Basic Concept of Union Find Algorithm
Prerequisites
Before reading this article, you should first study:
Summary in One Sentence
The Union-Find (or Disjoint Set) structure is a derivative of the binary tree structure and is used to efficiently solve connectivity problems in undirected graphs. It can merge two connected components in time, check if two nodes are connected in time, and determine the number of connected components in time.
There are several optimization methods for the Union-Find algorithm, which are supported by visualization panels. The following shows an unoptimized implementation of Union-Find, where the resulting multi-branch tree almost degenerates into a singly linked list, reducing algorithm efficiency:
The optimization strategies and visual demonstrations for this problem will be detailed in the subsequent sections.
This article will introduce the concept of the dynamic connectivity problem in graphs and explain why the Union Find algorithm is an efficient solution for this problem.
We will use a visualization panel to intuitively demonstrate the core principles of the Union Find algorithm and the effects of several optimization strategies.
As this is a foundational chapter, we will not delve into the implementation details of the algorithm code. The specific code implementation and application in algorithm problems will be covered in later sections: Union Find Algorithm Implementation and Application and Classic Union Find Exercises. It is recommended for beginners to follow the sequence in the directory for a step-by-step learning process.