Draw Out Red-Black Tree (RBT) with Given Nodes

Inserting Nodes to Red-Black Tree

Note: To maintain the balance and properties of a Red-Black Tree, such as the root being black, the number of black nodes in each path being the same, and no two consecutive red nodes in a path.

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:

  1. Start with an empty RBT.
  2. Insert the first node, 50, as the root of the tree. Since it is the first node, it is always colored black.
  3. Insert the next node, 20, as the left child of the root (50). The color of the node is initially red.
  4. 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.
  5. Insert the next node, 10, as the left child of 20. The color of the node is initially red.
  6. Perform a color flip between 20 and its left child 10.
  7. Insert the next node, 5, as the left child of 10. The color of the node is initially red.
  8. Perform a color flip between 10 and its left child 5.
  9. Insert the next node, 80, as the right child of the root (50). The color of the node is initially red.
  10. Perform a color flip between 50 and its right child 80.
  11. Insert the next node, 60, as the left child of 80. The color of the node is initially red.
  12. Perform a color flip between 80 and its left child 60.
  13. Insert the next node, 30, as the right child of 20. The color of the node is initially red.
  14. Perform a color flip between 20 and its right child 30.
  15. Insert the next node, 75, as the left child of 80. The color of the node is initially red.
  16. Perform a color flip between 80 and its left child 75.
  17. Insert the next node, 35, as the right child of 30. The color of the node is initially red.
  18. Perform a color flip between 30 and its right child 35.
  19. Insert the last node, 90, as the right child of 80. The color of the node is initially red.
  20. 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.
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