ASAp please!!dont use others answerswill rate !!THANK YOU!! **Educational Content on Red-Black Trees**---**4. Consider the Following Potential Red-Black Trees**These diagrams depict potential red-black trees without keys. Black nodes are represented by hashed lines, and red nodes by plain circles (no hashed lines). Your task is to determine which of these are valid red-black trees and to identify why any invalid trees fail to meet the criteria.### Diagrams Overview:- **Tree I:** - Root: Black node - Levels: Black root with alternating red and black nodes in subsequent layers. - Note: Validates the property where children of a red node must be black. - **Tree II:** - Root: Black node - Levels: Contains consecutive red nodes, violating the red-red property. - **Tree III:** - Root: Unclear due to lack of proper levels or structure. - Note: Insufficient nodes to determine red-black tree properties. - **Tree IV:** - Root: Black node - Levels: Alternates correctly between black and red nodes, adhering to all properties of a red-black tree. - **Tree V:** - Root: Black node - Levels: Violates the property where all paths from the root to the leaves contain the same number of black nodes. ### Task:For each tree that is not a valid red-black tree, identify and explain the violation:- **Tree II**: Contains consecutive red nodes, violating the red-red property.- **Tree III**: The structure is unclear, not enough nodes to form a valid tree.- **Tree V**: Unequal number of black nodes in different paths from root to leaves.### Conclusion:Assess each tree carefully, ensuring all red-black tree properties are met: the root must be black, red nodes cannot have red children, every path from a node to its descendant leaves must have the same number of black nodes, and all nodes except the root and leaves must be colored either red or black.

Answered: Image /qna-images/answer/49db401f-8a28-422b-9fdc-d09bf2754cba.jpg

4. Consider the following potential red-black trees (with the keys left out). We can represent black nodes by hashed lines and red nodes by no hashed lines. Which of the following are valid red-black trees? For each that is not a valid red-black tree, give a reason why it is not a red-black tree.

4. Consider the following potential red-black trees (with the keys left out). We can represent black nodes by hashed lines and red nodes by no hashed lines. Which of the following are valid red-black trees? For each that is not a valid red-black tree, give a reason why it is not a red-black 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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**Educational Content on Red-Black Trees**

---

**4. Consider the Following Potential Red-Black Trees**

These diagrams depict potential red-black trees without keys. Black nodes are represented by hashed lines, and red nodes by plain circles (no hashed lines). Your task is to determine which of these are valid red-black trees and to identify why any invalid trees fail to meet the criteria.

### Diagrams Overview:

- **Tree I:**
- Root: Black node
- Levels: Black root with alternating red and black nodes in subsequent layers.
- Note: Validates the property where children of a red node must be black.

- **Tree II:**
- Root: Black node
- Levels: Contains consecutive red nodes, violating the red-red property.

- **Tree III:**
- Root: Unclear due to lack of proper levels or structure.
- Note: Insufficient nodes to determine red-black tree properties.

- **Tree IV:**
- Root: Black node
- Levels: Alternates correctly between black and red nodes, adhering to all properties of a red-black tree.

- **Tree V:**
- Root: Black node
- Levels: Violates the property where all paths from the root to the leaves contain the same number of black nodes.

### Task:

For each tree that is not a valid red-black tree, identify and explain the violation:

- **Tree II**: Contains consecutive red nodes, violating the red-red property.
- **Tree III**: The structure is unclear, not enough nodes to form a valid tree.
- **Tree V**: Unequal number of black nodes in different paths from root to leaves.

### Conclusion:

Assess each tree carefully, ensuring all red-black tree properties are met: the root must be black, red nodes cannot have red children, every path from a node to its descendant leaves must have the same number of black nodes, and all nodes except the root and leaves must be colored either red or black.

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