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Topic: AVL tree

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	AVL Trees (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-09-10)
		AVL trees are nothing more than binary search trees that have the added benefit of being balanced.
		For a binary tree to be considered balanced, at least in the context of the AVL tree, the height of the right subtree and height of the left subtree for any node cannot differ by more than one.
		To determine whether your tree looks like one of the 2 last diagrams, you simply check the value of the node that was just inserted (level 3 on the diagram) against the value in the root node (level 1) and the inserted nodes parent (level 2).
	cs.montana.edu.cob-web.org:8888 /~sonder/222/avl_tree.html (578 words)

	Binary Trees (Site not responding. Last check: 2007-09-10)
		It is difficult to print trees down the page, because they quickly grow too wide, but it is relatively easy to print them across the page so that the root is at the left and the tree grows to the right.
		For non-emptyTree trees, it may be appropriate to try a tree of a "few" nodes and a tree of a single node.
		Output is the tree of the expression that is the result of differentiation with respect to a given variable.
	www.csse.monash.edu.au /~lloyd/tildeAlgDS/Tree (2822 words)

	AVL tree traversal (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-09-10)
		The AVL tree is the oldest and most well-known data structure for balanced trees, which has the property that the heights of the two subtrees of each node differ by at most one.
		The implementation is nearly identical to the (natural) binary tree with the exception that the remainder function is bound by a lower value (implicated by the strict AVL tree condition).
		As with the (natural) binary tree, we had to add 1 to support also empty trees, in wich case the loop body is executed exactly once.
	www.auto.tuwien.ac.at.cob-web.org:8888 /~blieb/woop/avl.html (374 words)

	AVL tree - Wikipedia, the free encyclopedia
		In an AVL tree the heights of the two child subtrees of any node differ by at most one, therefore it is also called height-balanced.
		While AVL trees are theoretically quite sound, they are not commonly implemented due to their high implementation complexity to keep it balanced, making development less effective when compared to self-correcting tree structures, such as splay trees or heaps.
		Insertion into an AVL tree may be carried out by inserting the given value into the tree as if it were an unbalanced binary search tree, and then retracing one's steps toward the root, rotating about any nodes which have become unbalanced during the insertion (see tree rotation).
	en.wikipedia.org /wiki/AVL_tree (552 words)

	B-Trees
		To ensure that the height of the tree is as small as possible and therefore provide the best running time, a balanced tree structure like a red-fl tree, AVL tree, or b-tree must be used.
		B-trees are balanced trees that are optimized for situations when part or all of the tree must be maintained in secondary storage such as a magnetic disk.
		Since the "branchiness" of a b-tree can be large compared to many other balanced tree structures, the base of the logarithm tends to be large; therefore, the number of nodes visited during a search tends to be smaller than required by other tree structures.
	www.bluerwhite.org /btree (2387 words)

	CIS Department > Tutorials > Software Design Using C++ > AVL Trees
		The height of a binary tree is the maximum path length from the root to a leaf.
		An AVL tree is a binary search tree in which every node is height balanced, that is, the difference in the heights of its two subtrees is at most 1.
		The tree is restored to an AVL tree by using a rotation.
	cis.stvincent.edu /html/tutorials/swd/avltrees/avltrees.html (2030 words)

	C AVL Tree "Generic Package"
		structure for the tree, or a (parameterless) macro that expands to an expression yielding a pointer to the
		Returns the handle of the node whose key is the maximum of the keys of all the nodes in the tree.
		A useful characteristic of the AVL tree data structure is the ability to do a final, destroying iteration over the nodes.
	www.geocities.com /wkaras/gen_c/cavl_tree.html (2938 words)

	Data Structures and Algorithms: AVL Trees (Site not responding. Last check: 2007-09-10)
		Balance requirement for an AVL tree: the left and right sub-trees differ by at most 1 in height.
		As with the red-fl tree, insertion is somewhat complex and involves a number of cases.
		This factor indicates whether the tree is left-heavy (the height of the left sub-tree is 1 greater than the right sub-tree), balanced (both sub-trees are the same height) or right-heavy (the height of the right sub-tree is 1 greater than the left sub-tree).
	cba.winthrop.edu /acm/PLDS210/AVL.html (302 words)

	PlanetMath: AVL tree
		An AVL tree is A balanced binary search tree where the height of the two subtrees (children) of a node differs by at most one.
		The structure is named for the inventors, Adelson-Velskii and Landis (1962).
		This is version 5 of AVL tree, born on 2003-02-01, modified 2003-02-12.
	planetmath.org /encyclopedia/AVLTree.html (72 words)

	AVL Trees
		An AVL tree is a binary search tree whose left subtree and right subtree differ in height by no more than 1, and whose left and right subtrees are themselves AVL trees.
		The AVL property of this tree is restored through a succession of rotations.
		In general the maximum path length from the root to any leaf for an AVL tree will be much closer to lg n (the best case result) for a randomly generated AVL tree.
	www.academic.marist.edu /~jzbv/ads/AVLTrees.htm (839 words)

	OpenCM: BaseAvlTree Class Reference
		In our experience with tree structures it is usually the case that the search key structure is stack allocated.
		The advantage of reusing the BaseAvlNode structure for this purpose is that it allows the tree itself to remain completely agnostic about key types and value types.
		On return, the node structure is no longer referenced by the tree (though it may be referenced by other user data structures).
	opencm.org /doxygen/classBaseAvlTree.html (515 words)

	AVL Trees (Site not responding. Last check: 2007-09-10)
		(with the convention that the height of an empty tree is 0).
		An AVL tree is defined to be a binary search tree in which every node has a balance factor of -1, 0 or 1.
		Moreover, the total height of the rotated tree is the same as the original height of the tree at A, so that balance factors higher up the tree will not have changed as a result of the rotation.
	www.ucfv.bc.ca /cis/watkissc/200009/200009Comp175/notes/avlTrees.html (1291 words)

	/* Rambling comments... /: AVL Tree (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-09-10)*
		AVL trees, named after the Russians, Adel'son-Vel'skii and Landis, who first defined them, are height balanced binary search trees.
		To be considered an AVL tree a binary search tree must satisfy only one condition: for any node, the height of the left sub-tree and the height of the right sub-tree must differ by no more than one.
		In all of the diagrams below the node "A" is being examined for the AVL property and requires a rotation to restore it.
	www.lenholgate.com.cob-web.org:8888 /archives/000460.html (919 words)

	AVL Trees
		As you move away from a balanced tree to a more linear structure, height approaches N and the maximum comparisons increases with the height of the the tree - ultimately becoming the same as searching a linked list.
		An AVL tree is a binary search tree in which the heights of the left and right subtrees of the root differ by at most 1, and in which the left and right subtrees are again AVL trees.
		With each node of an AVL tree is associated a balance factor which is left high, equal, or right high according, respectively, as to whether the left subtree has height greater than, equal to, or less than that of the right subtree.
	www.cs.wm.edu /~debbie/cs241/trees/AVLtrees.html (865 words)

	CS 660: AVL TREES (Site not responding. Last check: 2007-09-10)
		Height of a tree is the length of the longest path from the root to a leaf.
		A HB[1] tree is called an AVL tree.
		An insertion into an AVL tree requires at most one rotation to rebalance a tree.
	www.eli.sdsu.edu /courses/fall95/cs660/notes/AVL/AVL.html (204 words)

	AVL Trees: Tutorial and C++ Implementation
		The height of a tree with > 1 element is equal to 1 + the height of its tallest subtree.
		An AVL tree is a binary tree in which the difference between the height of the right and left subtrees (or the root node) is never more than one.
		And there we have it, the maintenance of AVL tree manipulations, the brunt of which is covered in 5 methods, none of which (except for delete which is about 1.5 pages) is greater than 1 normal page in length, including comments (and there are a lot).
	www.cmcrossroads.com /bradapp/ftp/src/libs/C++/AvlTrees.html (4410 words)

	MatrixPro Tutorial - Creating AVL tree example
		Keys can be inserted into the AVL tree by dragging them from the Table of Keys and dropping them onto the AVL tree.
		To use the insert-routine of the AVL tree, the key must be dropped onto the tree, not a node in the tree.
		Although the animation in Figure 3 could be used to teach the concept of AVL tree, it fails to properly visualize the rotation that occurs when inserting the key R. This problem can easily be solved by modifying the animation created in the last section.
	www.cs.hut.fi /Research/MatrixPro/tutorials/avl_tutorial.shtml (771 words)

	AVL Trees - CMPSCI 187
		To the extent that the tree is unbalanced, worst case performance degrades.
		For the second tree, it is (3 + 2 + 3 + 1 + 4 + 3 + 2 + 3)/8 = 21/8.
		In general, if we have an AVL tree, and either insert one new key or delete one old key, no subtree anywhere should be out of balance by more than two levels.
	www.cs.umass.edu /~utgoff/cs187/lectures-spring-97/avl-trees.html (3104 words)

	Animated AVL Tree (Site not responding. Last check: 2007-09-10)
		The reason for this is that I use a regular binary tree delete.
		I wrote an AVL delete method but it has a memory leak (I know, java, garbage collection, go figure) so until I fix it it's regular binary tree delete for me.
		The source code for both my binary tree and AVL tree is here and you're welcome to it.
	www.cs.jhu.edu /~goodrich/dsa/trees/avltree.html (233 words)

	Binary Search Trees and AVL Trees
		The roots of the trees are at the left-hand-side of the large TEXTAREA.
		The trees are shown with links, and also in infix order, after each insertion or deletion.
		Note that the AVL tree remains much shorter than the BST when, for example, alphabetically ordered names {a, b, c, d,...} are inserted.
	www.csse.monash.edu.au /~lloyd/tildeAlgDS/Tree/Search (182 words)

	Inserting into an AVL Tree - GNU libavl 2.0.2
		This is time well spent because we will be able to apply many of the same insights to AVL deletion and insertion and deletion in red-fl trees.
		The insertion or deletion itself is done in the first stage, in much the same way as in an unbalanced BST, and we may also do a bit of additional bookkeeping work, such as updating balance factors in an AVL tree, or swapping node “colors” in red-fl trees.
		When rebalancing does become necessary in an AVL or red-fl tree, its effects are limited to the nodes along or near the direct path from the inserted or deleted node up to the root of the tree.
	www.stanford.edu /~blp/avl/libavl.html/Inserting-into-an-AVL-Tree.html (524 words)

	[No title]
		Return // true if the insertion was successful // (key was added to the tree) or false // if the key was already present (the // data will be modified, so this // operation can act as an Update).
		If it spots that the // tree is invalid it prints the tree (if it is sufficiently small) // and terminates the program.
		path[0] is, therefore, // the root of the tree.
	www.cs.unm.edu /~shapiro/CS361/avl.h (904 words)

	[No title]
		Note that the implicit AVL tree is modified.
		Note that the implicit AVL tree object is modified.
		Return: Nothing directly, but the implicit AVL tree object is modified.
	www.angelfire.com /mo3/nateman/code/352_Project3/avltree.cpp (908 words)

	AVL tree - Wikipedia, the free encyclopedia
		Additions and deletions may require the tree to be rebalanced by one or more tree rotations.
		No special provisions need to be taken, and the tree's structure is not modified by lookups.
		AVL Trees: Tutorial and C++ Implementation by Brad Appleton
	en.wikipedia.org /wiki/Avl_tree (552 words)

	libspf.org - The Original ANSI C SPF Reference Library (Site not responding. Last check: 2007-09-10)
		If the option is not checked, the algorithm will no longer balance the tree after insertions and deletions.
		If this option is enabled for an existing structure, the whole tree will be rebalanced.
		Feel free to play with the tree and grab individual nodes with your mouse.
	www.libspf.org /api_avl_tree.html (161 words)

	AVL Template in C++ (Site not responding. Last check: 2007-09-10)
		An AVL tree is a mostly balanced tree that has the property that no subtree is every more than 1 longer than its sibling.
		This is slightly better than a red-fl tree which has the property that no subtree is ever more than twice as long as its sibling.
		I know that traditionally, ordered trees have only an Item, and sort based on that item, but a typical use for this template is for an asset cache, or state machine cache in a scripting engine.
	meshula.net /articles/AVL.html (339 words)

	avl.c (Site not responding. Last check: 2007-09-10)
		An AVL tree is a binary search tree that is 35 * almost perfectly balanced.
		In the code this is 656 * handled by temporarily swapping (d) and (c) in the tree and then using 657 * common code to delete (d) from the leaf position.
		This is handled by moving up the tree through 661 * parents and applying rotations as needed.
	cvs.opensolaris.org /source/xref/usr/src/common/avl/avl.c (2153 words)

	Ben Pfaff: GNU libavl
		Several AVL tree libraries are available on the net.
		AVL trees, red-fl tree, splay trees, and more, in a recursive implementation designed for multithreaded applications.
		Chris Hertel's data structures library, which includes ordinary binary trees and AVL and splay trees using an object-oriented design in C. GNU Lesser General Public License.
	www.stanford.edu /~blp/avl (713 words)

	CS 340 Stack Project (Site not responding. Last check: 2007-09-10)
		Diplay the values of all nodes in the AVL tree using in-order.
		Diplay the values of all nodes in the AVL tree using pre-order.
		Diplay the values of all nodes in the AVL tree using post-order.
	homepage.mac.com /jimklayder/java/AVLtree.html (183 words)

	C++ AVL Tree Template
		This is the maximum tree depth for an instance of the instantiated class.
		If, in a particular instantiation, the maximum number of nodes in a tree instance is 1,000,000, the maximum depth should be 28.
		Builds a tree from an sequence of nodes that are sorted ascendingly by their key values.
	www.geocities.com /wkaras/gen_cpp/avl_tree.html (2162 words)

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