<ul><li>The Union-Find algorithm, also known as Disjoint Set, manages connections between elements, merging groups when new connections are formed.</li><li>It is used in network connectivity, cycle detection, and image segmentation to group related elements.</li><li>Key operations include Find(x), Union(x, y), and Same(x, y) to identify groups and connections.</li><li>The algorithm is implemented using an array structure, where each element points to its parent in the group.</li><li>An example scenario demonstrates how Union-Find creates and tracks groups based on relationships between elements.</li><li>Optimizations like Path Compression and Union by Rank enhance the algorithm's efficiency by reducing time complexity for find and union operations.</li><li>Path Compression flattens the tree structure during find operations, while Union by Rank balances tree heights to improve performance.</li><li>With these optimizations, Union-Find offers near-constant time complexity, making it scalable for handling large graphs and queries.</li></ul>

Union-Find (Disjoint Set)

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