If you're going to be pedantic, you need to at least be correct. There is no such thing as an "NP class algorithm".

There are, instead, languages that are NP-complete, for which we hypothesize that there are no polynomial-time algorithms for, because that would imply P=NP. It's a further unproven hypothesis that NP-complete languages have no sub-exponential time algorithms (the "exponential time hypothesis").