Duplicate issue.

I agree with uuuhhh_meow. The example does not follow from the explanation, but rather serves to complicate the problem unnecessarily. Which is it: do we want to optimize the path such that it visits all the same nodes in the fewest steps? Do we want to optimize the path to be the shortest such that it doesn't explore any new nodes? Or, as in the question, do we want to optimize the path using some arbitrary rule? If the latter, and the question cannot be changed at this point, then the entire description can reflect this to be most clear.