treap

The result is one treap merged from the two original treaps.

This costs as much as a single insertion into the treap.

Such a data structure is known as a treap or a randomized binary search tree.

Treap is a randomized balanced search tree, which has O(log(n)) complexity to insert or find a key.

Treap: a randomized binary search tree.

Now, assign new next-touch-times for this subtree, and rearrange it into a new local treap.

Organize our BST into a treap which is organized in heap-order by next-touch-time.

The data structure resulting from this random choice is called a treap, due to its combination of binary search tree and binary heap features.

Searching in a treap is the same as searching for an element in any other BST.

Cartesian trees also arise in the definition of the treap and randomized binary search tree data structures for binary searching.

Treap was found to have the best average performance, while red-black tree was found to have the smallest amount of performance variations.

In a treap (tree heap), each node also holds a (randomly chosen) priority and the parent node has higher priority than its children.

An equivalent way of describing the treap is that it could be formed by inserting the nodes highest-priority-first into a binary search tree without doing any rebalancing.

TreapDB is a kind of NoSQL data store, and it is based on Treap data structure.

The treap was first described by Cecilia R. Aragon and Raimund Seidel in 1989; its name is a portmanteau of tree and heap.

A Kinetic Heater is a kinetic priority queue similar to a kinetic heap, that makes use of randomization to simplify its analysis in a way similar to a treap.

With his student Cecilia R. Aragon in 1989 he devised the treap data structure, and he is also known for the Kirkpatrick-Seidel algorithm for computing two-dimensional convex hulls.

It is also possible, as suggested by Aragon and Seidel, to reprioritize frequently-accessed nodes, causing them to move towards the root of the treap and speeding up future accesses for the same keys.

Since the ordering of siblings in a heap is not specified by the heap property, a single node's two children can be freely interchanged unless doing so violates the shape property (compare with treap).

Merging two treaps that are the product of a former split, one can safely assume that the greatest value in the first treap is less than the smallest value in the second treap.

In computer science, the 'treap' and the 'randomized binary search tree' are two closely-related forms of binary search tree data structures that maintain a dynamic set of ordered keys and allow binary searches among the keys.

After this insertion, x will be the root node of the treap, all values less than x will be found in the left subtreap, and all values greater than x will be found in the right subtreap.

Although the treap and the randomized binary search tree both have the same random distribution of tree shapes after each update, the history of modifications to the trees performed by these two data structures over a sequence of insertion and deletion operations may be different.

To insert a new key x into the treap, generate a random priority y for x. Binary search for x in the tree, and create a new node at the leaf position where the binary search determines a node for x should exist.

A minor technical difference is that, in a treap, there is a small probability of a collision (two keys getting the same priority), and in both cases there will be statistical differences between a true random number generator and the pseudo-random number generator typically used on digital computers.