Search tree

In computer science, a search tree is a binary tree data structure in whose nodes data values are stored from some ordered set, in such a way that in-order traversal of the tree visits the nodes in ascending order of the stored values. This means that for any internal node containing a value v, the values x stored in its left subtree satisfy x ≤ v, and the values y stored in its right subtree satisfy v ≤ y. Each subtree of a search tree is by itself again a search tree.

Search trees can implement the data type of (finite) multisets. The advantage of using search trees is that the test for membership can be performed efficiently provided that the tree is reasonably balanced, that is, the leaves of the tree are at comparable depths. Various search-tree data structures exist, several of which also allow efficient insertion and deletion of elements, which operations then have to maintain tree balance. If the multiset being represented is immutable, this is not an issue.

Search trees can also implement associative arrays by storing key–value pairs, where the ordering is based on the key part of these pairs.

In some kinds of search trees the data values are all stored in the leaves of the tree. In that case some additional information needs to be stored in the internal tree nodes to make efficient operations possible.

Examples

Some examples of search-tree data structures are:

• AVL trees, Red-black trees, splay trees and Tango Trees which are instances of self-balancing binary search trees;
• Ternary search trees, in which each internal node has exactly three children;
• B trees, commonly used in databases;
• B+ trees, like B trees but with all data values stored in the leaves;
• van Emde Boas trees, very efficient if the data values are fixed-size integers.

See also

• Trie, a tree data structure that allows searching for strings, which however does not store the actual data values in the nodes.