Draw Out Red-Black Tree (RBT) with Given Nodes
Inserting Nodes to Red-Black Tree
To draw out the Red-Black Tree (RBT) when inserting the given nodes (50, 20, 10, 5, 80, 60, 30, 75, 35, 90), you can follow these steps:
- Start with an empty RBT.
- Insert the first node, 50, as the root of the tree. Since it is the first node, it is always colored black.
- Insert the next node, 20, as the left child of the root (50). The color of the node is initially red.
- Perform a color flip on the parent-child relationship between the root (50) and its left child (20). This ensures that no two consecutive red nodes exist in a path.
- Insert the next node, 10, as the left child of 20. The color of the node is initially red.
- Perform a color flip between 20 and its left child 10.
- Insert the next node, 5, as the left child of 10. The color of the node is initially red.
- Perform a color flip between 10 and its left child 5.
- Insert the next node, 80, as the right child of the root (50). The color of the node is initially red.
- Perform a color flip between 50 and its right child 80.
- Insert the next node, 60, as the left child of 80. The color of the node is initially red.
- Perform a color flip between 80 and its left child 60.
- Insert the next node, 30, as the right child of 20. The color of the node is initially red.
- Perform a color flip between 20 and its right child 30.
- Insert the next node, 75, as the left child of 80. The color of the node is initially red.
- Perform a color flip between 80 and its left child 75.
- Insert the next node, 35, as the right child of 30. The color of the node is initially red.
- Perform a color flip between 30 and its right child 35.
- Insert the last node, 90, as the right child of 80. The color of the node is initially red.
- Perform a color flip between 80 and its right child 90.
The final Red-Black Tree would be:
20B / \ 10B 50B / \ / \ 5R 15R 35B 60B / \ 30R 80B \ 90R
This tree has been drawn based on the given nodes and the rules of a Red-Black Tree.
How is the Red-Black Tree (RBT) constructed with the given nodes? The Red-Black Tree is constructed by inserting each node (50, 20, 10, 5, 80, 60, 30, 75, 35, 90) in a specific order and adjusting the colors of nodes accordingly to maintain the properties of a Red-Black Tree.