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Topic: Tree traversal

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	PlanetMath: tree traversals
		A tree traversal is an algorithm for visiting all the nodes in a rooted tree exactly once.
		A traversal is also defined on a forest in the sense that each tree in the forest can be iteratively traversed (provided one knows the roots of every tree beforehand).
		This is version 7 of tree traversals, born on 2002-02-25, modified 2006-07-24.
	planetmath.org /encyclopedia/PreorderTraversal.html (479 words)

	Tree traversal - Wikipedia, the free encyclopedia
		In computer science, tree traversal is the process of visiting each node in a tree data structure.
		Tree traversal, also called walking the tree, provides for sequential processing of each node in what is, by nature, a non-sequential data structure.
		This is a particularly common way of traversing a binary search tree, because it gives the values in increasing order.
	en.wikipedia.org /wiki/Tree_traversal (727 words)

	Tree (data structure) - Wikipedia, the free encyclopedia
		In graph theory, a tree is a connected acyclic graph.
		A tree in which such distinctions are made is called an ordered tree, and data structures built on them are called ordered tree data structures.
		There are many different ways to represent trees; common representations represent the nodes as records allocated on the heap with pointers to their children, their parents, or both, or as items in an array, with relationships between them determined by their positions in the array (e.g., binary heap).
	en.wikipedia.org /wiki/Tree_data_structure (500 words)

	[No title]
		Traversal is like searching the tree except that in traversal the goal is to move through the tree in some particular order.
		When the tree is full, an examination of the number of right subtrees as we move down the left of the tree shows that two nodes have right subtrees when n = 7 since the far left leaf node has no subtrees.
		For a well formed tree this is essentially O(log2 n) and for the worst case (maximum stack size) the height of the tree is (n+1)/2.
	pages.cpsc.ucalgary.ca /~marina/335/tree2.doc (2660 words)

	Zoltan Developer's Guide: Refinement Tree
		The refinement tree based partitioning algorithm was developed and implemented by William Mitchell of the National Institute of Standards and Technology.
		Unless the user provides the order through which to traverse the elements of the initial grid, a path is determined through the initial elements along with the "in" vertex and "out" vertex of each element, i.e., the vertices through which the path passes to move from one element to the next.
		The third traversal determines the partitioning by adding subtrees to a partition until the size of the partition meets the desired weight, and counts the number of elements to be exported.
	www.cs.sandia.gov /Zoltan/dev_html/dev_reftree.html (885 words)

	Binary Trees
		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)

	flipCode - Harmless Algorithms (Site not responding. Last check: 2007-10-17)
		Walking a BSP tree front-to-back is virtually identical to a conventional binary tree's inorder traversal The only difference is the definition of which of the children is the first node to be visited depends upon the sign of the dot product of the viewpoint and the plane normal of the parent node.
		Traversal of a Planar BSP from front-to-back is basically a variant on a standard binary tree inorder traversal.
		Hierarchical traversal of a kd-tree is identical to hierarchical traversal of an octree as described above or to a front-to-back traversal of a BSP tree.
	www.flipcode.com /harmless/issue02.htm (2990 words)

	Binary Space Partitioning Trees FAQ
		Each node in the BSP tree defines a partition line (this does not have be a linedef in the world but usually is) which is the equivalent to the partition plane of a 3d BSP tree.
		Tree balancing is important for these applications because the time complexity for classification is based on the depth of the tree.
		This is because the expected time complexity for tree traversal is linear on the number of polygons in the tree, rather than the depth of the tree.
	www.faqs.org /faqs/graphics/bsptree-faq (6434 words)

	Help - Tree Animation Tool (Site not responding. Last check: 2007-10-17)
		The processing of the tree traversal as with the modification of a tree depends on the type of traversal operation chosen and the type of tree that is currently being traversed.
		The output of a tree traversal is a listing of the nodes in the order that they were traversed as well as the visual animations, and the code displayed while the operation is taking place.
		The processing for the tree animation is dependent on the current state of the tree, the type of tree currently being processed, and the operation chosen.
	www.engin.umd.umich.edu /CIS/course.des/cis350/treetool/help/help.html (1342 words)

	TREES (Site not responding. Last check: 2007-10-17)
		A breadth-first tree traversal or graph search always visits both the siblings of a node, or all of its neighbors in a graph, before it visits any of its grandchildren, or neighbor's neighbors in a graph.
		Each node of the tree is visited three times during each of the depth-first traversals, once on its way down the tree, a second time coming up from the left child, and a third time coming up from the right child.
		All binary tree traversals, regardless of the order that they visit the nodes, are linear with respect to the number of number of nodes in the tree.
	dimacs.rutgers.edu /~rkrane/clecs/trees.htm (603 words)

	ASPN : Python Cookbook : Breadth first traversal of tree (Site not responding. Last check: 2007-10-17)
		The first argument should be the tree root; children should be a function taking as argument a tree node and returning an iterator of the node's children.
		The recursive call is always traversing one level higher than the outer call, so if the two calls ever reach a situation where both have the same most-recently-output node, we must have traversed the whole tree.
		The first argument should be the tree root; visitable should be an iterable with all searchable nodes; children should be a function which takes a node and return an iterator of the node's children.
	aspn.activestate.com /ASPN/Cookbook/Python/Recipe/231503 (1010 words)

	c111 - page 1 of 1
		Traversing tree is to visit each node in the tree exactly once.
		In the inorder traversal, we traverse the left subtree of the root node +.
		In the main function, we assume that we have root to be a pointer to the root of the tree.
	www.cs.pitt.edu /~chang/bookds/c111.html (2655 words)

	topic8
		They are, in addition, the "flattest" type of tree, ie, they have the largest node to height ratio, where "height" is the maximum distance (number of edges traversed) between the root and any node in the tree.
		The position of an element in the tree is implied by its position in the array: it is an implicit data structure.
		But we can do better than this: remembering that any ordered tree can be uniquely mapped to a binary tree, we can represent each node by two bits, where the left-most bit represents the absence or presence of a left-child (0 or 1 respectively) and the right-most bit, the absence or presence of a right-child.
	cgm.cs.mcgill.ca /~hagha/topic8/topic8.html (2695 words)

	(Tree-Structured) Interpreter Pattern
		Represent a problem with a tree whose leaves are primitive objects and whose internal nodes are combination rule objects.
		One-pass tree traversal is often not the most efficient approach to interpretation.
		Traversal can be accelerated by not computing elements of the traversal state that will not be read before they are changed again.
	xenia.media.mit.edu /~tpminka/patterns/Interpreter.html (1508 words)

	Traversal Code
		The simplest traversal code is to use recursion to traverse the tree in depth-first order.
		Depth first traversal means that bounding box A is tested, then box B, then the boxes with primitives D, E, and F. The idea is to find an intersection as soon as possible by traveling down into the tree.
		Notice that when the traversal is at a leaf or when the ray misses a bounding volume, we compute the next node.
	www.cs.utah.edu /~bes/papers/fastRT/paper-node12.html (803 words)

	Binary Tree Traversals » jcmiras.net
		Binary tree is a non-linear data structures consist of a finite set of nodes which either empty, or consist of a root and two disjoint binary trees, called the left and right sub-trees.
		While a tree must have at least one node, a binary tree may be empty.
		Many algorithms pertaining to tree structures usually involve a process in which each node of the tree is “visited”, or processed, exactly once.
	www.jcmiras.net /computers_and_internet/binary_tree_traversals/index.html (568 words)

	GameDev.net - Trees Part 1
		Trees are the same way in that they are made up of a collection of nodes.
		Some tree implementations maintain pointers to their parents to ease traversal, but it is not explicitly required by a tree.
		The great thing about using a tree for decision-making is that the options are cut down for every level of the tree you go down, greatly improving the speed at which the AI makes a decision.
	www.gamedev.net /reference/articles/article1374.asp (3444 words)

	(Tree-Structured) Interpreter Pattern (Site not responding. Last check: 2007-10-17)
		Represent a problem with a tree whose leaves are primitive objects and whose internal nodes are combination rule objects.
		One-pass tree traversal is often not the most efficient approach to interpretation.
		Traversal can be accelerated by not computing elements of the traversal state that will not be read before they are changed again.
	research.microsoft.com /users/minka/patterns/Interpreter.html (1508 words)

	Tree Traversal
		A traversal of a binary tree is an operation which accesses each node in the tree exactly once.
		For the tree of Exercise 9.6, the corresponding sequence is
		The in-order traversal of the binary tree for an arithmetic expression produces the infix form of the expression, while the pre-order and post-order traversal lead to the prefix and postfix (reverse Polish) forms of the expression respectively.
	scom.hud.ac.uk /scomtlm/book/node244.html (594 words)

	NodeTreeWalker (HTML Parser 2.0)
		Whether the tree traversal method used is depth-first (default) or breadth-first.
		Creates a new instance of NodeTreeWalker using the specified type of tree traversal and maximum depth from the root Node to traverse.
		Traverses to the next Node from the current Node, using either depth-first or breadth-first tree traversal as appropriate.
	htmlparser.sourceforge.net /javadoc/org/htmlparser/util/NodeTreeWalker.html (921 words)

	Tree traversal without recursion: the tree as a state machine // plasmasturm.org
		Traversal is complete when an attempt to ascend to the parent node fails because there is no parent.
		in the case of in-order traversal, you visit the current node when you come from the left child node; but when a node has no left child node, you must still ensure that the node will be visited.
		Another benefit of using iterative traversal with an explicit stack is that you can swap the stack for a FIFO, which gives you breadth-first search for free.
	plasmasturm.org /log/453 (1014 words)

	Dynamically linked Trees
		Typically, we distinguish trees based on their representation, reserving the term, tree, for structures that are encoded as dynamically linked lists.
		Its name is derived from its traversal pattern since it visits all the nodes on a level beginning with the leftmost node.
		The inorder traversal follows the left branch of the tree until it reaches a null node.
	www.iwu.edu /~sander/CS255/Notes/dynTrees.html (1556 words)

	Ray tracing with BSP and Rope trees
		To traverse the rope tree, we have to compare the position of the splitting plane with the exit-point of the current leaf-cell and follow the appropriate child.
		This allows faster traversal of the BSP tree, since for each direction of the splitting plane, the code for traversing the node is slightly different.
		All BSP trees were constructed with maximal depht 20 and the number of primitives for a node to become a leaf was 4.
	www.cg.tuwien.ac.at /studentwork/CESCG/CESCG-2000/JKrivanek (1892 words)

	AVL tree traversal (Site not responding. Last check: 2007-10-17)
		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 /~blieb/woop/avl.html (374 words)

	CF_TraverseTree (Site not responding. Last check: 2007-10-17)
		CF_TraverseTree makes use of a modified tree traversal algorithm (described by Joe Celko in his book SQL for Smarties) to represent a data tree as a one-dimensional array.
		Looping through the left traversal values in ascending order groups each set of children together and places them immediately after their parent, no matter what order the records were in originally.
		For example, in a tree of folders and documents, it may only be necessary to display documents when the user has drilled down into a particular folder from a tree representation of all folders.
	www.georgetown.edu /users/niederhp/piet/dev/customtags/traversetree.html (1608 words)

	[No title]
		Preorder traversal of a general tree is equivalent to a preorder traversal of the binary implementation of a general tree.
		Postorder traversal of a general tree is equivalent to an inorder traversal of the binary implementation of a general tree.
		The preorder traversal is ABEFCGDHIJ; the postorder traversal is EFBGCHIJDA
	www.cstp.umkc.edu /~mullinsj/cs352/lecture7.html (2402 words)

	Dr. Dobb's \| A Generic Iterator for Tree Traversal \| July 22, 2001
		Generic tree traversal logic, on the other hand, can be used with any type of tree-like structure or tree node, which lets you focus on the application logic rather than the internals of the tree structure organization.
		Tree traversal algorithms usually go over all nodes of a tree, assuming that full traversal is required by the calling code.
		Tree traversal is a linear algorithm (O(n), where n is the number of nodes), so it is important to be able to limit the number of traversed nodes.
	www.ddj.com /184404325 (3459 words)

	Class notes CS251B: Topic 8: Intro to trees
		They are, in addition, the "flattest" type of tree, ie, they have the largest node to height ratio, where "height" is the maximum distance (number of edges traversed) between the root and any node in the tree.
		Given a pre-order traversal of AB and a post-order traversal of BA, one cannot determine whether B was a left child or a right child.
		The pre-order traversal and the degree of each node taken together also provide sufficient information to reconstruct a tree (remember, the degree of a node is the number of its children).
	www.cs.mcgill.ca /~cs251/OldCourses/1997/topic8 (2791 words)

	Glossary - GNU libavl 2.0.2
		(see binary tree) with the additional property that the key in each node's left child is less than the node's key, and that the key in each node's right child is greater than the node's key.
		(see traversal) where the root's left subtree is traversed, then the root is visited, then the root's right subtree is traversed.
		(see binary tree), a list of nodes such that, for each pair of nodes appearing adjacent in the list, one of the nodes is the parent of the other.
	www.stanford.edu /~blp/avl/libavl.html/Glossary.html (1215 words)

	Lecture 12 (Site not responding. Last check: 2007-10-17)
		While it's not real important for a five-line function, if you developed large programs where the data access details were intertwingled (it's a technical term) with the higher-level issues, you'd be one unhappy camper when somebody came along and insisted on changing the data structure specs.
		It could be very useful to come up with operations associated with binary trees that would serve as a way of separating the high-level algorithm from the low-level implementation details of this particular binary tree.
		In the a-list, the first element of each sublist is a node in the tree, and the next element is a list of the children of that node.
	www.cc.gatech.edu /classes/AY2001/cs1311x/lectureSpring2001/lecture12.html (1886 words)

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