Spanning tree

Q: How deeply does Classic Computer Science Problems in Swift: Essential techniques for practicing programmers cover spanning tree?

Defines trees, cycles, connectivity, and minimum spanning trees, then demonstrates an implementation with Prim’s algorithm.

As explained in Classic Computer Science Problems in Swift: Essential techniques for practicing programmers

A spanning tree is a tree that includes every vertex of a graph.

A spanning tree is a tree that connects every vertex in a graph. Because a tree has exactly one path between any two vertices, it contains no cycles; pruning suitable edges can turn a graph into one. section 4.3

In a weighted graph, the related minimum-spanning-tree problem asks for:

A set of edges touching every vertex. section 4.3
The smallest possible combined edge weight among spanning trees. section 4.3
A practical minimum-cost connection for transportation or computer networks. section 4.3

Connecting cities

A weighted graph of 15 United States metropolitan areas uses distances as edge weights. Prim’s algorithm selects connecting edges to produce a spanning tree with total weight 5,372.

How Classic Computer Science Problems in Swift: Essential techniques for practicing programmers covers it

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Also explained in

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Optimization Algorithms: AI techniques for design, planning, and control problemsA spanning tree is a cycle-free subgraph of an undirected graph that contains every vertex and connects them with the minimum number of edges.

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Related concepts

minimum spanning treeincludes · A minimum spanning tree is a spanning tree of a connected, weighted, undirected graph having the smallest possible total edge weight.
treekind of · A tree is a connected, acyclic structure of nodes, commonly organized hierarchically through parent-child relationships and optionally around a designated root.
spanning tree protocolproduced by · Spanning Tree Protocol is a Layer 2 protocol that prevents bridged-network loops by selecting a loop-free topology and blocking redundant paths.
spanning subgraphkind of · A spanning subgraph is a subgraph that contains every vertex of its original graph and a subset of its edges.

This explainer was generated by Manning's knowledge graph from the text of Classic Computer Science Problems in Swift: Essential techniques for practicing programmers. The section links point to the parts of the book it draws on.