look at the definitions. As a starter, is "f(n) = n!" a decision problem? – Juho Mar 31 '19 at 14:08
• A decision problem would be "given n and x, is n! = x?" How much time would it take you to decide that? In the non-decision problem "Given n, what is n! in decimal notation", how large would be the output, compared to the size of the input? Can that problem be solved in polynomial time? – gnasher729 Mar 31 '19 at 14:57