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For the given Red Black Tree, draw the tree, when the following entries are inserted: Jade, Bob, and Dave. You must show the intermediate states (after each rotation).

For the given Red Black Tree, draw the tree, when the following entries are inserted: Jade, Bob, and Dave. You must show the intermediate states (after each rotation).

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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## Red-Black Tree Insertion Example In this example, we illustrate how to insert the entries "Jade", "Bob", and "Dave" into a Red-Black Tree. We also show the intermediate states after each rotation: ### Initial State - **Root Node**: Eddie (Black) - **Left Child**: Beyonce (Red) - **Left Child**: Alicia (Red) - **Right Child**: Chris (Red) - **Right Child**: Dana (Red) - **Right Child**: George (Black) - **Left Child**: Frank (Black) - **Right Child**: Jane (Black) ### Diagram Explanation 1. **Eddie** is at the root and is colored **black**. 2. **Beyonce** is the left child of Eddie and is colored **red**. - **Alicia** is the left child of Beyonce and is colored **red**. - **Chris** is the right child of Beyonce and is colored **red**. - **Dana** is the right child of Chris and is colored **red**. 3. **George** is the right child of Eddie and is colored **black**. - **Frank** is the left child of George and is colored **black**. - **Jane** is the right child of George and is colored **black**. The tree maintains the red-black properties, such as entries being either red or black, and any red node having black children. The black height is consistent across paths, ensuring balance. ### Next Steps To insert "Jade", "Bob", and "Dave", follow these steps: - Insert the new entries maintaining red-black properties. - Perform necessary rotations and color changes. - Update the tree structure after each insertion. - Transitions should preserve the tree's balance and properties. This exercise helps visualize and understand the self-balancing nature of red-black trees, where insertions are followed by specific rotations and color adjustments to maintain order.
Transcribed Image Text:## Red-Black Tree Insertion Example In this example, we illustrate how to insert the entries "Jade", "Bob", and "Dave" into a Red-Black Tree. We also show the intermediate states after each rotation: ### Initial State - **Root Node**: Eddie (Black) - **Left Child**: Beyonce (Red) - **Left Child**: Alicia (Red) - **Right Child**: Chris (Red) - **Right Child**: Dana (Red) - **Right Child**: George (Black) - **Left Child**: Frank (Black) - **Right Child**: Jane (Black) ### Diagram Explanation 1. **Eddie** is at the root and is colored **black**. 2. **Beyonce** is the left child of Eddie and is colored **red**. - **Alicia** is the left child of Beyonce and is colored **red**. - **Chris** is the right child of Beyonce and is colored **red**. - **Dana** is the right child of Chris and is colored **red**. 3. **George** is the right child of Eddie and is colored **black**. - **Frank** is the left child of George and is colored **black**. - **Jane** is the right child of George and is colored **black**. The tree maintains the red-black properties, such as entries being either red or black, and any red node having black children. The black height is consistent across paths, ensuring balance. ### Next Steps To insert "Jade", "Bob", and "Dave", follow these steps: - Insert the new entries maintaining red-black properties. - Perform necessary rotations and color changes. - Update the tree structure after each insertion. - Transitions should preserve the tree's balance and properties. This exercise helps visualize and understand the self-balancing nature of red-black trees, where insertions are followed by specific rotations and color adjustments to maintain order.
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