Lecture
This lecture covers the correctness and implementation of Prim's and Kruskal's algorithms for finding minimum spanning trees in a graph. Prim's algorithm starts with a single vertex and grows the tree by adding the minimum weight crossing edge. Kruskal's algorithm begins with an empty forest and adds edges that do not create cycles. The lecture explains the cut property, the challenges in implementation, and the analysis of both algorithms, including the use of disjoint sets data structure. It also discusses the time complexity of the algorithms and provides examples of their application.