Path Compression in Union-Find: Optimizing Union-Find for Faster Lookups
Union-Find (Disjoint Set Union, DSU) is used to solve set merging and element membership problems, such as connectivity judgment. Its core operations are `find` (to locate the root node) and `union` (to merge sets). The basic version uses a `parent` array to record parent nodes, but long-chain structures lead to extremely low efficiency in the `find` operation. To optimize this, **path compression** is introduced: during the `find` process, all nodes along the path are directly pointed to the root node, flattening the tree structure and making the lookup efficiency nearly O(1). Path compression can be implemented recursively or iteratively, transforming long chains into "one-step" short paths. Combined with optimizations like rank-based merging, Union-Find efficiently handles large-scale set problems and has become a core tool for solving connectivity and membership judgment tasks.
Read MoreUnion-Find: What is Union-Find? A Method to Solve "Friendship" Problems
Union-Find (Disjoint Set Union, DSU) is an efficient data structure for managing element groups, primarily solving the "Union" (merge groups) and "Find" (check if elements belong to the same group) problems. It is ideal for scenarios requiring quick determination of element membership in a set. At its core, it uses a parent array to maintain parent-child relationships, where each group is represented as a tree with the root node as the group identifier. Initially, each element forms its own group. Key optimizations include **path compression** (shortening the path during Find to make nodes directly point to the root) and **union by rank** (attaching smaller trees to larger trees to prevent the tree from degrading into a linked list), ensuring nearly constant time complexity for operations. The core methods `find` (finds the root and compresses the path) and `union` (merges two groups by attaching the root of the smaller tree to the root of the larger tree) enable efficient group management. Widely applied in network connectivity checks, family relationship queries, minimum spanning trees (via Kruskal's algorithm), and equivalence class problems, Union-Find is a concise and powerful tool for handling grouping scenarios.
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