Binary tree

wikipedia Binary tree

NOTE:

最最常见的树结构

In computer science, a binary tree is a tree data structure in which each node has at most two children, which are referred to as the left child and the right child. 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.[1] Some authors allow the binary tree to be the empty set as well.[2]

From a graph theory perspective, binary (and K-ary) trees as defined here are actually arborescences.[3] A binary tree may thus be also called a bifurcating arborescence[3]—a term which appears in some very old programming books,[4] before the modern computer science terminology prevailed. It is also possible to interpret a binary tree as an undirected, rather than a directed graph, in which case a binary tree is an ordered, rooted tree.[5] Some authors use rooted binary tree instead of binary tree to emphasize the fact that the tree is rooted, but as defined above, a binary tree is always rooted.[6] A binary tree is a special case of an ordered K-ary tree, where k is 2.

In mathematics, what is termed binary tree can vary significantly from author to author. Some use the definition commonly used in computer science,[7] but others define it as every non-leaf having exactly two children and don't necessarily order (as left/right) the children either.[8]