The Tree Data StructureThe Tree Data Structure
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Guidelines and tips
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Tree Data Structure: Definition, Components, and Terminology, Summaries of Data Structures and Algorithms
An introduction to the tree data structure, covering its definition, components, and related terminology. The tree data structure is a rooted tree that stores information in nodes, with each node having zero or more children. Nodes are classified as internal or leaf, ordered or unordered, and the concepts of parents, children, siblings, paths, depth, height, ancestors, descendants, and subtrees are discussed. The document also includes examples using XHTML and CSS.
Typology: Summaries
2020/2021
1 / 35
This page cannot be seen from the preview
Don't miss anything!
Related documents
Partial preview of the text
Download Tree Data Structure: Definition, Components, and Terminology and more Summaries Data Structures and Algorithms in PDF only on Docsity!
The Tree Data StructureThe Tree Data Structure
2
Outline
In this topic, we will cover:
- Definition of a tree data structure and its components
- Concepts of:
- Root, internal, and leaf nodes
- Parents, children, and siblings
- Paths, path length, height, and depth
- Ancestors and descendants
- Ordered and unordered trees
- Subtrees
- Examples
- XHTML and CSS
4
Terminology
All nodes will have zero or more child nodes or children
- I has three children: J, K and L For all nodes other than the root node, there is one parent node
- H is the parent I 4.1.1.
5
Terminology
The degree of a node is defined as the number of its children: deg(I) = 3 Nodes with the same parent are siblings
- J, K, and L are siblings 4.1.1.
7
Terminology
Leaf nodes: 4.1.1.
8
Terminology
Internal nodes: 4.1.1.
10
Terminology
The shape of a rooted tree gives a natural flow from the root node, or just root 4.1.1.
11
Terminology
A path is a sequence of nodes (a 0 , a 1 , ..., an) where ak + 1 is a child of ak is The length of this path is n E.g., the path (B, E, G) has length 2 4.1.1.
13
Terminology
For each node in a tree, there exists a unique path from the root node to that node The length of this path is the depth of the node, e.g.,
- E has depth 2
- L has depth 3 4.1.1.
14
Terminology
Nodes of depth up to 17 9 14 17
4.1.1.
16
Terminology
The height of this tree is 17 17 4.1.1.
17
Terminology
If a path exists from node a to node b:
- a is an ancestor of b
- b is a descendent of a Thus, a node is both an ancestor and a descendant of itself
- We can add the adjective strict to exclude equality: a is a strict descendent of b if a is a descendant of b but a ≠ b The root node is an ancestor of all nodes 4.1.1.
19
Terminology
All descendants (including itself) of the indicated node 4.1.1.
20
Terminology
All ancestors (including itself) of the indicated node 4.1.1.