Codeforces Round #359 (Div. 2) - D. Kay and Snowflake

Problem Statement:
http://codeforces.com/contest/686/problem/D

Summary:
Given a tree of size n <= 300000, answer q <= 300000 queries of the form: find the centroid of subtree v. Centroid of subtree T is defined as a node in T such that when removed the resulting set of disjoint trees have sizes at most |T|/2 (half the size of initial subtree).

SPOJ - Another Tree Problem (MTREE)

Problem Statement:
SPOJ - Another Tree Problem (MTREE)

Summary:
Define weight of a path as the product of weights of edges in a path between node A and B in a tree, and define weight of a tree as the sum of the weight of path of all paths (inception!).
(Number of vertices  \(N \leq 10^5\))