Kruskal and Prim connect all nodes at minimum cost.
An MST connects all vertices with minimum total edge weight and no cycles. Kruskal sorts edges and adds the smallest not forming a cycle (union-find); Prim grows a tree from a vertex using a priority queue. Applications: network design and clustering.
Laying cable between towns at least cost is an MST problem.
Minimum spanning trees connect all points at the lowest total cost, which is useful for designing networks, cables and pipes.
Kruskal and Prim connect all nodes at minimum cost.
Minimum spanning trees connect all points at the lowest total cost, which is useful for designing networks, cables and pipes.
It must connect every node without any cycles, and a minimum spanning tree does this with the smallest total edge weight.
Kruskal adds the cheapest edges that do not form a cycle, while Prim grows one tree from a starting node by adding the cheapest edge.
Typical applications include planning a cable layout that connects all houses with the least wire, designing a road network that links towns with minimum length and clustering data points by cutting the largest edges of a tree.
Study "Shortest path algorithms" first (topic 27 of 104 in Software & Computing). It covers the groundwork this topic builds on.
Cut property. Union-find. Unique if weights distinct.
Laying cable between towns at least cost is an MST problem.
The next topic is "Dynamic programming", which builds directly on this one.
It is classed as Beginner in Software & Computing (topic 28 of 104). It is an entry-level topic. It relies only on basic school mathematics and the ideas introduced earlier in this discipline.
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