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AVL and tree
In computer science, an AVL tree is a self-balancing binary search tree, and it was the first such data structure to be invented.
In an AVL tree, the heights of the two child subtrees of any node differ by at most one.
In other words AVL tree is a binary search tree where the height of the left subtree differs from the height of the right subtree by at most 1 level, if it exceeds 1 level then rebalancing occurs.
The AVL tree is named after its two Soviet inventors, G. M. Adelson-Velskii and E. M. Landis, who published it in their 1962 paper " An algorithm for the organization of information.
Basic operations of an AVL tree involve carrying out the same actions as would be carried out on an unbalanced binary search tree, but modifications are preceded or followed by one or more operations called tree rotations, which help to restore the height balance of the subtrees.
Lookup in an AVL tree is performed exactly like in any unbalanced binary search tree.
* AVL tree applet – all the operations
* Self balancing AVL tree with Concat and Split operations
The AVL tree is another structure supporting O ( log n ) search, insertion, and removal.
Tree rotations are used in a number of tree data structures such as AVL trees, red-black trees, splay trees, and treaps.
Pictorial description of how rotations cause rebalancing in an AVL tree.
A type of tree which uses this rebalancing technique is the AVL tree.
** AVL tree
* AVL tree, a data structure used in computer programming
* AVL tree

AVL and red-black
AVL trees are often compared with red-black trees because they support the same set of operations and because red-black trees also take O ( log n ) time for the basic operations.
Because AVL trees are more rigidly balanced, they are faster than red-black trees for lookup intensive applications.
Similar to red-black trees, AVL trees are in general not weight-balanced, that is sibling nodes can have hugely differing numbers of descendants.
Both AVL trees and red-black trees are self-balancing binary search trees, so they are very similar mathematically.
AVL trees are more rigidly balanced than red-black trees, leading to slower insertion and removal but faster retrieval.
* Simple implementation — simpler than other self-balancing binary search trees, such as red-black trees or AVL trees.
AVL trees and red-black trees are two examples of binary search trees that use the left rotation.

AVL and splay
* AVL trees, Red-black trees, splay trees and Tango Trees which are instances of self-balancing binary search trees ;

AVL and data
GSM and EVDO are the most common services applied, because of the low data rate needed for AVL, and the low cost and near-ubiquitous nature of these public networks.
Large private telelocation or AVL systems send data from GPS receivers in vehicles to a dispatch center over their private, user-owned radio backbone.
The main purpose of using AVL is not only to locate the vehicles, but also to obtain information about engine data, fuel consumption, driver data and sensor data from i. e. doors, freezer room on trucks or air pressure.
Such data can be obtained via the CAN-bus, via direct connections to AVL systems or via open bus systems such as UFDEX that both sends and receives data via SMS or GPRS in pure ASCII text format.
Another scenario for sensor functions is to connect the AVL to driver information, to collect data about driving time, stops, or even driver absence from the vehicle.
The AVL display for a vehicle at the Heart Butte Post Office in Montana shows a latitude and longitude of 48. 28333 N ,-112. 83583 W. The CAD system uses degrees-minutes-seconds format data and shows the same location as 481700N, 1125009W.

AVL and use
* Passenger Information: Real-time Passenger information systems use predictions based on AVL input to show the expected arrival and departure times of Public Transport services.
AVL may use GPS technology.

AVL and rotations
This is loosely similar to AVL trees, in that the actual rotations depend on ' balances ' of nodes, but the means of determining the balance differs greatly.

AVL and balance
Specifically, Lehman and Carey's article describes a T-tree balanced like an AVL tree: it becomes out of balance when a node's child trees differ in height by at least two levels.
Since AVL trees check the balance value on every insertion / deletion, it is typically stored in each node ; scapegoat trees are able to calculate it only as needed, which is only when a scapegoat needs to be found.

AVL and .
After inserting a node, it is necessary to check each of the node's ancestors for consistency with the rules of AVL.
** Hans List, Austrian founder of the AVL List ( d. 1996 )
Under the Valencian Statute of Autonomy, the Acadèmia Valenciana de la Llengua ( AVL ) has been established as its regulator.
The AVL considers Catalan and Valencian to be simply two names for the same language.

tree and red-black
In 2008, Sedgewick introduced a simpler version of the red – black tree called the left-leaning red-black tree by eliminating a previously unspecified degree of freedom in the implementation.
He is noted for inventing three data sorting structures: the B-tree ( with Edward M. McCreight ), the UB-tree ( with Volker Markl ) and the red-black tree.
A red-black tree with branching factor 2.
For example, consider a comprehensive web-based thesaurus service that uses a large red-black tree to store its list of synonym relationships, and that allows each user to add their own custom words to their personal thesaurus.
A better approach is to store the words in an immutable ( and therefore purely functional ) red-black tree.
With a mutable red-black tree, this approach would not work, since changes to the main tree would affect all users.
In other words, for every 2-3-4 tree, there exists at least one red-black tree with data elements in the same order.
Wineberry is a dioecious tree or shrub with male and female individuals ; male and female flowers arise on separate plants, so both sexes are required for the production of red-black berries.
It provides list ( and inlined list ), hash, red-black tree, shared string, rectangle, array, iterator and accessor, memory pool, module, fixed point and magic check helper.
AA trees are a variation of the red-black tree, which in turn is an enhancement to the binary search tree.
Unlike red-black trees, red nodes on an AA tree can only be added as a right subchild.
The maintenance algorithms for a red-black tree need to consider seven different shapes to properly balance the tree:
A link where the child's level is equal to that of its parent is called a horizontal link, and is analogous to a red link in the red-black tree.
These are more restrictive constraints than the analogous ones on red-black trees, with the result that re-balancing an AA tree is procedurally much simpler than re-balancing a red-black tree.

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