Israel has an excellent year round program.

We have ~70 students divided into 2 groups, beginner and advanced, with ~15 people in the advanced group from which we choose the delegation. Because Israel is so small, we can meet every week or 2 weeks for a 5 hour simulation and a lecture. According to the results of the simulations done all year, the coaches choose the delegation.

Obviously it is not enough and it is expected that the students do more at home. I can say a lot of us do high quality contest simulations (like APIO, BOI, and JOI), and we save recent years IOIs to simulate in the couple of months between the announcement of the delegation and the IOI itself. Also it is standard practice for students to become coaches when they finish 12th grade.

I personally don't agree with the statement that CF helps at OI, I think it's mainly correlation. Solving a lot of questions obviously helps a lot, but I don't think that participating at CF contests helps. OI questions are different than CF ones, and the strategy involved in OI is different than the one in CF.

My teammates DnlPrs809 and Davdav1232 got 10th place and 14th place respectively!

A bit of a troll on the stats (obviously we don't do CF) :)

1. I am not sure what algorithm you are exactly talking about but it is possible to solve the mentioned problem using offline techniques (I cannot think of an easy offline algorithm that has O(n*log(n)) complexity), but the main usage of the DS is when using it online. Most of the problems I mentioned need the algorithm to be online and since writing the post I encountered a lot of problems which are solvable using the DS and all need the DS to be online(One big application of the DS is doing undo priority queue in O(log(n)) on dsu).
2. You are correct to note that what I described has simmilarities with krusakl reconstruction tree, espically the warmup problem (which krusakl reconstruction tree can solve), but the rest of what I dsecribed cannot be done with krusakl reconstrucion tree since it doesnt support edge insertions. I highly advise you to read the post again in order to understand what my DS supports.

Undoing operations online is quite hard. This is a solution to the online problem without undoing operations: Maintaing mst with onl8ne edge insertions You can use offline deletion trick on the above DS for your general problem. Hope it is still relevent