- Treap
In
computer science , a treap is abinary search tree that orders the nodes by adding a random "priority" attribute to a node, as well as a key. Citation | title=Introduction to Algorithms , Second Edition
publisher=MIT Press and McGraw-Hill | year=2001 | isbn=0-262-03293-7 | pages=296-300
author=Thomas H. Cormen ,Charles E. Leiserson ,Ronald L. Rivest , andClifford Stein ] The nodes are ordered so that the keys form a binary search tree and the priorities obey themax heap order property. The name treap is a portmanteau of tree and heap.Definitions
The treap was first described by
Cecilia R. Aragon andRaimund G. Seidel in 1989,Citation | title=Randomized Search Trees
first1=Cecilia R. | last1=Aragon | first2=Raimund | last2=Seidel
journal=Foundations of Computer Science, 30th Annual Symposium on | pages=540-545 | year=1989
doi=10.1109/SFCS.1989.63531 | isbn=0-8186-1982-1] Citation | title=Randomized Search Trees
first1=Raimund | last1=Seidel | first2=Cecilia R. | last2=Aragon
journal=Algorithmica | volume=16 | issue=4/5 | pages=pp. 464-497 | year=1996
url=http://citeseer.ist.psu.edu/seidel96randomized.html
doi=10.1007/s004539900061] though the authors credit Jean Vuillemin with studying essentially the same data structure in 1980.* If v is a left descendant of u, then key [v] < key [u] ;
* If v is a right descendant of u, then key [v] > key [u] ;
* If v is a child of u, then priority [v] <= priority [u] ;During insertion, the value is also assigned a priority. (This priority may be random, in which case the use of a
pseudorandom number generator is applicable.) Initially, insertion proceeds in a manner identical to generalbinary search tree insertion. After this is done,tree rotation s are employed to restore the heap property: the in-order traversal sequence is invariant under rotations, so an in-order traversal still yields the same sequence of values.If priorities are non-random, the tree will usually be unbalanced; this worse theoretical average-case behavior may be outweighed by better expected-case behavior, as the most important items will be near the root.
Treaps exhibit the properties of both
binary search trees and heaps.Related data structures
When the priority is randomly allocated according to subtree size, the structure is known as a
randomized binary search tree or RBST.References
External links
* [http://people.ksp.sk/~kuko/bak/index.html Treap Applet] by Kubo Kovac
* [http://www.ibr.cs.tu-bs.de/lehre/ss98/audii/applets/BST/Treap-Example.html Animated treap]
* [http://www-tcs.cs.uni-sb.de/Papers/rst.ps Scientific paper about treaps from Raimund Seidel]
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