Tree

Programming basics

In computer science, a tree is a widely used abstract data type (ADT)—or data structure implementing this ADT—that simulates a hierarchical tree structure, with a root value and subtrees of children with a parent node, represented as a set of linked nodes.

A tree data structure can be defined recursively (locally) as a collection of nodes (starting at a root node), where each node is a data structure consisting of a value, together with a list of references to nodes (the "children"), with the constraints that no reference is duplicated, and none points to the root.

Image of a tree

tree vocabulary

• root node
• parent node
• child node
• leaf node

Practical applications of a tree

• Trees can be used to store data that has an inherent hierarchical structure. For example, an operating system may use a tree for directories, files and folders in its file management system.
• They are dynamic, which means that it is easy to add and delete nodes.
• They are easy to search and sort using standard traversal algorithms.
• They can be used to process the syntax of statements in natural and programming languages so are commonly used when compiling programming code.

Tree - video example

This video provides a basic introduction to trees. It also summarizes, very nicely, other data structures. Please keep in mind the example at the beginning is not a binary tree, but binary trees are discussed later. Ignore the discussion about cousins and uncles. It's ridiculous. But the rest of the video is really good.

Standards

• Describe how trees operate logically (both binary and non-binary).
• Define the terms: parent, left-child, right-child, subtree, root and leaf.
• State the result of inorder, postorder and preorder tree traversal.
• Sketch binary trees.

See Also

• Abstract data structures

External Links

high level discussion of binary trees

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