Freaks City

This problem involves calculating valid colorings of a tree under certain constraints. The solution uses inclusion-exclution principle combined with polynomial multiplication via Number Theoretic Transform (NTT). Basic Approach We approach the problem by computing the complement: count arrangements where at least one node violates the coloring ...

Problem A: Tree Value Maximization Approach Define subtree_value[i] as the value generated by the subtree rooted at node i: subtree_value[i] = subtree_size[i] + Σ subtree_value[j] for all children j of i. The initial selection of i as root gives subtree_size[i] value, followed by contributions from its subtrees. Direct computation for each root ...