. B-TREE B-TREE
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.B-TREEB-TREE
• 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 NODE IS A LEAF A BOOLEAN VARIABLE TO INDICATE WHETHER THE NODE IS A LEAF NODE OR AN INTERNAL NODENODE OR AN INTERNAL NODE
2.2. EVERY NODE CAN STORE AT MOST 2*MD-1 NUMBER OF KEYS WHERE MD IS THE EVERY NODE CAN STORE AT MOST 2*MD-1 NUMBER OF KEYS WHERE MD IS THE MINIMUM DEGREE OF THE B-TREE.MINIMUM DEGREE OF THE B-TREE.
3.3. EVERY NODE EXCEPT ROOT MUST CONTAIN AT LEAST MD NUMBER OF KEYS.EVERY NODE EXCEPT ROOT MUST CONTAIN AT LEAST MD NUMBER OF KEYS.
4.4. THE KEYS ARE STORED IN SORTED ORDER WITHIN A NODE AND IT SEPARATES THE KEYS ARE STORED IN SORTED ORDER WITHIN A NODE AND IT SEPARATES THE KEY VALUES THAT ARE STORED IN THE CORRESPONDING SUBTREE. THE KEY VALUES THAT ARE STORED IN THE 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.
6.6. THE POINTER VALUES OF LEAF NODES ARE UNDEFINED.THE POINTER VALUES OF LEAF NODES ARE UNDEFINED.
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insert 45insert 22insert 90insert 4insert 77insert 34insert 37insert 65insert 45insert 95insert 23insert 77insert 33insert 66insert 29
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45
insert 45insert 22insert 90insert 4insert 77insert 34insert 37insert 65insert 45insert 95insert 23insert 77insert 33insert 66insert 29
22
45
90
insert 45insert 22insert 90insert 4insert 77insert 34insert 37insert 65insert 45insert 95insert 23insert 77insert 33insert 66insert 29
45
insert 45insert 22insert 90insert 4insert 77insert 34insert 37insert 65insert 45insert 95insert 23insert 77insert 33insert 66insert 29
4 22 90
45
insert 45insert 22insert 90insert 4insert 77insert 34insert 37insert 65insert 45insert 95insert 23insert 77insert 33insert 66insert 29
4 22 77 90
45
insert 45insert 22insert 90insert 4insert 77insert 34insert 37insert 65insert 45insert 95insert 23insert 77insert 33insert 66insert 29
4 22 34 77 90
22 45
insert 45insert 22insert 90insert 4insert 77insert 34insert 37insert 65insert 45insert 95insert 23insert 77insert 33insert 66insert 29
4 77
90
34 37
22 45
insert 45insert 22insert 90insert 4insert 77insert 34insert 37insert 65insert 45insert 95insert 23insert 77insert 33insert 66insert 29
4 65
77
90
34 37
22 45
insert 45insert 22insert 90insert 4insert 77insert 34insert 37insert 65insert 45insert 95insert 23insert 77insert 33insert 66insert 29
4 65
77
90
34 37
Key 45 already exists
22 45 77
insert 45insert 22insert 90insert 4insert 77insert 34insert 37insert 65insert 45insert 95insert 23insert 77insert 33insert 66insert 29
4 65
34 37
90
95
22
insert 45insert 22insert 90insert 4insert 77insert 34insert 37insert 65insert 45insert 95insert 23insert 77insert 33insert 66insert 29
4 65
23 34
37
90
95
77
45
22
insert 45insert 22insert 90insert 4insert 77insert 34insert 37insert 65insert 45insert 95insert 23insert 77insert 33insert 66insert 29
4 65
23 34
37
90
95
77
45
Key 77 already exists
22 34
insert 45insert 22insert 90insert 4insert 77
insert 34insert 37insert 65insert 45insert 95insert 23insert 77insert 33insert 66insert 29
4 65
23
33
90
95
77
45
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