Dynamic operations that mix path updates and queries on a tree defeat simple prefix‑sum or difference‑based preprocessing. Heavy‑light decomposition (HLD) assigns each vertex to a heavy path and gives every path, as well as every complete subtree, a contiguous interval in a preorder. By flattening t...
Concept of a Tree A tree is a abstract data type (ADT) or a data structure implementing this ADT that simulates a hierarchical tree structure with a set of linked nodes. It consists of n (n ≥ 1) finite nodes organized in a hierarchical relationship. It is called a "tree" because it resemb...
Introduction This article presents various implementations of the DSU on Trees technique, also known as 'DSU on Tree'. The method involves processing each node's subtree in a specific order to efficiently compute answers for queries related to subtree properties. Standard DSU Approach The standard i...
This article demonstrates how to transform a nested tree structure into a flat array representation using recursive traversal. This technique is commonly used for converting hierarchical data (such as exam modules, organizational charts, or file systems) into a linear format suitable for tabular dis...
Core Concepts and Queue Usage Breadth-First Search (BFS) is fundamental for traversing graphs and trees, particularly useful for level order traversal, identifying connected components, topological sorting, and finding the shortest path in unweighted graphs (where all edges possess a length of 1). W...
