Data Structure- B Tree

1. ..B-TREEB-TREE

2. • A B-TREE IS A TREE SATISFYING THE FOLLOWING PROPERTIES.A B-TREE IS A TREE SATISFYING THE FOLLOWING PROPERTIES.
1.1. EVERY NODE CONTAINS THE FOLLOWING FIELDSEVERY NODE CONTAINS THE FOLLOWING FIELDS
a.a. AN ARRAY TO HOLD THE KEY VALUESAN ARRAY TO HOLD THE KEY VALUES
b.b. A DATA ARRAY TO HOLD THE ASSOCIATED DATA VALUESA DATA ARRAY TO HOLD THE ASSOCIATED DATA VALUES
c.c. A POINTER ARRAY TO POINT TO THE CHILD NODESA POINTER ARRAY TO POINT TO THE CHILD NODES
d.d. THE NUMBER OF KEYS THAT IS CURRENTLY STORED, NTHE NUMBER OF KEYS THAT IS CURRENTLY STORED, N
e.e. A BOOLEAN VARIABLE TO INDICATE WHETHER THE NODEA BOOLEAN VARIABLE TO INDICATE WHETHER THE NODE
IS A LEAF NODE OR AN INTERNAL NODEIS A LEAF NODE OR AN INTERNAL NODE
2.2. EVERY NODE CAN STORE AT MOST 2*MD-1 NUMBER OF KEYSEVERY NODE CAN STORE AT MOST 2*MD-1 NUMBER OF KEYS
WHERE MD IS THE MINIMUM DEGREE OF THE B-TREE.WHERE MD IS THE MINIMUM DEGREE OF THE B-TREE.
3.3. EVERY NODE EXCEPT ROOT MUST CONTAIN AT LEAST MD NUMBEREVERY NODE EXCEPT ROOT MUST CONTAIN AT LEAST MD NUMBER
OF KEYS.OF KEYS.
4.4. THE KEYS ARE STORED IN SORTED ORDER WITHIN A NODE AND ITTHE KEYS ARE STORED IN SORTED ORDER WITHIN A NODE AND IT
SEPARATES THE KEY VALUES THAT ARE STORED IN THESEPARATES THE KEY VALUES THAT ARE STORED IN THE
CORRESPONDING SUBTREE.CORRESPONDING SUBTREE.
5.5. ALL THE LEAF NODES ARE IN THE SAME DEPTH FROM THE ROOT.ALL THE LEAF NODES ARE IN THE SAME DEPTH FROM THE ROOT.

3. 45
insert 45
insert 22
insert 90
insert 4
insert 77
insert 34
insert 37
insert 65
insert 45
insert 95
insert 23
insert 77
insert 33
insert 66
insert 29

4. 22 45
insert 45
insert 22
insert 90
insert 4
insert 77
insert 34
insert 37
insert 65
insert 45
insert 95
insert 23
insert 77
insert 33
insert 66
insert 29

5. 22 45 90
insert 45
insert 22
insert 90
insert 4
insert 77
insert 34
insert 37
insert 65
insert 45
insert 95
insert 23
insert 77
insert 33
insert 66
insert 29

6. 45
insert 45
insert 22
insert 90
insert 4
insert 77
insert 34
insert 37
insert 65
insert 45
insert 95
insert 23
insert 77
insert 33
insert 66
insert 29
4 22 90

7. 45
insert 45
insert 22
insert 90
insert 4
insert 77
insert 34
insert 37
insert 65
insert 45
insert 95
insert 23
insert 77
insert 33
insert 66
insert 29
4 22 77 90

8. 45
insert 45
insert 22
insert 90
insert 4
insert 77
insert 34
insert 37
insert 65
insert 45
insert 95
insert 23
insert 77
insert 33
insert 66
insert 29
4 22 34 77 90

9. 22 45
insert 45
insert 22
insert 90
insert 4
insert 77
insert 34
insert 37
insert 65
insert 45
insert 95
insert 23
insert 77
insert 33
insert 66
insert 29
4 77 9034 37

10. 22 45
insert 45
insert 22
insert 90
insert 4
insert 77
insert 34
insert 37
insert 65
insert 45
insert 95
insert 23
insert 77
insert 33
insert 66
insert 29
4 65 77 9034 37

11. 22 45
insert 45
insert 22
insert 90
insert 4
insert 77
insert 34
insert 37
insert 65
insert 45
insert 95
insert 23
insert 77
insert 33
insert 66
insert 29
4 65 77 9034 37
Key 45 already exists

12. 22 45 77
insert 45
insert 22
insert 90
insert 4
insert 77
insert 34
insert 37
insert 65
insert 45
insert 95
insert 23
insert 77
insert 33
insert 66
insert 29
4 6534 37 90 95

13. 22
insert 45
insert 22
insert 90
insert 4
insert 77
insert 34
insert 37
insert 65
insert 45
insert 95
insert 23
insert 77
insert 33
insert 66
insert 29
4 6523 34 37 90 95
77
45

14. 22
insert 45
insert 22
insert 90
insert 4
insert 77
insert 34
insert 37
insert 65
insert 45
insert 95
insert 23
insert 77
insert 33
insert 66
insert 29
4 6523 34 37 90 95
77
45
Key 77 already exists

15. 22 34
insert 45
insert 22
insert 90
insert 4
insert 77
insert 34
insert 37
insert 65
insert 45
insert 95
insert 23
insert 77
insert 33
insert 66
insert 29
4 6523 33 90 95
77
45
37