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Kruskal's algorithm

Last updated on Friday, April 26, 2024.

 

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Kruskal's algorithm is a greedy algorithm used in computer science for finding the minimum spanning tree of a connected, edge-weighted graph. It works by sorting the graph's edges in non-decreasing order of their weights and then iteratively adding the smallest edge that doesn't create a cycle in the current spanning tree.

The Concept of Kruskal's Algorithm

Kruskal's algorithm is a popular method in computer science for finding the minimum spanning tree of a connected, undirected graph. This algorithm is used in the field of software development to solve a variety of problems related to network design, transportation planning, and circuit layout optimization.

How Kruskal's Algorithm Works

The algorithm works by repeatedly adding the next lightest edge to the spanning tree, as long as adding the edge does not create a cycle. This process continues until all vertices are connected, resulting in a tree with the smallest possible total edge weight.

Key Steps of Kruskal's Algorithm:

  1. Sort all the edges in non-decreasing order of their weight.
  2. Iterate through the sorted edges and add them to the spanning tree if they do not form a cycle.
  3. Repeat step 2 until all vertices are included in the spanning tree.

This algorithm is efficient and guarantees the creation of a minimum spanning tree, making it a valuable tool in various practical applications.

 

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