### Understanding Balance Factors in Binary Trees - Educational Guide#### What is the balance factor of the node of this tree labeled with the red triangle?In this educational example, we address the evaluation of the balance factor within a binary tree structure. The tree depicted in the provided diagram has various nodes with values, connected via edges, forming a hierarchical structure and the balance factor is a crucial attribute of every node in this tree.##### Explanation of the Binary Tree Diagram1. **Nodes and Values**: Each rectangle represents a node within the binary tree. The number inside the yellow section of each node represents its value. For reference, the nodes and their values are: - The root node has the value 14. - Further nodes are connected hierarchically with values 17, 4, 15, 21, 19, 25, and so on.2. **Edges and Connections**: Black lines with arrows depict the parent-child relationships. Nodes have left and right children, connected down the hierarchy.3. **Node Specifics**: - The node labeled with a red triangle has the value **14**.##### Determining the Balance FactorThe balance factor for any node in a binary tree is calculated using the formula:\[ \text{Balance Factor} = \text{Height of Right Subtree} - \text{Height of Left Subtree} \]To find the balance factor of the node labeled with the red triangle (node with value 14), let's determine the heights of its left and right subtrees.- **Left Subtree of Node 14**: - **Root Node**: 4 - Height Calculation: - Node 4 has children 3 and 12. - Node 3 has no children. - Node 12 has children 9 and 15. - Node 9 has children 7 and 11. - Node 7 has one child, 10. - Longest path: 4 → 12 → 9 → 7 → 10 (4 edges) - Height = 4- **Right Subtree of Node 14**: - **Root Node**: 17 - Height Calculation: - Node 17 has children 15 and 21 - Node 21 has children 19 and 25. - Node 25 has one child, 24.

ExplanationA balanced factor of a node in a tree is a measure of the relative balance of the…

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What is the balance factor of the node of this tree labeled with the red triangle?

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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