1. Red-Black Implementation of 2-3 Trees

2. Represent 3-nodes using “red links”
Red links indicate that the node comprises a 3-node with its parent.
A field in the Node class indicates whether the parent link is red.

3. Restrictions on Representation (from Sedgewick)
Red links lean left
We only want to limit red links to left links
When we make a right red link we will use rotation to make it a left red link.
After the rotation the child remains red
This requires swapping the colors of the parent and child involved in the rotation.

4. Restrictions on Representation (from Sedgewick)
No node has two red links connected to it
because that would amount to a 4-node
Flipping colors is like pushing the middle
key to the parent in a 2-3 tree. After flipping,
the root will be red, unless it is the root to
the whole tree, in which case it will be black.

5. Restrictions on Representation (from Sedgewick)
The tree has perfect black balance
The number of black links traversed to every leaf is the same.

6. Restrictions on Representation (from Sedgewick)
There is a 1-1 correspondence between red-black BST’s and 2-3 trees
If we collapse the red links, we get a 2-3 tree.

7. Observations
When we add a new node to a 2-3 tree, it always combines with an existing node, with the exception of when adding to a null tree.
With the execption of the root, all inserted nodes will be red.
After flipping colors, the root will be red, with the exception of the root for the whole tree.
Since the tree root is always black, we can simply color it black after each insertion.

8. Example
Example