Union-Find algorithm

The Union-Find algorithm helps manage and keep track of groups or sets of connected items. Imagine you have a collection of items, and you want to quickly find which group each item belongs to, or to combine two groups into one. It does this efficiently by assigning a unique leader or representative to each group. When groups merge, the leaders are updated, so future queries can identify the correct group quickly. This algorithm is useful in network connectivity, image processing, and Kruskal's algorithm for minimum spanning trees, enabling fast, dynamic grouping and connectivity checks.