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4. Insert the following letters into an empty B-tree of order 5 in the order given: BOX IN YOUR FINAL B-TREE. PGEVT DLAHBI YOSN F

4. Insert the following letters into an empty B-tree of order 5 in the order given: BOX IN YOUR FINAL B-TREE. PGEVT DLAHBI YOSN F

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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**Inserting Elements into a B-tree of Order 5** **Problem Statement:** Insert the following letters into an empty B-tree of order 5 in the order given and box in your final B-tree: **Sequence:** P G E V T D L A H B I Y O S N F **Solution Process:** A B-tree of order 5 is a self-balancing tree data structure that maintains sorted data and allows searches, sequential access, insertions, and deletions in logarithmic time. For a B-tree of order 5, every node can have at most 4 keys and at minimum 2 keys (except for the root which can have fewer keys). **Step-by-Step Insertion:** 1. Insert 'P' into the B-tree. 2. Insert 'G' into the B-tree and place it before 'P' since 'G' < 'P'. 3. Insert 'E' into the B-tree and place it before 'G'. 4. Insert 'V' into the B-tree. Now we have ['E', 'G', 'P', 'V'] in the root. 5. Insert 'T' into the B-tree. Node becomes full: ['E', 'G', 'P', 'T', 'V'] 6. Insert 'D' which causes the split since the root cannot accommodate more than 4 keys. The middle key 'P' moves up, and ['E', 'G', 'D'] becomes one child, and ['T', 'V'] becomes another. 7. Continue the insertion for 'L', 'A', 'H', 'B', 'I', 'Y', 'O', 'S', 'N', 'F' following similar procedures of splitting child nodes and promoting middle keys as necessary. **Note:** The detailed structure showing all the intermediary steps, splits, and promotion of keys would need a visual diagram for better understanding. Ensure that the final B-tree after inserting all the elements looks correctly balanced and follows the B-tree structural properties. Mark the final B-tree structure clearly with boxed nodes to denote the final arrangement. Visual diagrams for each step typically help to demonstrate the tree transformations more effectively. For educational purposes, detailed diagrams can be integrated into the explanation to show the insertion steps and resulting tree structure after each insertion to demonstrate how B-trees balance themselves during insertions.
Transcribed Image Text:**Inserting Elements into a B-tree of Order 5** **Problem Statement:** Insert the following letters into an empty B-tree of order 5 in the order given and box in your final B-tree: **Sequence:** P G E V T D L A H B I Y O S N F **Solution Process:** A B-tree of order 5 is a self-balancing tree data structure that maintains sorted data and allows searches, sequential access, insertions, and deletions in logarithmic time. For a B-tree of order 5, every node can have at most 4 keys and at minimum 2 keys (except for the root which can have fewer keys). **Step-by-Step Insertion:** 1. Insert 'P' into the B-tree. 2. Insert 'G' into the B-tree and place it before 'P' since 'G' < 'P'. 3. Insert 'E' into the B-tree and place it before 'G'. 4. Insert 'V' into the B-tree. Now we have ['E', 'G', 'P', 'V'] in the root. 5. Insert 'T' into the B-tree. Node becomes full: ['E', 'G', 'P', 'T', 'V'] 6. Insert 'D' which causes the split since the root cannot accommodate more than 4 keys. The middle key 'P' moves up, and ['E', 'G', 'D'] becomes one child, and ['T', 'V'] becomes another. 7. Continue the insertion for 'L', 'A', 'H', 'B', 'I', 'Y', 'O', 'S', 'N', 'F' following similar procedures of splitting child nodes and promoting middle keys as necessary. **Note:** The detailed structure showing all the intermediary steps, splits, and promotion of keys would need a visual diagram for better understanding. Ensure that the final B-tree after inserting all the elements looks correctly balanced and follows the B-tree structural properties. Mark the final B-tree structure clearly with boxed nodes to denote the final arrangement. Visual diagrams for each step typically help to demonstrate the tree transformations more effectively. For educational purposes, detailed diagrams can be integrated into the explanation to show the insertion steps and resulting tree structure after each insertion to demonstrate how B-trees balance themselves during insertions.
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