A binary tree is a tree data structure in which each node has at most two child nodes. The two children are commonly referred to as left and right children, and the structure is used in search, sorting, parsing, decision processes, and many other algorithms.
A tree data structure in which each node has at most two children, which are referred to as the ' and the '. A recursive definition using just set theory notions is that a (non-empty) binary tree is a tuple (L, S, R), where L and R are binary trees or the empty set and S is a singleton set. Some authors allow the binary tree to be the empty set as well.