# Chapter 6 - PowerPoint PPT Presentation

PPT – Chapter 6 PowerPoint presentation | free to download - id: 84fb13-YjMyZ

The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
Title:

## Chapter 6

Description:

### Chapter 6 Trees Notice that in a tree, there is exactly one path from the root to each node Trees linked lists, stacks, and queues which are linear data ... – PowerPoint PPT presentation

Number of Views:7
Avg rating:3.0/5.0
Slides: 12
Provided by: stf89
Category:
Tags:
Transcript and Presenter's Notes

Title: Chapter 6

1
Chapter 6 Trees
2
Notice that in a tree, there is exactly one path
from the root to each node
3
Trees
• linked lists, stacks, and queues which are linear
data structures
• A tree is a nonlinear data structure a tree is a
collection of nodes connected by edges
• root at the top
• the leaves (i.e., terminal nodes) at the bottom
• The root has no parent Leaves, on the other
hand, have no children, or rather, their children
are empty structures

4
A Recursive Definition
• 1. An empty structure is a tree (a tree is a
collection of nodes and the collection can be
empty)
• 2. If T1, , Tk are trees, then the structure
whose root has as its children the roots of T1,
, Tk is also a tree
• 3. Only structures generated by rules 1 and 2
are trees

5
A Recursive Definition (contd)
ROOT OF TREE T
T2
T3
T1
Tk
SUBTREES
6
An Example
A
B
C
D
E
H
G
F
I
N nodes, N-1 edges in a tree.
7
Some Definitions
• Nodes with no children are leaves (C,E,F,H,I),
they are also called external nodes. Nodes which
are not leaves are called internal nodes
• Nodes with the same parents are siblings
(B,C,D,E) and (G,H)
• A path from node ni to node nj is the sequence of
directed edges from ni to nj
• The level or depth of a node ni is the number of
edges from the root to ni. The depth of the root
is 0

8
Some Definitions (contd)
• The height of a node ni is the length of the
longest path from ni to a leaf. The height of a
leaf node is 0
• The height of a tree is equal to the height of
the root

9
Binary Trees An Informal Definition
• A binary tree is a tree in which no node can have
more than two children
• Each node has 0, 1, or 2 children

10
Binary Trees A Recursive Definition
• 1. An empty structure is a binary tree
• 2. If T1 and T2 are binary trees, then the
structure whose root has as its children the
roots of T1 and T2 is also a binary tree
• 3. Only structures generated by rules 1 and 2
are binary trees

11
Trees vs. Binary Trees
• No node in a binary tree may have more than 2
children, whereas there is no limit on the number
of children of a node in a tree