Red-Black Trees

• A red-black tree is a binary search tree that efficiently represents a 2-3-4 tree. (It uses less memory.)
• Small sub-trees of the red-black tree are used to represent the 3-nodes and 4-nodes of the 2-3-4 tree.
• The correspondence between a 4-node and a subtree of the red-black tree is:

  
    S   M   L    ==>       M
   /  |   |  \           /   \  <== red links
  a   b   c   d         S     L
                       / \   / \   <== black links
  		    a   b c   d
  

• There are two ways to represent a 3-node as a subtree of a red-black tree:

  
    S   L    ==>       L             S
   /  |  \            / \           / \
  a   b   c          S   c    OR   a   L
                    / \               / \
                   a   b             b   c