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Topic: Tree rotation

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	Tree rotation
		A tree rotation is an operation on a binary search tree that changes the structure without interfering with the order of the elements.
		Tree rotations are used to balance some kinds of trees to improve performance.
		Tree rotations are used in AVL trees, Red-Black trees, splay trees, and others.
	www.ebroadcast.com.au /lookup/encyclopedia/tr/Tree_rotation.html (189 words)

	NAC \| The Biology of Silvopastoralism
		Tree pattern is as important as the number of trees planted per acre in governing agroforest effects upon tree and pasture production.
		For a given pattern, the number of trees planted per acre is determined by the number of trees desired in the final forest, number of trees to be sold as commercial thinnings and the expected proportion of trees lost to mortality or thinned for poor form or growth.
		Grouping of trees is especially helpful under very low tree densities where single, free standing trees may blow over in strong winds or have poor growth and form from being exposed to the weather.
	www.unl.edu /nac/afnotes/sil-2/index.html (1768 words)

	[No title]
		Height Balanced Trees A height balanced tree is one in which the difference in the height of the two subtrees for any node is less than or equal to some specified amount.
		This definition of a height balanced tree is the one chosen but obviously it would be possible to define a height balanced tree in which the height difference may be no more than 2.
		A rotation consists of moving the child of the high subtree into the position occupied by the pivot, and moving the pivot down into the low subtree.
	pages.cpsc.ucalgary.ca /~marina/331/tree4.doc (1940 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.
		Additions and deletions may require the tree to be rebalanced by one or more tree rotations.
		While AVL trees are theoretically quite sound, they are not commonly implemented due to the high complexity required to maintain balance, making development less effective when compared with self-correcting tree structures, such as splay trees or heaps.
	en.wikipedia.org /wiki/AVL_tree (886 words)

	Class notes CS251B -- Winter 1997 : Topic#20 : Augmented Data Structures
		Rotation is a local operation and it invalidates only the two size fields in the nodes incident on the link around which the rotation is performed.
		The rotations in the Phase 2 are handled in the same manner as for insertion.
		Overlap(x, i) for interval i and a tree rooted at x, returns a pointer to an interval in the collection that overlaps the given interval i or returns NIL otherwise.
	www.cs.mcgill.ca /~cs251/OldCourses/1997/topic20 (1549 words)

	The Seattle Times: Nation & World: Virginia is shining proud to give U.S. Capitol's tree
		They were equipped with a chain saw, a double-rotor helicopter and a specially formulated glue meant to freeze the tree's needles in place for the weeks of gawking to come, a giant crane, 10,000 feet of nylon parachute rope and a water-filled rubber bladder for the butt to nourish the tree during its voyage north.
		The community tracked the tree's progress with telephones and ham radios, and residents spent the afternoon with necks craned, watching the odd sight of a massive flying tannenbaum.
		The helicopter lowered the tree at the county fairground.
	seattletimes.nwsource.com /html/nationworld/2002090407_tree14.html (1094 words)

	JOT: Journal of Object Technology - Generic Red-Black Tree and its C# Implementation, Richard Wiener
		Whenever a new object is inserted or deleted, the resulting tree continues to satisfy the conditions required to be a red-fl tree.
		The alternative is to stay with the same structure as used in the implementation of the binary search tree and AVL tree in which each node is linked to its two children and not to its parent.
		The two types of red-fl tree implementations, with and without links to parent nodes, are included in the table even though only the implementation of the version with links to parent nodes will be presented.
	www.jot.fm /issues/issue_2005_03/column6 (2468 words)

	Tree rotation - Wikipedia, the free encyclopedia
		They are used to change the shape of the tree, and in particular to decrease its height by moving smaller subtrees down and larger subtrees up, resulting in improved performance of many tree operations.
		The tree rotation renders the inorder traversal of the binary tree invariant.
		Tree rotations are used in a number of tree data structures such as AVL trees, red-fl trees, and splay trees.
	en.wikipedia.org /wiki/Tree_rotation (387 words)

	Balanced Binary Tree
		A red-fl tree is a binary representation of a B-tree.
		During a tree rotation the tree algorithm may have to reorder the tree by prompting or demoting the current node, its parent, its grandparent, or the left or right siblings of the effected nodes.
		Tree operations that manage more variables then just the nodes themselves do not use an explicit stack because the state of the variables are already saved on some type of stack.
	karmak.org /archive/2002/03/rbtree.html (5890 words)

	Commercial Christmas Tree Crops
		Christmas trees are unique among most crops, though, since their value is based on their aesthetic quality and not their biomass yield.
		Christmas tree fertilization is generally considered at the time a new crop is planted (Establishment) or periodically during the course of the rotation (Maintenance).
		As a Christmas tree crop matures, nutrients are moved from the soil and stored in the needles, branches, trunks, and roots of the trees.
	www.ext.vt.edu /pubs/forestry/soiltestnotes/note23.html (2095 words)

	drawtree (Site not responding. Last check: 2007-11-03)
		If the tree that was read in had a full set of branch lengths, it will be assumed as a default that you want to use them in the diagram, but you can specify that they are not to be used.
		If the rotation of the tree is (say) 90.0 degrees (the default under option R), the fan starts at +270 degrees and runs clockwise around to -90 degrees (i.e., it starts at the bottom of the plot and runs clockwise around until it returns to the bottom.
		If you are unhappy with the appearance of the tree when using this option, you could try rotating it slightly (option R) as that may cause some branches to change their angle by a large amount, by having the angles be "rounded off" to a different value.
	evolution.genetics.washington.edu /phylip/doc/drawtree.html (2582 words)

	Soils from the July 2003 Crop and Soil News/Notes
		Since Christmas trees routinely receive nitrogen fertilizers and the soil calcium was lower in late rotations than early rotations in our study, we desired to know if the differences measured in the soil were manifested in the plant.
		The average potassium concentration for both rotation ages was substantially lower than the OSU critical concentration and probably caused by very dry late summer conditions.
		The average nitrogen concentration for later rotation trees was not significantly lower than nitrogen concentration from first rotation trees and sufficient for growth and color development.
	cropandsoil.oregonstate.edu /newsnotes/0309/soils.html (1269 words)

	Environmental Enhacement Using Short-Rotation Tree Crops
		Erosion and chemical movement from an annual row crop, switchgrass, and tree crop with and without a groundcover are being compared in the Southeast.
		For example, placement of short-rotation tree plantings within the agricultural landscape in prairie landscapes of the north-central region of the U.S. may interfere with the broad skyline expanse required by species such as the sharp-shinned grouse (a species experiencing severe decline in numbers).
		This interference may be particularly during their breeding season as the tree crops mature to a taller, more closed canopy and provide a larger, more extensive presence on the horizon.
	bioenergy.ornl.gov /papers/bioen96/tolbert.html (3122 words)

	Update of Short Rotation Intensive Culture in Canada
		Bush logging residues, composed of tree tops, branches and foliage, are estimated at 30.6 million oven dry tonnes per year (M o.d.t./yr) (Simons, 1994) and across Canada, discarded wood mill residues are evaluated at 8.4 M o.d.t./yr.
		Because the exploitation of short rotation tree plantations for pulp, veneer, oriented strand board and energy is relatively new, there are few commercial plantations in Canada.
		In action, opposite rotation of the cutting units forces the woody stems to pass between the cylinders where they are cut by the blades.
	www.woodycrops.org /mechconf/tardiff.html (3349 words)

	: Class BinaryTree (Site not responding. Last check: 2007-11-03)
		The elements of the binary tree rooted at node node are traversed in inorder
		The elements of the binary tree rooted at node node are traversed in postorder
		The elements of the binary tree rooted at node node are traversed in levelorder
	www.cs.williams.edu /JavaStructures/doc/structure/BinaryTree.html (796 words)

	[No title]
		Whenever an insertion of case 1 or 4 occurs, the resulting tree will be unbalanced and a single rotation can be used to rebalance the tree.
		To restore the balance in the tree and return it to the status of an AVL tree, a double rotation of S about P followed by S about G is needed as shown below.
		tree after insertion tree after first rotation of 35 about 30 balance factors after first rotation rotate 35 about 40 tree after second rotation of 35 about 40 final balance factors The steps in the double rotation are: Interchange parent and grandparent of new node (nodes 35 and 30).
	www.cs.ucf.edu /courses/cop3503h/day19.doc (783 words)

	c1132 - page 1 of 1
		The balance factor of node t is EH = 0 and the height of tree T1 is unchanged.
		the parent of x to the root in the tree.
		2 by the deletion, the single left rotation is performed to restore balance.
	www.cs.pitt.edu /~chang/bookds/c1132.html (1082 words)

	CPS 100E, Fall 1996, Lab 10 (Site not responding. Last check: 2007-11-03)
		To understand the different "tree rotations" that are used in AVL trees.
		In this part of the lab, you will read a tree from a file, you will observe what happens when you insert nodes into the tree, delete nodes from a tree, and search for a node in a tree.
		However, the rotations occur so quickly, you cannot see what is actually going on during a balancing operation.
	www.cs.duke.edu /~ola/courses/cps100e/lab/lab10.html (1395 words)

	Single Rotations (Site not responding. Last check: 2007-11-03)
		This is called an LL rotation , because the first two edges in the insertion path from node B both go to the left.
		Notice, the LL rotation was called for because the root became unbalanced with a positive balance factor (i.e., its left subtree was too high) and the left subtree of the root also had a positive balance factor.
		An RR rotation is called for when the root becomes unbalanced with a negative balance factor (i.e., its right subtree is too high) and the right subtree of the root also has a negative balance factor.
	www.brpreiss.com /books/opus5/html/page325.html (318 words)

	PMap::Remove
		It is impossible to predict at what point tree rotation will finally bring the tree into balance (that is, at least into the balance tolerance band).
		Note that this may require a double rotation involving the non-ascendent subtree if its imbalance is opposite to the imbalance of node to which we have ascended.
		Finally, it should be noted that if a step to the parent of the parent is to be taken and discovers that the parent is, in fact, the patriarch of the entire tree, then the height of the entire tree has been reduced by one and is so recorded in the tree header.
	www.grc.nasa.gov /WWW/price000/pfc/htm/pmap_remove.html (1781 words)

	CSC 378 tutorial on Binary Search Tree rotations
		Restructuring is useful to maintain a short or ``well balanced'' tree in which searching for a key takes little time.
		Note that the BST property is maintained by the rotation operation: For any node n, all keys in the left subtree of n are less than the key of n and all keys in the right subtree of n are greater than the key of n.
		Consider this tree, in which 12 is between 9 and 15.
	www.cs.queensu.ca /home/jstewart/applets/bst/bst-rotation.html (532 words)

	CS660: AVL Trees
		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/fall96/cs660/notes/avl/avl.html (542 words)

	Nutkin Knoll Farm, Maine Tree
		From the first X-mas trees we planted 14 years ago when Wesley was 6 months old.
		to this spring's start of the 2nd tree rotation and our burly 8th grade young man, the years have been richly rewarding.
		Wes mowed tree aisles and basal pruned 2,500 trees for his summer work.
	www.maine-christmas-trees.com (331 words)

	[No title]
		In the worst-case, an AVL removal will require at most 1 rotation to correct any unbalanced nodes.
		An AVL tree is a Binary Search Tree that a) has all the values in a different order b) has all of the data stored at the leaf nodes c) has additional access methods d) maintains a partial balance Answer: d
		In an AVL tree, a node is unbalanced if a) the heights of its subtrees are not the same b) the number of nodes in each of its subtrees are not equal c) both of the above d) none of the above Answer: d
	www.cs.uiuc.edu /class/fa05/cs400/_quiz/_quizsol/quiz5sol.html (789 words)

	Leyland Cypress
		In the 1800's numerous tree species from all over the world were planted in an arboreturm on the Leighton Hall estate in England.
		While many have mistakenly turned to artificial trees, others like to buy a living tree either B and B or in a large pot so they can enjoy it as a Christmas Tree and plant it in their yard afterwards.
		But the tree so produced will not be of sufficient quality to compete with other well maintained Leylands and the top quality trees being shipped in these days from the North.
	www.bugwood.org /christmas/97012.html (4887 words)

	rotation (Site not responding. Last check: 2007-11-03)
		Definition: To switch children and parents among two or three adjacent nodes to restore balance to a tree.
		See also left rotation, right rotation, balanced tree.
		Note: A rotation may change the depth of some nodes, but does not change their relative ordering.
	www.nist.gov /dads/HTML/rotation.html (100 words)

	2002 NAICS Definitions: 111421 Nursery and Tree Production
		This U.S. industry comprises establishments primarily engaged in (1) growing nursery products, nursery stock, shrubbery, bulbs, fruit stock, sod, and so forth, under cover or in open fields and/or (2) growing short rotation woody trees with a growth and harvest cycle of 10 years or less for pulp or tree stock.
		Retailing nursery, tree stock, and floriculture products primarily purchased from others--are classified in Industry 444220, Nursery, Garden Center, and Farm Supply Stores.
		Tree crop farming (except forestry), short rotation growing and harvesting cycle
	www.census.gov /epcd/naics02/def/ND111421.HTM (172 words)

	Rotating Christmas Tree Stands
		Double-bearing construction- two sets of precision bearing support the weight of both tree and decorations.
		Bi-directional clutch protects the motor mechanism if tree is obstructed or forced either forward or backward.
		If tree rotation is obstructed, a warning click sounds.
	www.nelsons-christmas.com /stands/revstand.htm (141 words)

	[No title]
		AVL trees have 4 different rotations they can apply to maintain the necessary balance.
		For any possible imbalance, one of these rotations will rebalance the tree.êø
		For any possible imbalance, one of these rotations will rebalance the tree.êîiï 0ù²L0 Àð¸ððPð( ð ððr ð Sð²¦¿ÿð `}ðÃ ¦ ð ð ð Sð³¦¿ÿðð `ð
	www.auburn.edu /~boxjame/rotations.ppt (165 words)

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