How is a binary tree defined?

A binary tree is defined as a data structure in which each node can have at most two children, often referred to as the left child and the right child. This specific constraint on the number of children is what distinguishes binary trees from other tree structures, where nodes can have an arbitrary number of children.

The design of a binary tree allows for efficient searching, insertion, and deletion operations, especially in binary search trees where the nodes are organized in a way that facilitates quick retrieval of data. The structure is often used in various applications, including expression parsing and representing hierarchical data.

The other possibilities do not accurately capture the essence of a binary tree. For instance, allowing each node to have multiple children describes a general tree structure rather than a binary one. Organizing data linearly pertains more to structures such as linked lists or arrays, while organizing in a circular manner suggests a circular linked list, which is not related to the binary tree concept at all.