Random binary tree

In computer science and probability theory, a random binary tree is a binary tree selected at random from some probability distribution on binary trees. Different distributions have been used, leading to different properties for these trees.

Random binary trees have been used for analyzing the average-case complexity of data structures based on binary search trees. For this application it is common to use random trees formed by inserting nodes one at a time according to a random permutation. Adding and removing nodes directly in a random binary tree will in general disrupt its random structure, but the treap and related randomized binary search tree data structures use the principle of binary trees formed from a random permutation in order to maintain a balanced binary search tree dynamically as nodes are inserted and deleted.

Other distributions on random binary trees include the uniform discrete distribution in which all distinct trees are equally likely, distributions on a given number of nodes obtained by repeated splitting, and trees generated by Galton–Watson processes, for which (unlike the other models) the number of nodes in the tree is not fixed.

For random trees that are not necessarily binary, see random tree.