Hello Codeforces!

Today was Codeforces Round #720 (Div.2), in which I solved problem D — Nastia Plays with a Tree. As I find my solution different from the solutions I heard of after the contest, I will explain it in detail in this blog post. I will note that you still might find value in reading this if you solved the problem, as my proposed solution also maintains at every stage the graph being a forest (i.e I don't create any cycles).

The Solution

We should first note that bamboo is simply a tree that looks like a single line of connections (i.e a simple path).

We observe that given the sequence of moves the order we delete/link edges in does not change the resultant underlying graph. We consider the following question: how can we delete edges such that we can link the remaining forest via link operations to make a bamboo after we delete all of them?