Recently I decided to look for some problems involving queries on trees and the last I found was this — http://acm.timus.ru/problem.aspx?space=1&num=1752 (note that this is not the problem I am asking about). In short, there is an unweighted tree with N<=20000 nodes and Q<=50000 queries are given. Each query contains a vertex V and distance D. You are to find some vertex that is on distance exactly D from V or report that there is no such vertex.
The problem above has a fairly simple solution if you have solved some problems about diameters and LCA. However, when I first read the problem, I misunderstood it and I thought it was asking for how many vertices are there such that the distance from them to V is exactly D. After spending an hour of thinking, I looked at the discussions for some hints and I saw that this was not the problem.
Anyway, I think the problem which I thought I should solve is quite interesting and I wonder if someone has a solution to it. If so, please share your ideas. Also, I would love it if you can give me some more problems about queries on trees, here is one I really liked — http://www.spoj.com/problems/DRTREE/ and also one prepared by myself — http://www.spoj.com/problems/MAXCHILDSUM/.
Thanks in advance! :)