Definitions

This section will include some basic terminology used when describing trees. To help you understand the terminology, use the following diagram:

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Node: data stored by the tree (All the circles)

Root Node: the top most node from which all other nodes come from. A is the root node of the tree.

Subtree: Some portion of the entire tree, includes a node (the root of the subtree) and every node that goes downwards from there. A is the root of the entire tree. B is the root of the subtree containing B,D,E and F

Empty trees: A tree with no nodes

Leaf Node: A node with only empty subtrees (no children) Ex. D,E,F,I,J,and G are all leaf nodes

Children: the nodes that is directly 1 link down from a node is that node's child node. Ex. B is the child of A. I is the child of H

Parent the node that is directly 1 link up from a node. Ex. A is parent of B. H is the parent of I

Sibling: All nodes that have the same parent node are siblings Ex. E and F are siblings of D but H is not

Ancestor: All nodes that can be reached by moving only in an upward direction in the tree. Ex. C, A and H are all ancestors of I but G and B are not.

Descendants or Successors of a node are nodes that can be reached by only going down in the tree. Ex. Descendents of C are G,H,I and J

Depth: Disthance from root node of tree. Root node is at depth 0. B and C are at depth 1. Nodes at depth 2 are D,E,F,G and H. Nodes at depth 3 are I and J

Height: Total number of nodes from root to furthest leaf. Our tree has a height of 4.

Path: Set of branches taken to connect an ancestor of a node to the node. Usually described by the set of nodes encountered along the path.

Binary tree: A binary tree is a tree where every node has 2 subtrees that are also binary trees. The subtrees may be empty. Each node has a left child and a right child. Our tree is NOT a binary tree because B has 3 children.

The following are NOT trees