B-trees are used for indexing and have a specified order that determines the maximum number of keys per node. The document demonstrates inserting elements into an empty B-tree of order 3, showing how nodes split as they exceed the maximum 2 keys per node, with the splitting element moving up the tree. Elements are inserted into nodes based on being less than or greater than splitting keys, maintaining the binary search tree property.

1. B tree
B tree follow binary search tree property
Order of tree is the number of pointers stored in tree.
If order = 3 then number of key elements in each node =2 (i.e, order-1)
Btree is used for indexing
The node values are primary keys

2. Insertion into B tree
8
Insert the following elements into B-tree of order 3
8 5 7 1 3 9
Since order of Btree =3
Number of keys that can be stored in each node = 2
Number of pointers in each node =3 Keys
pointers

3. Insert 5
5
Since there is place to insert one more key in the root node, we insert 5 in the
root node itself
Since 5 is < 8 we insert 5 to the left of 8 in the root node
8

4. Insert 7
7
We cannot insert 7 in root node as each node can store only 2 keys
So of the three elements 5 7 and 8 , the middle element is 7
So we split as shown below.
In this way all the elements that are less than 7 is to the left of 7
And all the elements that are greater than 7 is to the right
5 8

5. Insert 1
7
Since 1 is < 7 , we move to the node that is left of root node
In left node, since 1< 5 we insert 1 as shown below
1 85

6. Insert 3
3
Since 3 is < 7 , we move to the node that is left of root node
In left node, since 1<3 and 3< 5 we have to insert 3 in the left node
As a node cannot store more than 2 keys we cannot insert 3
So n 1,3,5 the middle element is 3 and so we move 3 to the root node
As follows
1 8
7
5

7. Insert 9
3
1 8
7
5 9