# How to prove NP-hardness of a Hamiltonian Path problem by reducing longest-path problem?

I know how to prove longest-path problem by reducing Hamiltonian Path problem.

Here I want to prove NP-hardness of a Hamiltonion Path problem by reducing longest-path problem. (pretend we know longest-path problem is NP-hardness, not Hamiltonion Path problem)

I'm wondering if it is possible to reduce Hamiltonian Path problem to longest path problem.

Is there any way I can do that?

Suppose you have a graph $$G$$ of order $$n$$. $$G$$ has a simple path of length $$\geq n - 1$$ if and only if $$G$$ has a hamiltonian path.