1. Data Structures and Algorithms
Prof. Ajit A. Diwan
Prof. Ganesh Ramakrishnan
Prof. Deepak B. Phatak
Department of Computer Science and Engineering
IIT Bombay
Session: Basic Operations on Binary Tree
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

2. Binary Tree 60 40 20 25 23 90 80 95 85 Nodes Parent Left Child
Right Child
Can have either left, right, or both
Leaf Node
Does not have left and right child 60 40 20 25 23 90 80 95 85
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

3. Represented Internally as
Each node in the tree is represented with
Data: The element
leftIndex: Index of the left child
rightIndex: Index of the right child
Data
Left Index
Right Index
Data
Left Index
Right Index
Data
Left Index
Right Index
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

4. Represented Internally as
Data of the left child is less than the data of the parent
Data of the right child is greater than the data of the parent
Value of -1 in leftIndex or rightIndex denotes that it does not have a left or right child respectively At
Index: 10 1 2 10 8 12 1 2 At
Index: 1 At
Index: 2 8 -1 12 -1
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

5. Basic Operations Making a node (Root) Inserting Insert Left node
Insert Right node
Traversing
Pre-Order
In-Order
Post-Order
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

6. Making a Node (60) 60 Initialized only when the tree is empty
Make node with data as ‘60’
Data: 60
Left Index: -1
Right Index: -1 60
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

7. Insert (40)
‘40 < 60’, and there is no left child of ‘60’, so insert ‘40’ as left child of ‘60’
Left Index of 60: 1
Data: 40
Left Index: -1
Right Index: -1 60 1 40
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

8. Insert (20) 60 40 20 Traverse from root
‘20 < 60’, ‘20 < 40’, and there is no left child of ‘40’, so insert ‘20’ as left child of ‘40’
Left Index of 40: 2
Data: 20
Left Index: -1
Right Index: -1 60 1 40 2 20
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

9. Insert (25) 60 40 20 25 Traverse from root ‘25 < 60’, ‘25 < 40’,
Now, ‘25 > 20’, and there is no right child of ‘20’,
so insert ‘25’ as right child of ‘20’
Right Index of 20: 3
Data: 25
Left Index: -1
Right Index: -1 60 1 40 2 20 3 25
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

10. Insert (90) 60 40 90 20 25 Traverse from root
‘90 > 60’, and there is no right child of ‘60’,
so insert ‘90’ as right child of ‘60’
Right Index of 60: 4
Data: 90
Left Index: -1
Right Index: -1 60 1 4 40 90 2 20 3 25
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

11. Insert (23) 60 40 90 20 25 23 Traverse from root
‘23 < 60’, ‘23 < 40’,
‘23 > 20’, but right child (25) is present, so continue comparing.
‘23 < 25’, and there is no left child of ‘25’, so insert ‘23’ as left child of ‘25’
Left Index of 25: 5
Data: 23
Left Index: -1
Right Index: -1 60 1 4 40 90 2 20 3 25 5 23
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

12. Insert (95) 60 40 90 20 95 25 23 Traverse from root
‘95 > 60’, ‘95 > 90’, and there is no right child of ‘90’, so insert ‘95’ as right child of ‘90’
Right Index of 90: 6
Data: 95
Left Index: -1
Right Index: -1 60 1 4 40 90 2 6 20 95 3 25 5 23
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

13. Insert (80) 60 40 90 20 80 95 25 23 Traverse from root ‘80 > 60’,
But, ‘80 < 90’, and there is no left child of ‘90’, so insert ‘80’ as left child of ‘90’
Left Index of 90: 7
Data: 80
Left Index: -1
Right Index: -1 60 1 4 40 90 2 7 6 20 80 95 3 25 5 23
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

14. Insert (85) 60 40 90 20 80 95 25 85 23 Traverse from root
‘85 > 60’, ‘85 < 90’, but left child of ‘90’ is present, so continue
‘85 > 80’ and there is no right child of ‘80’, so insert ‘85’ as right child of ‘80’
Right Index of 80: 8
Data: 85
Left Index: -1
Right Index: -1 60 1 4 40 90 2 7 6 20 80 95 3 8 25 85 5 23
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay

15. Thank you
Ajit A. Diwan, Ganesh Ramakrishnan, and Deepak B. Phatak, IIT Bombay