This time I've decided to choose a task from my own contest which took place last April and was known as the Grand Prix of Poland. If you want to write this contest virtually in the future, then consider not reading this blog. If you've participated in this contest and maybe even solved this task, then anyway I recommend reading it, cause this task has many very different solutions, each of them being very interesting (in my opinion). It's also a reason why this blog is longer than previous ones.
I'll write about task C "cutting tree" (not uploaded to the ejudge yet :/). The statement goes as follows:
You are given a tree with n vertices (1 ≤ n ≤ 2·105). The task is to calculate f(k) for each integer k from the range [1, n] where f(k) is defined as the maximum number of connected components of size k which we can "cut off" from the tree. A connected component of size k is a set of k vertices such that it's possible to traverse in the tree between any pair of these vertices using only vertices from this set. Chosen components are not allowed to intersect, so each vertex must belong to at most one component.