A binary tree is an Ordered Tree with the following properties:
- each internal node has at most two children
- each child node is labelled as a left or right child
- a left child precedes a right child in the ordering of children
The sub-tree rooted at a left or right child of an internal node is called a left or right sub-tree, respectively, of .
A binary tree is proper (full) if each node has either zero or two children. Each internal node has exactly two children.