Trees and Tree Traversals

1
Trees and Tree Traversals
CS146 Lecture 7

• Prof. Sin-Min Lee
• Department of Computer Science
• San Jose State University

2
Outline

• Graph-Tree
• Basic Definition
• Rooted Trees
• Applications of Trees
• Game Tree

3
(No Transcript)
4
(No Transcript)
5
(No Transcript)
6
(No Transcript)
7
(No Transcript)
8
(No Transcript)
9
Basic Definition

• Tree
• a connected graph with no simple circuits
• No multiple edges or loops
• Theorems
• a graph is a tree iff a unique simple path
  between any two of its vertices
• A tree with n vertices has n 1 edges
• Forest

10
(No Transcript)
11
(No Transcript)
12
Rooted Tree

• Is a directed graph T satisfying
• It is a tree when the directions of the edges are
  ignored.
• There is a unique vertex r (called the root) such
  that the indegree of r is 0 and the indegree of
  any other vertex is 1.
• Examples family tree, position tree
• Terminology parent, child, terminal vertex,
  internal vertex, subtree, ancestor, descendant
• An m-ary tree, A full m-ary tree, A balanced
  m-ary tree with height h

13
Order Rooted Tree

• Is a rooted tree where the children of each
  internal vertex are ordered.
• ordered binary tree two child, left/right

14
(No Transcript)
15
(No Transcript)
16
(No Transcript)
17
Tree Traversal

• Is a procedure that systematically visits every
  vertex of an ordered rooted tree
• Three most commonly used algorithms
• Preorder traversal.
• Inorder traversal.
• Postorder traversal.

18
(No Transcript)
19
(No Transcript)
20
Example1

• List three kinds of traversals.

21
Binary Search Trees

• Is a binary tree in which each vertex is labeled
  with a key such that
• No two vertices have the same key
• If vertex u belongs to the left subtree of vertex
  v, then u ? v
• If vertex w belongs to the right subtree of
  vertex v, then v ? w
• construction algorithm

22
(No Transcript)
23
S122223s4262263
2S2222324262263264
26424260 161018
2S-SS264-1
150 years to get this produce
24
  A Pale Blue Planet Mourns the Passing of a
Passionate Scientist
Carl Sagan (1934-1996.12.20)
25
(No Transcript)
26
(No Transcript)
27
(No Transcript)
28
(No Transcript)
29
(No Transcript)
30
(No Transcript)
31
(No Transcript)
32
(No Transcript)
33
(No Transcript)
34
(No Transcript)
35
(No Transcript)
36
(No Transcript)
37
(No Transcript)
38
(No Transcript)
39
(No Transcript)
40
(No Transcript)
41
(No Transcript)
42
(No Transcript)
43
(No Transcript)
44
(No Transcript)
45
(No Transcript)
46
(No Transcript)