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a rooted tree in which each node has no more than two children

A binary tree is a tree type data structure where each node has at most two child nodes.

The image shows the rough model of binary tree.

Single parent or single level, complete binary tree

A binary tree is usually used in binary search. Further reading of binary search trees on Wikipedia. There are many types of binary trees on level of nodes and completion of child with a parent.

Example: A binary tree with complete nodes filled (i.e. every parent has two child nodes) is called a full binary tree. In respect to the image, a full binary tree will have the same structure as in image in all its nodes.

Full detailed reading of binary trees.