Insert 48 into the following AVL tree and draw the results. Use the boxesto 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.After InsertAfter 1st Rotation (if there is one)After 2nd Rotation (if there is one) This diagram represents a binary search tree, which is a data structure used in various computing applications to organize data in a hierarchical manner. ### Explanation of the Diagram:- **Structure:** - The tree is composed of nodes, each surrounded by a circle and containing a numerical value. - Each node can have zero, one, or two children nodes.- **Node Details:** - **Root Node:** The topmost node is labeled "0050." - Nodes connected to "0050" are its children: "0025" on the left and "0075" on the right, indicating left and right subtrees. - The node "0025" has further children: "0012" on the left and "0040" on the right. - Continuing down, "0040" has two children: "0030" on the left and "0045" on the right. - The node "0075" has one child, "0080," on its right.- **Arrows:** - Directed arrows indicate the parent-child relationship among nodes. The direction points from parent to child, emphasizing the hierarchical flow.- **Binary Search Property:** - For each node, values in the left subtree are lesser, and values in the right subtree are greater. This property ensures efficient data retrieval, insertion, and deletion operations.This representation of a binary search tree helps in understanding the organization and traversal of data efficiently within computer science and programming topics.

Answered: Insert 48 into the following AVL tree…

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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Question

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.

After Insert	After 1st Rotation (if there is one)
After 2nd Rotation (if there is one)

This diagram represents a binary search tree, which is a data structure used in various computing applications to organize data in a hierarchical manner.

### Explanation of the Diagram:

- **Structure:**
- The tree is composed of nodes, each surrounded by a circle and containing a numerical value.
- Each node can have zero, one, or two children nodes.

- **Node Details:**
- **Root Node:** The topmost node is labeled "0050."
- Nodes connected to "0050" are its children: "0025" on the left and "0075" on the right, indicating left and right subtrees.
- The node "0025" has further children: "0012" on the left and "0040" on the right.
- Continuing down, "0040" has two children: "0030" on the left and "0045" on the right.
- The node "0075" has one child, "0080," on its right.

- **Arrows:**
- Directed arrows indicate the parent-child relationship among nodes. The direction points from parent to child, emphasizing the hierarchical flow.

- **Binary Search Property:**
- For each node, values in the left subtree are lesser, and values in the right subtree are greater. This property ensures efficient data retrieval, insertion, and deletion operations.

This representation of a binary search tree helps in understanding the organization and traversal of data efficiently within computer science and programming topics.

Expert Solution

Step 1

The given AVL tree is as below-

We have to insert 48 in the given AVL tree so according to the rules defined for AVL tree we will insert 48 in the tree.

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