Given a graph with nodes $N$ and two sets of edges $E_1$, $E_2$ where no two edges from $E_2$ can be used consecutively, find the shortest path between $n_1, n_2 \in N$.
Is there a smart way to approach this problem other than a brute force search?
Edit: My first attempt involved trying to construct a graph that satisfies the constraint on $E2$. However if a node $n$ is connected with edges in both $E1$ and $E2$, it is impossible to know whether edges in $E2$ will be available on $n$ because it depends on which edge was used to arrive to $n$.