Mapping 2-3-4 Trees into Red-Black Trees

Mapping 2-3-4 trees into Red-Black trees

• Since we're implementing 2-3-4 trees using binary trees, all nodes must be 2-nodes.
• This will inherently make the tree deeper, but the benefits outweigh this slight overhead.
• A 2-node requires one red/black node, a 3-node requires two red/black nodes, and a 4-node requires 3 red/black nodes.

  

• Splitting a 4-node (implemented in a Red-Black tree) is trivial:

Splitting a 4-node connected to a 2-node

Orientation #1 (2-3-4 tree):

Orientation #1 (Red-Black tree):

Orientation #2 (2-3-4 tree):

Orientation #2 (Red-Black tree):

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Splitting a 4-node connected to a 3-node

2-3-4 Trees

Orientation #1:

Orientation #2:

Orientation #3: