Union-Find and Prim's Algorithm

This lecture covers the Union-Find data structure, which includes operations like MAKE-SET, UNION, and FIND. It also explains Prim's algorithm for finding minimum spanning trees in graphs, starting with a single vertex and greedily adding edges based on their weights. The lecture delves into the concept of cuts in graphs and how they relate to finding minimum spanning trees. Additionally, it explores the history of the Minimum Spanning Tree problem, originating from an electrical power network construction challenge. The application of Prim's algorithm in scenarios like leasing communication lines for multinational companies is also discussed.