How does Kruskal's algorithm work?

Can you explain how Kruskal's algorithm works?

Sure! Kruskal's algorithm is a method for finding the minimum spanning tree of a graph. It works by sorting all the edges in the graph by their weight and adding them one by one to the spanning tree, as long as they don't form a cycle.

What do you mean by 'minimum spanning tree'?

A minimum spanning tree is a subset of the edges in a graph that connects all the vertices together without any cycles and with the minimum possible total edge weight.

How does it handle cycles?

Kruskal's algorithm uses a union-find data structure to keep track of which vertices are connected. Before adding an edge, it checks if the two vertices it connects are already in the same set. If they are, adding that edge would create a cycle, so it skips that edge.

Can you give me an example of how it works?

Absolutely! Imagine a graph with vertices A, B, C, and D, and edges with weights. First, sort the edges by weight, then add the smallest edge that doesn't form a cycle, repeating until all vertices are connected.