khing-fm / binary_trees

0x1D.C - Binary_trees

In computer science, a binary tree is a k-ary

k=2 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 containing the root. Some authors allow the binary tree to be the empty set as well.

From a graph theory perspective, binary (and K-ary) trees as defined here are arborescences.A binary tree may thus be also called a bifurcating arborescence—a term which appears in some very old programming books,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.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.A binary tree is a special case of an ordered K-ary tree, where K is 2.

Source: Binary tree