Probably a mistake in DFS problem in CS practice

Original problem: https://brilliant.org/practice/depth-first-search/?p=1

I don't actually know if a solution to the problem is correct or not, but I have noticed a flaw in the explanation witch sometime yields wrong results. I outline the problem on paper, so please forgive my terrible handwriting (and my grammar, I am Russian, don't hurt me).

I am not sure if I am correct or not, but if this is of any use I am happy to help! (don't mind a little reward if you're do that, hehe)

My notes:

1:

2:

3:

P.S. I forgot to mention on paper: the problem is a little bit modified -- we only looking for number of vertices that are two hops from vertex 1.

Note by Андрей Антонов
3 months, 2 weeks ago

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Hi Андрей, thank you for notifying us. We will respond to you shortly.

Brilliant Mathematics Staff - 3 months ago

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Hi Андрей, sorry for the late response.

We looked at the NSA problem and how it would consume the network structure. It might be instructive to run the code on the examples you came up with. One of the early steps is to store the neighbor relationships in a dictionary, which is symmetric. After that is done, all information as to the order of how they appeared in the original file is lost, so the algorithm does not know about it.

In light of this, we still feel the answer and solution are correct, i.e., the output does not depend on the order of the edges in the given input.

It's possible we've missed something, so if you have more detailed critique of the problem, we're happy to take another look.

Best,
Brilliant

Brilliant Mathematics Staff - 2 months, 1 week ago

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