What is an “internal node” in a binary search tree?

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  •  06-07-2019
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Question

I'm scouring the internet for a definition of the term "Internal Node." I cannot find a succinct definition. Every source I'm looking at uses the term without defining it, and the usage doesn't yield a proper definition of what an internal node actually is.

Here are the two places I've been mainly looking: http://planetmath.org/encyclopedia/ExternalNode.html assumes that internal nodes are nodes that have two subtrees that aren't null, but doesn't say what nodes in the original tree are internal vs. external.

http://www.math.bas.bg/~nkirov/2008/NETB201/slides/ch06/ch06-2.html seems to insinuate that internal nodes only exist in proper binary trees and doesn't yield much useful information about them.

What actually is an internal node!?

Was it helpful?

Solution 

     I         ROOT (root is also an INTERNAL NODE, unless it is leaf)
   /   \
  I     I      INTERNAL NODES
 /     / \
o     o   o    EXTERNAL NODES (or leaves)

As the wonderful picture shows, internal nodes are nodes located between the root of the tree and the leaves. Note that the root is also an internal node except in the case it's the only node of the tree.

What is said in one of the sites about an internal node having to have two children is for the tree to be a complete binary tree, not for the node to be internal.

OTHER TIPS

As far as i understand it, it is a node which is not a leaf.

From "Introduction To Algorithms", edited by Thomas H Cormen:

A node with no child is called 'leaf node'. A non-leaf node is an 'internal node'.

An internal node or inner node is any node of a tree that has child nodes and is thus not a leaf node. An intermediate node between the root and the leaf nodes is called an internal node.

Source: http://en.wikipedia.org/wiki/Tree_data_structure

The most upvoted answer is incorrect. According to Mathematical Structures for Computer Science by Judith Gersting, an internal node is "A node with no children is called a leaf of the tree; all non-leaves are called internal nodes"

So, for example (I = INTERNAL NODE): I / \ * I /\ * *

An internal node (also known as an inner node, inode for short, or branch node) is any node of a tree that has child nodes. Similarly, an external node (also known as an outer node, leaf node, or terminal node) is any node that does not have child nodes.

quick and simple.

Internal node: a node which is not the root and has at least one child.

Generally, an internal node is any node that is not a leaf (a node with no children).

In extended binary trees (also comparison trees), internal nodes all have two children because each internal node corresponds to a comparison that must be made [The Art of Computer Programming (TAoCP) vol.3 Sorting and Searching, discussion and figure in section 5.3.1, p.181 (ed.2). By the way, the use of these trees to represent pairings (and byes) for elimination tournaments is addressed in section 5.4.1 of this material.]

Vinko's diagram reflects this distinction, although the root node is also always either an internal node or a leaf node, in addition to being the only node with no parent.

There is a broader discussion in Knuth's treatment of information structures and properties of trees [TAoCP vol.1 Fundamental Algorithms, discussion of path lengths in trees in section 2.3.4.5, p.p. 399-406 (ed.3) including exercises (many worked-out in the back of the book)].

It is useful to notice that binary search trees (where internal nodes also hold single values as well as having up to two children) are somewhat different [TAoCP vol.3, section 6.2.2]. The nomenclature still works, though.

A binary tree can have zero , one nodes and can have maximum of two nodes. A binary tree have a left node and a right node in itself.

Internal node – a node with at least one child. External node – a node with no children.

An internal node or inner node is any node of a tree that has child nodes and is thus not a leaf node or An intermediate node between the root and the leaf nodes is called an internal node

A node which has at least one child.

Ya internal node does not include the root. And a complete binary tree as terminology tells each internal node should have exact 2 nodes. But in a simple binary tree each internal node have atmost 2 nodes i.e it cannot contain more then 2 nodes but less then 2 is permisable

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