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Insert 48 into the following AVL tree and draw the results. Use the boxes to show the stages of your work, such as required rotations. In the event that a box is not needed, place a large "X" in the appropriate box.

Insert 48 into the following AVL tree and draw the results. Use the boxes to show the stages of your work, such as required rotations. In the event that a box is not needed, place a large "X" in the appropriate box.

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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Insert 48 into the following AVL tree and draw the results. Use the boxes
to show the stages of your work, such as required rotations. In the event that a box is not needed, place a large "X" in the appropriate box.

The image depicts a binary search tree (BST) structure. Here is the transcription and explanation of the diagram: ### Binary Search Tree Diagram This diagram illustrates a Binary Search Tree (BST) with the following nodes: - **0050**: This is the root node of the tree. - **Left Child (0025)**: Has a left child node **0012** and a right child node **0040**. - **Left Subtree of 0025**: - **0012**: This node does not have any children. - **Right Subtree of 0025**: - **0040**: Consists of a left child node **0030** and a right child node **0045**. - **0030**: This node does not have any children. - **0045**: This node does not have any children. - **Right Child (0075)**: Has a right child node **0080**. - **Right Subtree of 0075**: - **0080**: This node does not have any children. ### Explanation In a Binary Search Tree, each node follows the property: - The left subtree of a node contains only nodes with values less than the node’s value. - The right subtree of a node contains only nodes with values greater than the node’s value. This structure helps in efficient searching, insertion, and deletion operations - usually with time complexity of O(log n) if the tree is balanced. ### Educational Value Understanding and working with binary search trees is critical for students and professionals interested in computer science and programming. This data structure supports various applications like database indexing, sorting algorithms, and maintaining a dynamically sorted sequence of numbers.
Transcribed Image Text:The image depicts a binary search tree (BST) structure. Here is the transcription and explanation of the diagram: ### Binary Search Tree Diagram This diagram illustrates a Binary Search Tree (BST) with the following nodes: - **0050**: This is the root node of the tree. - **Left Child (0025)**: Has a left child node **0012** and a right child node **0040**. - **Left Subtree of 0025**: - **0012**: This node does not have any children. - **Right Subtree of 0025**: - **0040**: Consists of a left child node **0030** and a right child node **0045**. - **0030**: This node does not have any children. - **0045**: This node does not have any children. - **Right Child (0075)**: Has a right child node **0080**. - **Right Subtree of 0075**: - **0080**: This node does not have any children. ### Explanation In a Binary Search Tree, each node follows the property: - The left subtree of a node contains only nodes with values less than the node’s value. - The right subtree of a node contains only nodes with values greater than the node’s value. This structure helps in efficient searching, insertion, and deletion operations - usually with time complexity of O(log n) if the tree is balanced. ### Educational Value Understanding and working with binary search trees is critical for students and professionals interested in computer science and programming. This data structure supports various applications like database indexing, sorting algorithms, and maintaining a dynamically sorted sequence of numbers.
This image illustrates a blank template for visualizing a process involving insertions and rotations, typically used in data structure algorithms like AVL trees. The template is divided into four sections: 1. **After Insert**: This space is reserved for depicting the state of the data structure after inserting a new element. Initially, the structure is unbalanced, which may necessitate rotations. 2. **After 1st Rotation (optional)**: This section is allocated for showing the data structure after the first rotation is performed. Rotations help in maintaining balance within the structure by rearranging nodes. 3. **After 2nd Rotation (optional)**: In cases where the first rotation does not completely balance the structure, a second rotation may be required. This section shows the new configuration following the second rotation. Overall, this template serves as a guide for visualizing and understanding the rebalancing process in self-balancing trees and similar data structures.
Transcribed Image Text:This image illustrates a blank template for visualizing a process involving insertions and rotations, typically used in data structure algorithms like AVL trees. The template is divided into four sections: 1. **After Insert**: This space is reserved for depicting the state of the data structure after inserting a new element. Initially, the structure is unbalanced, which may necessitate rotations. 2. **After 1st Rotation (optional)**: This section is allocated for showing the data structure after the first rotation is performed. Rotations help in maintaining balance within the structure by rearranging nodes. 3. **After 2nd Rotation (optional)**: In cases where the first rotation does not completely balance the structure, a second rotation may be required. This section shows the new configuration following the second rotation. Overall, this template serves as a guide for visualizing and understanding the rebalancing process in self-balancing trees and similar data structures.
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