presentation about 2-3 tree(B tree)

1. RITAMBHARA
2-3 TREE-INSERTION

2. 2-3 Trees were developped by John hopcraft in 1974.
To keep the height of a binary search tree low, 2-3 trees were
developped.
A2-3 tree is a binary search tree that can have the following
nodes.
i) Leaf node
ii) 2-node
iii) 3-node
A 2-node contains a single data element (or) key element and it
has two children. X
L R

3. A 3- node contains two ordered Key elements (or) Data
Element and it has 3 children.
X | Y
L M R
3 -node
Two key elements are ordered i.e., x<y

4. Example of 2-3 tree:
40
25 65 | 85
20 35 55 70 95 | 102
Leaf nodes does not have child and one or two
data elements (or) key elements.

5. PROPERTIES
 Every internal node is a 2-node or a 3-node.
 Data or key elements are stored in sorted
order.
 Each node has either one data value or two
data values.
 Leaf nodes have no children and one or two
data elements or key elements.

6. Operation performed on 2-3 tree are:
i) Insert
ii) Delete
iii) Search
All the operations completed in o(logn)
time.
The time completely of 2-3 tree is o(log2n).

7. EXAMPLE
 45,67,88,34,12,77,23,55
 take 45 as root node
 Insert 67
67 is greater than 45, so it go right of 45
45
45 | 67

8. Insert 88
88 is greater than 67, so it go right of 67
45 | 67 | 88
Now, it is invalid tree
It break from middle…
67
45 88

9. Now insert 34
34 is lesser than 45, so 34 go left of 45..
67
34 | 45 88
Insert 12…

10. 12 is lesser than 34, so it go to left of
34..
67
12 | 34 | 45 88
Now, it is invalid
tree

11. 34 | 67
12 45 88
Insert 77
77 is lesser than 88, so 77 go to left of 88
34 | 67
12 45 77 | 88

12. Insert 23
23 is lesser than 12, so 23 is right of 12
34 | 67
12 | 23 45 77 | 88
Insert 55
55 is greater than 45, so 55 is right of 45

13. 34 | 67
12 | 23 45 |55 77 | 88