Tree 2-3-4

A tree 2-3-4 is one 2-4 Arbre B or tree B of order 2, i.e. a tree comprising only 2-nodes, 3-nodes and 4-nodes (a Node being a node having key N-1 and NR wire), and whose keys limit the keys under trees (one will defer to the article Arbre B for a precise definition).

As a Tree B, one can use it to implement the abstract type Table of symbols. Research operations, of insertion and suppression are in O (ln N) .

The most interesting aspect of trees 2-3-4 is their representation in the form of two-tone trees:

  • a 2-node is represented by a black node only.
  • a 3-node is represented by a red node plus his/her black father (a 3-node can be directed on the right or on the left according to whether the red node is the right or left son).
  • a 4-node is represented by 2 red nodes plus their black father.
This representation is simpler to handle because it is about a binary Tree of research, moreover it wastes less place memory when the tree contains few 4-nodes.

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