Consider the AVL Tree below. Use the AVL Tree Deletion algorithm to delete 0068 from the tree. List the nodes of the resulting tree in pre-order traversal order separated by one blank character. For example, the tree below can be described in the above format as: 64 33 20 55 40 60 70 68 95 98

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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Consider the AVL Tree shown in the diagram. You are required to use the AVL Tree Deletion algorithm to delete the node with the value 0068 from the tree.

After performing the deletion, list the nodes of the resulting tree in pre-order traversal order, separated by a single blank space. For instance, the tree before deletion can be described in pre-order format as: 

64 33 20 55 40 60 70 68 95 98

### Explanation of the AVL Tree Diagram:

- **Root Node**: 0064, with a balance factor of 4.
- **Left Subtree of Root**:
  - Node 0033, with a balance factor of 3.
  - Left child: 0020, with a balance factor of 1.
  - Right child: 0055, with a balance factor of 2.
    - Left child: 0040, with a balance factor of 1.
    - Right child: 0060, with a balance factor of 1.
  
- **Right Subtree of Root**:
  - Node 0070, with a balance factor of 3.
  - Left child: 0068, with a balance factor of 2.
  - Right child: 0095, with a balance factor of 2.
    - Right child: 0098, with a balance factor of 1. 

The numbers inside each node represent the node's balance factor (the height difference between the left and right subtrees).

Use this information to correctly re-balance the tree after deleting node 0068 and perform a pre-order traversal on the updated tree.
Transcribed Image Text:Consider the AVL Tree shown in the diagram. You are required to use the AVL Tree Deletion algorithm to delete the node with the value 0068 from the tree. After performing the deletion, list the nodes of the resulting tree in pre-order traversal order, separated by a single blank space. For instance, the tree before deletion can be described in pre-order format as: 64 33 20 55 40 60 70 68 95 98 ### Explanation of the AVL Tree Diagram: - **Root Node**: 0064, with a balance factor of 4. - **Left Subtree of Root**: - Node 0033, with a balance factor of 3. - Left child: 0020, with a balance factor of 1. - Right child: 0055, with a balance factor of 2. - Left child: 0040, with a balance factor of 1. - Right child: 0060, with a balance factor of 1. - **Right Subtree of Root**: - Node 0070, with a balance factor of 3. - Left child: 0068, with a balance factor of 2. - Right child: 0095, with a balance factor of 2. - Right child: 0098, with a balance factor of 1. The numbers inside each node represent the node's balance factor (the height difference between the left and right subtrees). Use this information to correctly re-balance the tree after deleting node 0068 and perform a pre-order traversal on the updated tree.
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