Minimum Spanning Trees: Prims Algorithm

This lecture covers the concept of minimum spanning trees, starting with a recap of disjoint-set data structures. It explains the operations involved in maintaining disjoint sets and the list representation of sets. The lecture then delves into different union methods, including weighted-union heuristic and union by rank. It discusses the forest of trees representation and path compression. The pseudocode for MAKE-SET, FIND-SET, and UNION operations is presented. The running time analysis of these operations is also discussed. The lecture concludes with an explanation of Prim's algorithm for finding minimum spanning trees and the cut property that justifies its correctness.