### 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.

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

Database System Concepts

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ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

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Question

### 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 Diagram

1. **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 Factor

The 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.

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