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Personally, I don't think it is a very good interview question at all. Since it says nothing at all about whether you can actually do the job I hired you you to do or not.

Sure, you might be able to solve a generic math problem like coming up with a recursive solution for navigating through a maze... But do do you know the first thing about Java EE? Do have any understanding of the technologies I need to you to be able to use to do the job I am hiring you for?

Sorry to say, but that interview question only proves you can do something I will never need you to do. But it says nothing about whether you can do the things I need you to do or not.

Its a graph question. Convert to edges and nodes and the question is "is this one graph or two graphs in a forest ?"

I'd not be able to implement an efficient solution without referencing my algorithms book.

In the workplace, you'd have access to reference materials, co-workers, the internet, and likely a meeting or two to discuss the most efficient means of solving whatever real-world problem arose. This is another example of someone trying to judge the ability and knowledge of a programmer by testing to see if they can remember an algorithm they learned in university. In the real world, you'd look up the algorithm, or download a freely available piece of sample code that does this already, and modify it for your specific purposes.

On the other hand, this would be a good way to create a short list of those who are actually worth interviewing. I think giving the person a computer to use would be better, as hand-writing code can be a real pain at times if the code is sufficiently complex. But, I can see the good and the bad in this.