Given a directed graph $G=(V,E)$ and a subset $A\subseteq E$. I need to find an efficient algorithm to find a path (it doesn't have to be a simple one) which cross all of the edges of A, or inform that there is no such path. The path can cross other edges which are not in A.
Sadly, I didn't come up to any smart algorithm.
I'd really appreciate your help with this