Freaks City

Weighted Independent Set with Point Updates on a Tree Consider a rooted tree where every node carries a weight. We must support point-weight modifications and after each change report the maximum-weight independent set of the entire tree. Node count and operation count are up to (10^5), weights are bounded in absolute value by (10^2). Standard ...

Weighted Path Distribution via Greedy DFS When distributing a fixed number of routes across a rooted tree, an optimal strategy balances load evenly before allocating surplus paths based on subtree potential. The algorithm performs a depth-first traversal where each node divides incoming routes equally among its children. The remainder is assign ...

Heavy-Light Decomposition (HLD) is a powerful technique that partitions a rooted tree into a set of disjoint paths (chains). This transformation allows for efficient range-based operations (like updates and queries) on tree structures by mapping the nodes into a linear array using a Segment Tree. Core Definitions Heavy Edge: An edge connecting ...