Tree

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

A tree is a connected, acyclic structure of nodes, commonly organized hierarchically through parent-child relationships and optionally around a designated root.

A tree is a graph with exactly one path between any two vertices, so it contains no cycles. Removing an edge from a cycle can turn a graph into a tree. section 4.3

Figure 4.6. In (a), a cycle exists between vertices B, C, and D, so it is not a tree. In (b), the edge connecting C and D has been pruned, so the graph is a tree.

The diagram contrasts a cycle through B, C, and D with the tree formed by removing the edge between C and D. section 4.3

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

How deep it goes

Defines trees through unique paths and cycles, then distinguishes connected graphs, spanning trees, and minimum spanning trees.

Examples

Uses a cycle among vertices B, C, and D, then removes the edge between C and D to form a tree.

What you can do after

Understand how removing an edge from a cycle can turn a graph into a tree.

How it connects

Connects trees to graphs, cycles, connected graphs, spanning trees, and minimum spanning trees.

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Also explained in

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  Functional Programming in Scala, Second EditionA recursive data structure whose values are formed from nodes such as leaves and branches, with this section focusing on structural shape during combination.
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  Grokking Algorithms, Second EditionA tree is a connected graph with no cycles, so no path of edges leads back to an earlier vertex.
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  Object-Oriented Software Design in C++A hierarchical data structure composed of nodes connected by parent-child relationships without cycles.
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  Functional Programming in JavaScriptA hierarchical data structure of nodes connected by parent-child relationships with a root.
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  Optimization Algorithms: AI techniques for design, planning, and control problemsA connected acyclic data structure consisting of nodes linked by hierarchical edges.
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  Grokking Data StructuresA tree is a hierarchical data structure whose elements are connected by parent-child relationships without cycles.
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  Advanced Algorithms and Data StructuresA tree is a hierarchical data structure composed of nodes connected by parent-child relationships without cycles.
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  Software Design for Python ProgrammersA tree is a hierarchical data structure composed of nodes connected in parent-child relationships.
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  Grokking AI Algorithms, Second EditionA tree is a connected acyclic data structure organized into nodes with a single root and hierarchical parent-child relationships.
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  100 Java Mistakes and How to Avoid ThemA tree-like data structure organizes elements into parent-child relationships and ordinarily has no cycles.

Compare how 11 books explain tree →

Related concepts

• binary treeincludes · A binary tree is a tree data structure in which each node has at most two children.
• graphkind of · A graph is a mathematical structure consisting of vertices connected by edges that represent relationships or connections.
• acyclic graphkind of · An acyclic graph is a graph that contains no cycles.
• minimum spanning treeincludes · A minimum spanning tree is a spanning tree of a connected, weighted, undirected graph having the smallest possible total edge weight.
• directory structureincludes · A directory structure is the hierarchical arrangement of directories and files in a filesystem or software project.

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.