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2-3 tree

A 2-3 tree in computer science is a type of data structure, a B-tree where every node with children (internal node) has either two children and one data element (2-nodes) or three children and two data elements (3-nodes). Nodes on the outside of the tree (leaf nodes) have no children and two data elements.

2-3 trees are an isometry of AA trees, meaning that they are equivalent data structures. In other words, for every 2-3 tree, there exists at least one AA tree with data elements in the same order. 2-3 trees are balanced, meaning that each right, center, and left subtree contains the same or close to the same amount of data.

Properties

• Every non-leaf node has 2 or 3 children
• All leaves are at the same level (the bottom level)
• All data is kept in sorted order
• Every non-leaf node will contain 1 or 2 fields.

Non-leaf nodes

These contain one or two fields which indicate the range of values in its subtrees. If a node has two children, it will have one field; if the node has three children, it will have two fields. Each non-leaf node will contain a value in field 1 which is greater than the largest item in its left sub-tree, but less than or equal to the smallest item in its right sub-tree (or center sub-tree, if it has three children). If that node has three children, field 2 contains a value which is greater than the largest value in the center sub-tree, but less than or equal to the smallest item in its right sub-tree. The purpose of these values is to direct a search function to the correct sub-tree and eventually to the correct data node.

See also

• B-tree
• AA tree (a 2-3 tree implemented using a binary tree)
• 2-3-4 tree

External links

• 2-3 Trees Complete Description
• B-Tree animation (Java Applet)