In his spare time, Farmer John has created a new video-sharing service, which he names MooTube. On MooTube, Farmer John's cows can record, share, and discover many amusing videos. His cows already have posted N videos (1 \leq N \leq 100,000), conveniently numbered 1 \ldots N. However, FJ can't quite figure out how to help his cows find new videos they might like.

FJ wants to create a list of "suggested videos" for every MooTube video. This way, cows will be recommended the videos most relevant to the ones they already watch.

FJ devises a metric of "relevance," which determines, as the name suggests, how relevant two videos are to each other. He picks N-1 pairs of videos and manually computes their pairwise relevance. Then, FJ visualizes his videos as a network, where each video is a node and the N-1 pairs of videos he manually considered are connected. Conveniently, FJ has picked his N-1 pairs so that any video can be reached from any other video along a path of connections in exactly one way. FJ decides that the relevance of any pair of videos should be defined as the minimum relevance of any connection along this path.

Farmer John wants to pick a value K so that next to any given MooTube video, all other videos with relevance at least K to that video will be suggested. However, FJ is worried that too many videos will be suggested to his cows, which could distract them from milk production! Therefore, he wants to carefully set an appropriate value of K. Farmer John would like your help answering a number of questions about the suggested videos for certain values of K.

Problem credits: Jay Leeds

#4048 upload 14 done 6 how_to_reg 5

MooTube timer 2s memory 512MB

#4048

MooTube 2s 512MB