Graph and tree

1. Graph

2. What is Graph ?
A graph G = { V , E }; a finite set of ordered pairs, called
edges E, and vertices V.

3. Example of Graph:

4. Graph Definitions
Directed graph  Undirected graph
7
19
21
1
12
4
3
22
2
3
G
J
F
D
A
E C H
4

5. Adjacency Matrix:

6. Adjacency List:

7. Degree:

8. Implementation of Graph:
calculating degree:
#include <stdio.h>
int main ()
{
int graph[4][4],i,j,in=0,out=0;
for(i=0; i<4; i++)
{
for(j=0; j<4; j++)
{
scanf("%d",&graph[i][j]);
}
}

9. for(j=0; j<4; j++)
{
for(i=0; i<4; i++)
{
if (graph[i][j]==1)
in++;
}
printf("In degree of %d is %dn",j,in);
in=0;
}

10. for(i=0; i<4; i++)
{
for(j=0; j<4; j++)
{
if (graph[i][j]==1)
out++;
}
printf("Out degree of %d is %dn",i,out);
out=0;
}
return 0;
}

11. TREE

12. Introduction of a Tree
B C
FD E G
A

13. subtree
Tree Terminology
 Root
 Siblings
 Internal node
 External node
 Ancestors
 Descendant
 Depth
 Height
 Degree
 Subtree
A
B DC
G HE F
I J K

14. Binary Trees
 Each node has at most 2 children
10
17
159
6 5 8
Root node
Left subtree
Right child
Right child
Left child
14

15. Binary Search Tree:
17
199
6 12 25
15

16. Tree Traversal
Preorder
Data Left Right
<root><left><right>
F,D,B,A,C,E,J,G,I,H,K
void preorder(node *root){
if(root!=NULL){
printf(“%c”,root->data);
if(root->left!=NULL)
preorder(root->left);
if(root->right!=NULL)
preorder(root->right);
}
}
F
JD
I
E KB G
A C
Root
H
16

17. Tree Traversal
Inorder
<left><root><right>
A,B,C,D,E,F,G,H,I,J,K
void inorder(node *root){
if(root!=NULL){
if(root->left!=NULL)
inorder(root->left);
printf(“%c”,root->data);
if(root->right!=NULL)
inorder(root->right);
}
}
F
JD
I
E KB G
A C
Root
H
17

18. Tree Traversal
pOSTORDER
Left Right Data
<left><right><root>
A,C,B,E,D,H,I,G,K,J,F,A,B
void postorder(node *root){
if(root!=NULL){
if(root->left!=NULL)
postorder(root->left);
if(root->right!=NULL)
postorder(root->right);
printf(“%c”,root->data);
}
}
F
JD
I
E KB G
A C
Root
H
18

19. Thank You