Union find

11 videos • 103 views • by LetsCode Union-Find, also known as Disjoint Set Union (DSU), is a data structure that efficiently keeps track of a partition of a set into disjoint subsets. It supports two main operations: union (merge) and find, which are useful for solving various problems. Here are some problems that can be efficiently solved using Union-Find: 1. Connected Components in a Graph: - Determine the number of connected components in an undirected graph. - Identify the connected components of a graph. 2. Cycle Detection in a Graph: - Detect whether an undirected graph contains a cycle. 3. MST (Minimum Spanning Tree): - Kruskal's algorithm for finding the minimum spanning tree of a graph. 4. Dynamic Connectivity: - Determine whether two elements in a set are connected. - Perform union and find operations on sets. 5. Percolation: - Determine whether a system percolates (e.g., water percolating through a material). - Useful in grid-based problems where cells can be open or closed, and you need to check if water can flow from the top to the bottom. 6. Friend Circles: - Identify the number of friend circles in a social network. 7. Image Segmentation: - Segment an image into connected components. 8. Equivalence Relations: - Determine whether two elements are equivalent in a set under some equivalence relation. 9. Job Scheduling: - Schedule jobs in such a way that no two jobs clash if they are in the same set. 10. Sudoku Solver: - Solve Sudoku puzzles by considering cells in the same row, column, and box as connected components. Union-Find is a versatile data structure that finds applications in various algorithms and problem-solving scenarios where efficient connectivity operations are required.