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A B-tree of order 4 is built from scratch by 10 successive insertions. What is the maximum number of node splitting operations that may take place?
- a)3
- b)4
- c)5
- d)6
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A B-tree of order 4 is built from scratch by 10 successive insertions....
A B-tree is similar to 2-3 tree. Consider a B-tree of order 4.
A B-tree of order m contains n records and if each contains b records on the average then the tree has about [ n / b ] leaves, if we split k nodes along the path from leaves then
in given problem n = 10, b = 3, m = 4
so,
Most Upvoted Answer
A B-tree of order 4 is built from scratch by 10 successive insertions....
Solution:
B-tree of order 4 means that each node can have at most 4 children. The root node can have at least 2 children. We need to insert 10 keys in the B-tree.
Maximum number of splitting operations that may take place can be calculated as follows:
1. Insertion of 1st key:
- Create a new node and insert the key.
- No split operation is required.
2. Insertion of 2nd key:
- Insert the key in the root node.
- No split operation is required.
3. Insertion of 3rd key:
- Insert the key in the root node.
- No split operation is required.
4. Insertion of 4th key:
- Insert the key in the root node.
- No split operation is required.
5. Insertion of 5th key:
- Insert the key in the root node.
- No split operation is required.
6. Insertion of 6th key:
- Insert the key in the root node.
- No split operation is required.
7. Insertion of 7th key:
- Insert the key in the root node.
- No split operation is required.
8. Insertion of 8th key:
- Insert the key in the root node.
- Split operation is required as the root node already has 4 children.
- The root node is split into two nodes, and the middle key is promoted to the parent node.
9. Insertion of 9th key:
- Insert the key in the appropriate child node.
- No split operation is required.
10. Insertion of 10th key:
- Insert the key in the appropriate child node.
- No split operation is required.
Therefore, the maximum number of node splitting operations that may take place is 3. Hence, the correct option is A.
B-tree of order 4 means that each node can have at most 4 children. The root node can have at least 2 children. We need to insert 10 keys in the B-tree.
Maximum number of splitting operations that may take place can be calculated as follows:
1. Insertion of 1st key:
- Create a new node and insert the key.
- No split operation is required.
2. Insertion of 2nd key:
- Insert the key in the root node.
- No split operation is required.
3. Insertion of 3rd key:
- Insert the key in the root node.
- No split operation is required.
4. Insertion of 4th key:
- Insert the key in the root node.
- No split operation is required.
5. Insertion of 5th key:
- Insert the key in the root node.
- No split operation is required.
6. Insertion of 6th key:
- Insert the key in the root node.
- No split operation is required.
7. Insertion of 7th key:
- Insert the key in the root node.
- No split operation is required.
8. Insertion of 8th key:
- Insert the key in the root node.
- Split operation is required as the root node already has 4 children.
- The root node is split into two nodes, and the middle key is promoted to the parent node.
9. Insertion of 9th key:
- Insert the key in the appropriate child node.
- No split operation is required.
10. Insertion of 10th key:
- Insert the key in the appropriate child node.
- No split operation is required.
Therefore, the maximum number of node splitting operations that may take place is 3. Hence, the correct option is A.
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A B-tree of order 4 is built from scratch by 10 successive insertions. What is the maximum number of node splitting operations that may take place?a)3b)4c)5d)6Correct answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about A B-tree of order 4 is built from scratch by 10 successive insertions. What is the maximum number of node splitting operations that may take place?a)3b)4c)5d)6Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A B-tree of order 4 is built from scratch by 10 successive insertions. What is the maximum number of node splitting operations that may take place?a)3b)4c)5d)6Correct answer is option 'A'. Can you explain this answer?.
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