Traversing the complement graph in linear/near-linear time in multiple ways
In this post, I will focus on the following problem: 920E. More generally, we will look at how to do efficiently traverse the complement graph of a given graph in both dfs and bfs orders. In particular, the bfs order also allows us to find a shortest-path tree of the complement graph. This is my first post, so please let me know of any errors/typos that might have crept in. Note 1: I will present the algorithms in the order I came up with them, so it might not be the most clean presentation, but I hope that it might give some insight into how to come up with new ideas in graphs. Note that I don’t claim to be the first person to come up with these ideas (especially the naive algorithm, which is identical to the solution in the editorial), but I haven’t seen any of these implementation tricks being used in any implementation before. Resources pointing to similar ideas/implementations are welcome! ...