Learn how to find the minimum spanning tree of a graph using Kruskal's algorithm, which sorts the edges in ascending order and adds them to the forest without cycles. See examples, pseudocode, and C++, Java, and Python implementations. The Kruskal algorithm is a popular algorithm used to find the Minimum Spanning Tree (MST) in a graph, ensuring that the total edge weight is minimized while connecting all vertices. This algorithm is especially useful in network design and optimization. Given a weighted, undirected, and connected graph with V vertices and E edges, the task is to find the sum of the weights of the edges in the Minimum Spanning Tree (MST) of the graph using Kruskal's Algorithm. The graph is represented as an edge list. Kruskal's algorithm receives a graph G= (V, E) from which it creates a minimum spanning tree G'= (V, E'). What is a minimum spanning tree? A spanning tree is a subgraph of an undirected and connected graph G. The following conditions must hold for the subgraph: All nodes contained in the graph G are also contained in the subgraph. The subgraph is connected and free of cycles. The set of edges of the subgraph is a subset of the edge set of G. A spanning tree G' is a minimum spanning tree of G ...
