Assuming I have a set of integers that can range from 0 to INT64MAX, but I know the set in its entirety so I can generate a perfect hash.
If I want to use these hashes as array indices, I need to modulus with the size of the array I want to store this in.
This brings a problem where I want to find a non-colliding set for my hashes that map to integers such that minimal array size is needed and I still have no collisions.
Is this NP complete? It "feels" NP Complete.
There exist algorithms that construct perfect hashes (even minimal perfect hashes) in linear time. See for example the CMPH docs which list a couple of them.
Linear time means deterministic polynomial problem, thus the problem lies in P. P is contained in NP, but the problem certainly is not at least as hard as the hardest problems in NP, thus it is not in NP-hard.
NP-complete is defined as being in both NP and NP-hard. Therefore, it is not NP-complete.