Someone in class responded immediately: "Build another bridge."
The prof congratulated him on his lateral thinking.
May be this is lateral thinking to some people but it's actually changing the problem and not solving the original problem.
I can always to pretend to solve the problem by just changing it.
Respectfully submitted.
> We take all the destinations that have an odd number of connections in this tree (Euler proved there must be an even number of these), and carefully pair them up. Because all the destinations now have an even number of edges, we’ve created an Eulerian graph, so we create a route that crosses each edge exactly once.
For theoretical problems sure, you want to solve that problem, though a lot of solutions rely on analyzing a partial graph with some edges removed
For practical problems, changing the problem might be much cheaper/easier than keeping to the original one
I always appreciate three hours of deep compsci thinking interrupted by someone outside saying "why wouldn't we just run an extra cable?" or something. I'm glad your professor encouraged it, because it is very often useful.