Tree Operations

TREE-OPERATIONS
ASADULLAH TAREEN
asadullah.tareen@gmail.com
Ghazni University
Computer Science Department
©Sem-II-2017
ALGORITHM & DATA-
STRUCTURE

Outline
This Topic Will Cover Tree Operations:
 1. Insertion of a Node into a tree
 2. Deletion of a Node from a tree
 Cases:
2.1 Case: The node to be deleted is a leaf
2.2 Case: The node to be deleted has 1 child
2.3 Case: The node to be deleted has 2 children
Tree Operations
27-Sep-2017 2Lecturer: Asadullah Tareen Ghazni University Computer Science Department

Insert Node
Given a Sorted List
5 8 9 13 21 44 45 46
1.1
Tree Operations

Insert Node
Given a Sorted List
5 8 9 13 21 44 45 46
If 14 is inserted, the list become:
5 8 9 13 14 21 44 45 46
1.1
Tree Operations

Insert Node
Given a Sorted List
5 8 9 13 21 44 45 46
5 8 9 13 14 21 44 45 46
1.1
Tree Operations

Insert Node
Given a Sorted List
5 8 9 13 21 44 45 46
5 8 9 13 14 21 44 45 46
FEATURES OF A SORTED LIST IS PRESERVED
1.1
Tree Operations

Insert Node
Given a Sorted List
5 8 9 13 21 44 45 46
5 8 9 13 14 21 44 45 46
Features of a Sorted List is Preserved
So
WHAT ARE THE FEATURES OF A SORTED LIST ????
1.1
Tree Operations

Insert Node
Given a BST
1.1
Tree Operations

Insert Node
Given a BST
1.1
Tree Operations
64
33
88
7 99
10

Insert Node
Given a BST
If 14 to be inserted
1.1
Tree Operations
64
33
88
7 99
10

Insert Node
Given a BST
If 14 to be inserted
1.1
Tree Operations
64
33
88
7 99
10
How does the new BST look like ?

Insert Node
Given a BST
If 14 to be inserted,
1.1
Tree Operations
64
33
88
7 99
10
How does the new BST look like ?
How do you do it?

Insert Node
Given a BST
Are the features of a BST preserved???
1.1
Tree Operations
64
33
88
7 99
10
14

Insert Node
Algorithm to Insert 14
1.1
Tree Operations
64
33
88
7 99
10

Insert Node
1.1
Tree Operations
64
33
88
7 99
10
14 < 64?

Insert Node
1.1
Tree Operations
64
33
88
7 99
10
14 < 10?

Insert Node
1.1
Tree Operations
64
33
88
7 99
10
14 < 33?

Insert Node
1.1
Tree Operations
64
33
88
7 99
10
NULL

Insert Node
1.1
Tree Operations
64
33
88
7 99
10
Insert here
14

Insert Node
1.1
Tree Operations
64
33
88
7 99
10
14

Insert Node
Now try to Insert 99
1.1
Tree Operations
64
33
88
7 99
10
14
99 < 64 ?

Insert Node
1.1
Tree Operations
64
33
88
7 99
10
14
99 < 88?

Insert Node
1.1
Tree Operations
64
33
88
7 99
10
14
99 < 99 ?

Insert Node
This algorithm is not so effective
Try building a BST using the Same algorithm for the
following Sequence:
K N G I C U
K U C I N G
C G I K N U
1.1
Tree Operations

Insert Node
ALKHWARIZMI:
• Inserting Node in such algorithm is less effective (insert
algorithms described above to the following sequence:)
K N G I C U
K U C I N G
C G I K N U
1.1
Tree Operations

Insert Node
This algorithm is not so effective
Try building a BST using the Same algorithm for the
following Sequence:
K N G I C U
K U C I N G
C G I K N U
It is difficult to produce a balanced Tree
One way is using the AVL Tree algorithm
1.1
Tree Operations

Insert Node
• Try to develop PGD ( Proper Generalized Decompositions) use insert
algorithms described above to the following sequence:
K N G I C U
K U C I N G
C G I K N U
• It is difficult to produce a balanced Tree
•  one way is using the AVL Tree algorithm
1.1
Tree Operations

Delete Node
3 Cases:
I. The node to be deleted is a leaf
II. The node to be deleted has 1 child
III. The node to be deleted has 2 children
2
Tree Operations

Delete Node (1st Case)
To delete D:
2.1
Tree Operations
M
E
D
P
B VN
T ZA

To delete D:
2.1
Tree Operations
M
E
D
P
B VN
T ZA

To delete D:
2.1
Tree Operations
M
E
D
P
B VN
T ZA
Parent

To delete D:
2.1
Tree Operations
M
E
D
P
B VN
T ZA
Parent
x

To delete D:
2.1
Tree Operations
M
E
D
P
B VN
T ZA
Parent
x
Set the right child of Parent as null

To delete D:
2.1
Tree Operations
M
E
D
P
B VN
T ZA
Parent
x
Free X

To delete D:
2.1
Tree Operations
M
E P
B VN
T ZA
Parent
x
Free X

Delete Node (2nd Case)
To delete E:
2.2
Tree Operations
M
E
D
P
B VN
T ZA

To delete E:
2.2
Tree Operations
M
E
D
P
B VN
T ZA

To delete E:
2.2
Tree Operations
M
E
D
P
B VN
T ZA
x
Parent
Set the Lchild (@ Rchild) of x as the Lchild (@ Rchild) of parent

To delete E:
2.2
Tree Operations
M
E
D
P
B VN
T ZA
x
Parent

To delete E:
2.2
Tree Operations
M
E
D
P
B VN
T ZA
x
Parent
Free x

To delete E:
2.2
Tree Operations
M
D
P
B VN
T ZA
Parent
Free x

To delete E:
2.2
Tree Operations
M
D
PB
VN
T Z
A
Parent
Free x

Delete Node (3rd Case)
To delete P:
2.3
Tree Operations
M
E
D
P
B VN
T ZA

To delete P:
2.3
Tree Operations
M
E
D
P
B VN
T ZA
Parent
x

To delete P:
2.3
Tree Operations
M
E
D
P
B VN
T ZA
Parent
xDetermine the next node
based on Inorder(LNR)
*Usually, the Inorder node has only one child or no children at all

To delete P:
2.3
Tree Operations
M
E
D
P
B VN
T ZA
Parent
xDetermine the next node
based on Inorder(LNR)
y
Parent of y

To delete P:
2.3
Tree Operations
M
E
D
P
B VN
T ZA
Parent
x
y
Parent of y
Copy
x->data = y->data

To delete P:
2.3
Tree Operations
M
E
D
P
B VN
T ZA
Parent
x
y
Parent of y
Copy
x->data = y->data
x = y

To delete P:
2.3
Tree Operations
M
E
D
P
B VN
T ZA
Parent
x
y
Parent of y
Delete T

To delete P:
2.3
Tree Operations
M
E
D
P
B VN
T ZA
Parent
x
y
Parent of y
Delete T (as in case 1)
parent_y->Lchild = NULL

To delete P:
2.3
Tree Operations
M
E
D
P
B VN
T ZA
Parent
y
Parent of y

To delete P:
2.3
Tree Operations
M
E
D
T
B VN
ZA
Parent
Parent of y

Your
?

Tree Operations

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