Question
Write Kruskal’s algorithm for finding minimum cost spanning tree using greedy approach and apply to the following graph and show step by step results.
Answer :
Word Count : 732
Kruskal’s algorithm is a classical greedy algorithm used for finding the minimum spanning tree (MST) of a weighted, undirected graph. The minimum spanning tree of a graph is a subset of edges that connects all the vertices together without any cycles, and the total weight of the edges is minimized. Kruskal's algorithm follows a greedy approach, which means it makes the locally optimal choice at each step with the hope of finding the global optimum.
Steps in Kruskal’s Algorithm:
- Sort all the edges in the graph in increasing order of their weights.
- Initialize a forest, where each vertex is its own component (or tree).
- Pick the smallest edge. If the edge connects two different components (trees), include it in the MST and merge the components. If it forms a cycle, discard it.
- Repeat the process until there are V−1V - 1 edges in the MST, __________ ________ ________ ___ __________ ___ ______ _____ ________ ___ _______.
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