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1.9 b trees 02

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Krish_ver2

Data Structure- 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 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.
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
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
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
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
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
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
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
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
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
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
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
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
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

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1.9 b trees 02

  • 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