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Insert the value "8" into the following AVL tree; draw the result:

Insert the value "8" into the following AVL tree; draw the result:

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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Insert the value "8" into the following AVL tree; draw the result:

This image represents a binary tree. A binary tree is a hierarchical data structure in which each node has at most two children. Here's a detailed breakdown of the binary tree presented: 1. **Root Node**: The root of the tree is the node with the number 4. 2. **Left Subtree**: Starting from the root node 4: - The left child of node 4 is node 2. - Node 2 further branches into two nodes: - The left child of node 2 is node 1. - The right child of node 2 is node 3. 3. **Right Subtree**: Starting from the root node 4: - The right child of node 4 is node 7. - Node 7 has a right child node 10. This binary tree can be used to illustrate concepts such as binary search trees, tree traversal algorithms (in-order, pre-order, post-order), and tree-depth calculations. Each node is connected by edges, represented by lines with arrows indicating the direction from parent to child.
Transcribed Image Text:This image represents a binary tree. A binary tree is a hierarchical data structure in which each node has at most two children. Here's a detailed breakdown of the binary tree presented: 1. **Root Node**: The root of the tree is the node with the number 4. 2. **Left Subtree**: Starting from the root node 4: - The left child of node 4 is node 2. - Node 2 further branches into two nodes: - The left child of node 2 is node 1. - The right child of node 2 is node 3. 3. **Right Subtree**: Starting from the root node 4: - The right child of node 4 is node 7. - Node 7 has a right child node 10. This binary tree can be used to illustrate concepts such as binary search trees, tree traversal algorithms (in-order, pre-order, post-order), and tree-depth calculations. Each node is connected by edges, represented by lines with arrows indicating the direction from parent to child.
Expert Solution
Step 1

AVL Tree: -

Self-balancing binary search tree. It follows the following properties: -

Binary Tree Property: -

  • It follows Binary Search tree properties, that is each node has <=2 children.

Order Property: -

  • All keys in the left subtree must be smaller than the node's key
  • All keys in the right subtree must be larger than the node's key

Height Property: -

  • The left and right subtrees of every node have heights differing by at most 1.
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