I am thinking about using euler theorem, and try to create edges such that all vertices (except at most 2) have even degree, which can be done by dijkstra.

However, the number of vertices will be 2^n and the number of edges can be more than that, which I think is not feasible since n can be as large as 25..

However, the number of vertices will be 2^n and the number of edges can be more than that, which I think is not feasible since n can be as large as 25..

Why 2^n? In my way, the number of vertics is only 5x5 = 25, which is feasible.