1) Trees are hierarchical data structures that store data in nodes connected by edges. They are useful for representing hierarchical relationships. 2) Binary search trees allow quick search, insertion, and deletion of nodes due to the organizational property that the value of each node is greater than all nodes in its left subtree and less than all nodes in its right subtree. 3) Common tree traversal algorithms include preorder, inorder, and postorder traversals, which visit nodes in different orders depending on whether the left/right children or root is visited first.

1. PRESENTATION ON
Tree
in
Data Structure
1

2. DATA STRUCTURE
Store and organize data in computer.
Linear Data Structure
Arrays
Linked List
Stacks
Queues 2

3. LOGIC OF TREE
Used to represent hierarchica data.
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Shawon(CTO ) Tarun(Presedent)
Bithi Moni Sila Rashel Raj
Dola Shakila Riaj Shakib 3

4. Used to represent hierarchical data.
Shuvo(CEO)
Shawon(CTO ) Tarun(Presedent)
Bithi Moni Sila Rashel Raj
Dola Shakila Riaj Shakib 4

5.  A Collection of entities called Nodes.
 Tree is a Non-Linear Data Structure.
 It’s a hierarchica Structure.
TREE
Nodes
5

6. Root-The top most Node.
Children
Parents
Siblings- Have same parents.
Leaf- Has no Child.
RELATION OF TREE
1
3
2
4
6
5
8
7
11109
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7. EDGES, DEPTH, HEIGHT
 Edges: If a tree have N nodes
It have N-1 edges.
 Depth of x: Length of path from
Root to x.
 Hight of x: No. Of edges in longest
Path from x to a leaf
Nodes
Leaf7

8. SOME APPLICATION OF TREE IN COMPUTER SCIENCE
1. Storing naturally hierarchicl data- File system.
2. Organige data for quick search, insertion, deletion- Binary search
tree.
3. Dictionary
4. Network Routing Algorithm.
8

9. Each node can have at most 2 childern.
A node have only left and right child or
Only left child or
Only right child.
A leaf node has no left or right child.
A leaf node has only NULL.
BINARY TREE
Root
Right- child
of root.
Left-child
of root
Leaf
NULL9

10. STRICT/PROPER BINARY TREE
Each node can have either
2 or 0 child
Root
10

11. COMPLETE BINARY TREE
 The last level is completely filled.
 All nodes are as left as possible.
Root
L-2
L-3
L-4
L-1
11

12. PARFECT BINARY TREE
All the levels are comletely filled.
Root
L-2
L-3
L-1
12

13. WE CAN IMPLEMENT BINARY TREE USING
A) Dynamically created nodes.
struct node
{
int data;
struct node* left;
struct node* right
}
2
4 6
13

14. OR
0 1 2 3 4 5 6
B) Arrays: It only works “complete Binary tree”.
For node at index i;
Left-child-index=2i+1
Right-child-index=2i+2
2 4 1 5 8 7 9
14

15. IMPLEMENT OF BINARY SEARCH TREE
Value of all the nodes in left subtree is Lesser or Equal.
Value of all the nodes in right subtree is greater.
Left-Subtree Right-Subtree
(Lesser) (Greater)
15

16. EXAMPLE
 15>10-Left
 15<20-Right
 10>8-Left
 10<12-Right
 20>17-Left
 20<25-Right
15
2010
12 258 17
Root
16

17. BINARY TREE TRAVERSAL
Tree traversal
Breadth-first or
Lever-order
F,D,J,B,E,G,K,A,C,I,H
Depth-first
Preorder, Inorder &
Postorder
F
JD
I
E KB G
A C
Root
H
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18. PREORDER(DLR)
Data Left Right
<root><left><right>
F,D,B,A,C,E,J,G,I,H,K
Void Postorder(struct bstnode* root)
{
if(root==NULL)
Postorder(root->right);
Postordrt(root->right);
printf(“%c”,root->data);
}
F
JD
I
E KB G
A C
Root
H
18

19. INORDER(LDR)
Left Data Right
<left><root><right>
A,B,C,D,E,F,G,H,I,J,K
Void Inorder(struct bstnode* root)
{
if(root==NULL) return;
Inorder(root->left);
printf(“%c”,root->data);
Inorder(root->right);
}
F
JD
I
E KB G
A C
Root
H
19

20. POSTORDER(LRD)
Left Right Data
<left><right><root>
A,C,B,E,D,H,I,G,K,J,F,A,B
Void Postorder(struct bstnode* root)
{
if(root==NULL)
Postorder(root->right);
Postordrt(root->right);
printf(“%c”,root->data);
}
F
JD
I
E KB G
A C
Root
H
20

21. SEARCH AN ELEMENT IN BST
bool Search( bstnode* root, data type)
{
if (root==NULL) return false;
else if(root->data == data) return true;
else if(root->data <= data)
return Search(root->left, data);
else
return Search(root->right, data);
}
12
155
14
7 173 13
8 11
Root
21

22. DLELETE A NODE FROM BST
 There are three items to delete.
 Case 1: No Child
 Case 2: One Child
 Case 3: Two Child
12
155
14
7 173 13
8 11
Root
22

23. CASE 1: NO CHILD
 Remove to reference of the Node
 From it’s parent &
 Return NULL
12
155
14
7 173 13
8 11
Root
23

24. CASE 2: ONE CHILD
 Find the Node to Delete
 Link it’s parent to this only child.
 Remain attached to the tree.
12
155
14
7 173 13
8 11
Root
24

25. CASE 3: TWO CHILD
Two way to delete.
1.
Find minimum in right
Copy the value in targetted node
Delete duplicate from right subtree.
12
155
14
7 173 13
8 11
Root
25

26. CASE 3: TWO CHILD
2.
Find maximum in left
Copy the value in targetted node
Delete duplicate from left-subtree.
12
155
14
7 173 13
8 11
Root
26

27. RUNNING TIME OF OPERATION
Operation Array Link List Binary Search
Tree(average case)
Search(x)-Search
for an element x.
O(Log n) O(n) O(Log n)
Insertion(x)-Insert
an element x.
O(n) O(1) O(Log n)
Remove(x)-
Remove an
element x.
O(n) O(n) O(Log n)
27

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