This document discusses B-trees, which are self-balancing search trees where all leaves are at the same level. It provides examples of constructing a B-tree by inserting keys in order, and describes how insertion and deletion operations are performed. Advantages of B-trees are that they are self-balancing and nodes at all leaf levels are equal. Disadvantages are that insertion and deletion algorithms are more complex than other search trees.

1. DIVYANSH
PARMARTHI
ROLL NO. :-
MCA/25016/18
BIRLA
INSTITUTE
OF
TECHNOLOGY

2. B- TREE
 A B-tree is an m-way tree.
 In a B- tree all leaves are on the same level.
 All non-leaf nodes except the root have at least m / 2 children.
 The number m should always be odd.
 A leaf node contains no more than m – 1 keys

3. Constructing a B- tree
 Suppose we start with an empty B-tree and keys arrive in the following
order:1 12 8 2 25 5 14 28 17 7 52 16 48 68 3 26 29 53 55 45
 We want to construct a B-tree of order 5
 The first four items go into the root:
 To put the fifth item in the root would violate condition
1 2 8 12

4.  Therefore, when 25 arrives, pick the middle key to make a new root
8
1 2 12 25

5. INSERTION
Inserting 6, 14, 28 we get :-
8
1 2 6 12 14 25 28

6.  Adding 17
the right leaf node would over-fill it, so we take the middle key, promote it
(to the root) and split the leaf
8 17
12 14 25 281 2 6
Adding :- 7, 52, 16, 48
8 17
12 14 25 281 2 6 16 48 527

7.  Adding 68
causes us to split the right most leaf, promoting 48 to the root, and adding
3- causes us to split the left most leaf, promoting 3 to the root adding -
26, 29, 53, 55
 Adding 45 causes a split of
and promoting 28 to the root then causes the root to split
3 8 17 48
52 53 55 6825 26 28 291 2 6 7 12 14 16
25 26 28 29

8. B-Trees 8
17
3 8 28 48
1 2 6 7 12 14 16 52 53 55 6825 26 29 45

9. 128
2 3 13 2710 11
Deleting 8 – It might force us to move another key up from one of the
children. It could either be the 3 from the 1st child or the 10 from the
second child.
However, neither child has more than the minimum number of children (3),
so the two nodes will have to be merged. Nothing moves up.
DELETION

10. 2 3
12
13 2710 11

11. ADVANTAGES
 It is a self balancing tree.
 It not a ling tree all the leaf nodes are at same level.

12. DISADVANTAGES
 Insertion and deletion are complex in B-tree .

13. REFERENCES
 https://courses.cs.washington.edu/courses/cse373/05wi
 http://cecs.wright.edu/~tkprasad/courses/cs707/L04-X-B-Trees

14. THANK
YOU