Well, a very common method for graphs...

Vitaliy Goldstein at the Winter School talked about graphs, white, black, and gray vertices, and solving many graph problems using the depth-first search method. At the end, he began to speak about the difficult life of a programmer and therefore forgot to give everyone at the Winter School in Kharkiv 2011 one more problem that can also be solved by the indicated method. Naturally, Vitaliy could not forget about it and asked us to offer this problem to everyone, for as a true master lecturer, he should not miss the opportunity to pose any, even a simple problem, whenever communicating with the audience, even if this communication happens remotely.

Thus, here is another simple problem that can be solved using the depth-first search method: "You are given an undirected graph with $N$ vertices and $M$ edges (1 \leq N \leq 20000, 0 \leq M \leq 200000). The graph contains no loops or multiple edges. Determine the connected components of the given graph."