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Exercise 3: Multi-way Trees A way to reduce the height of tree and ensure balance is to allow multiple children of nodes. In your class you learned 2-3 trees which allows up to 2 keys in a node, and the number of children is equal to the number of keys + 1. B-trees extend this concept to any arbitrary number of keys (usually number of keys is even and number of children (equal to number of keys+1) is odd). Assume we want to design a 5-way B-Tree. This will mean that there can be maximum 4 keys in a node, and if the number of keys becomes 5, we can split it into two (the same way we split 2-3 tree when number of keys becomes 3). Design a 5-way B-tree. Starting with an empty tree, insert the following keys in order. 2.3.5. 7. 10. 50. 22. 44. 45. 55. 66. 68. 70. 17. 6. 21. 67

Exercise 3: Multi-way Trees A way to reduce the height of tree and ensure balance is to allow multiple children of nodes. In your class you learned 2-3 trees which allows up to 2 keys in a node, and the number of children is equal to the number of keys + 1. B-trees extend this concept to any arbitrary number of keys (usually number of keys is even and number of children (equal to number of keys+1) is odd). Assume we want to design a 5-way B-Tree. This will mean that there can be maximum 4 keys in a node, and if the number of keys becomes 5, we can split it into two (the same way we split 2-3 tree when number of keys becomes 3). Design a 5-way B-tree. Starting with an empty tree, insert the following keys in order. 2.3.5. 7. 10. 50. 22. 44. 45. 55. 66. 68. 70. 17. 6. 21. 67

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
Problem 1PE
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Exercise 3: Multi-way Trees A way to reduce the height of tree and ensure balance is to allow multiple children of nodes. In your class you learned 2-3 trees which allows up to 2 keys in a node, and the number of children is equal to the number of keys + 1. B-trees extend this concept to any arbitrary number of keys (usually number of keys is even and number of children (equal to number of keys+1) is odd). Assume we want to design a 5-way B-Tree. This will mean that there can be maximum 4 keys in a node, and if the number of keys becomes 5, we can split it into two (the same way we split 2-3 tree when number of keys becomes 3). Design a 5-way B-tree. Starting with an empty tree, insert the following keys in order. 2, 3, 5, 7, 10, 50, 22, 44, 45, 55, 66, 68, 70, 17, 6, 21, 67
Transcribed Image Text:Exercise 3: Multi-way Trees A way to reduce the height of tree and ensure balance is to allow multiple children of nodes. In your class you learned 2-3 trees which allows up to 2 keys in a node, and the number of children is equal to the number of keys + 1. B-trees extend this concept to any arbitrary number of keys (usually number of keys is even and number of children (equal to number of keys+1) is odd). Assume we want to design a 5-way B-Tree. This will mean that there can be maximum 4 keys in a node, and if the number of keys becomes 5, we can split it into two (the same way we split 2-3 tree when number of keys becomes 3). Design a 5-way B-tree. Starting with an empty tree, insert the following keys in order. 2, 3, 5, 7, 10, 50, 22, 44, 45, 55, 66, 68, 70, 17, 6, 21, 67
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