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	PlanetMath: binary tree
		A balanced binary tree is a binary tree that is also a balanced tree.
		The two (potential) children of a node in a binary tree are often called the left and right children of that node.
		This is version 4 of binary tree, born on 2002-02-25, modified 2004-05-20.
	planetmath.org /encyclopedia/BinaryTree.html (341 words)

	Topic #9: Binary search trees
		A tree is defined as a nonempty finite set of labeled nodes such that there is only one node called the root of the tree, and the remaining nodes are partitioned into subtrees.
		Consider a binary tree with p as the element to be deleted.
		Note that one of the advantages of using this operation is that the only part of the tree to be affected by the operation is the subtree of p (the shaded triangle), which consists of all the nodes inserted after p, falling between the two ropes of p.
	www.cs.mcgill.ca /~cs251/OldCourses/1997/topic9 (2726 words)

	Binary Tree - the source for migration tools and services
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	www.shopbinarytree.com /terms.asp (1191 words)

	NationMaster - Encyclopedia: Binary tree (Site not responding. Last check: )
		The height of a tree is the length of the path from the root node to its furthest leaf.
		Binary trees can also be stored as an implicit data structure in arrays, and if the tree is a complete binary tree, this method wastes no space.
		Binary trees are a specific implementation of an m-ary tree where there are m = 2 child nodes for every node on the tree.
	www.nationmaster.com /encyclopedia/Binary_tree/References (2526 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 (2823 words)

	Javanotes 5.0, Section 9.4 -- Binary Trees
		In the standard picture of a binary tree, the root node is shown at the top and the leaf nodes at the bottom -- which doesn't show much respect for the analogy to real trees.
		A binary sort tree is a binary tree with the following property: For every node in the tree, the item in that node is greater than every item in the left subtree of that node, and it is less than or equal to all the items in the right subtree of that node.
		Not all binary trees are balanced, but if the tree is created by inserting items in a random order, there is a high probability that the tree is approximately balanced.
	math.hws.edu /javanotes/c9/s4.html (4327 words)

	Cprogramming.com Tutorial: Binary Trees
		A binary tree is composed of parent nodes, or leaves, each of which stores data and also links to up to two other child nodes (leaves) which can be visualized spatially as below the first node with one placed to the left and with one placed to the right.
		Ideally, the tree would be structured so that it is a perfectly balanced tree, with each node having the same number of child nodes to its left and to its right.
		The search function shown above recursively moves down the tree until it either reaches a node with a key value equal to the value for which the function is searching or until the function reaches an uninitialized node, meaning that the value being searched for is not stored in the binary tree.
	www.cprogramming.com /tutorial/lesson18.html (1402 words)

	Binary Trees
		Binary trees have an elegant recursive pointer structure, so they are a good way to learn recursive pointer algorithms.
		The formal recursive definition is: a binary tree is either empty (represented by a null pointer), or is made of a single node, where the left and right pointers (recursive definition ahead) each point to a binary tree.
		A "binary search tree" (BST) or "ordered binary tree" is a type of binary tree where the nodes are arranged in order: for each node, all elements in its left subtree are less-or-equal to the node (<=), and all the elements in its right subtree are greater than the node (>).
	cslibrary.stanford.edu /110/binarytrees.html (4373 words)

	Binary Tree - Data Structures Visualization - Boanerges Aleman-Meza
		Binary trees are one of the fundamental data storage structures used in programming.
		The two children of each node in a binary tree are called the "left child" and the "right child", corresponding to their position when you draw a picture of a tree.
		A node in a binary tree doesn't necessarily have the maximum of two children; it may have only a left child, or only a right child, or it can have no children at all (in which case it's a leaf).
	lsdis.cs.uga.edu /~aleman/mams/csci6900/hci/partc/bintree (1045 words)

	BinaryTreeLab.html
		Because of the recursive nature of the binary tree structure (trees are sometimes referred to as recursive data structures), the depth-first traversals can be implemented with recursion.
		Another useful method for a binary tree would be a method that calculated the maximum or minimum value in the tree.
		We will define two binary trees as equal if they contain the same nodes (and the same number of each node), although the order of the nodes and the shape of the trees may differ.
	max.cs.kzoo.edu /AP/ABMaterials/Trees/BinaryTreeLab.html (1641 words)

	Levitated \| Binary Tree \| Macromedia Flash open source
		A binary tree is defined as a system of nodes in which each node may or may not contain a left and right child node.
		Unlike other tree structures, each node of the binary tree is limited to two child nodes.
		To give this binary tree a slightly more asthetic appearance, the width in which child nodes are spawned is randomized and is kept small relative to the depth.
	www.levitated.net /daily/levBinaryTree.html (117 words)

	Binary Trees in C++
		Each of these functions can be applied to the binary tree shown in the illustration at the beginning of this section.
		Not all binary trees are balanced, but if the tree is created randomly, there is a high probability that the tree is approximately balanced.
		If the tree is empty, then we have to set the tree equal to a new tree, consisting of a single node that holds the item.
	math.hws.edu /eck/cs225/s03/binary_trees (3698 words)

	Binary Search Tree
		A tree is another data structure that you can use to store pieces of information, or rather, a bunch of elements.
		A tree whose elements have at most 2 children is called a binary tree.
		First, remember that the letters in the tree are keys for the elements held in the tree.
	www.cs.bu.edu /teaching/c/tree/bst (1673 words)

	Binary Tree Example
		When data are stored in a binary tree, the place of the data is determined by some order: it is necessary to determine how the objects should be sorted.
		When processing a binary tree containing objects, the tree is recursively descended and a given operation is performed for each object.
		When the tree is already partially filled, then it is necessary to determine whether the object to add should come `before' or `after' the object of the current node.
	www.ccs.neu.edu /home/prakash/COM3116/BinaryTree.html (933 words)

	Self-Balancing Binary Search Tree
		After working with the binary tree (BiT) and binary search tree (BST) for some time it was realized that a BST was not a BiT or vice versa.
		Now BST and BiT would have one execute (the ones they currently have) which would override the execute inherited from the immutable tree since immutable binary tree algorithms are now subclasses of BST Algorithm and BiT Algorithm and we are allowing parameters to be of a super class to the ones they are over riding.
		It also prevented visitors from entering the tree because at that time the tree was still implemented in terms of a BiT which would have exposed methods that it is invalid to use on a BST.
	cs.oberlin.edu /~jwalker/tree (2378 words)

	What is binary tree? - a definition from Whatis.com
		- A binary tree is a method of placing and locating files (called records or keys) in a database, especially when all the data is known to be in random access memory (RAM).
		The number of leaves in a binary tree is always a power of 2.
		Binary trees are used when all the data is in random-access memory (RAM).
	searchsqlserver.techtarget.com /sDefinition/0,,sid87_gci509290,00.html (485 words)

	Binary Trees
		The height of a tree is the maximum length of a branch from the root to a leaf.
		In the average case it is pretty fast to insert a new item into a binary tree, because in the average case the data is fairly random and the binary tree is reasonably "bushy".
		Notice that it is handed a pointer to a node of the binary search tree and then follows a postorder traversal pattern to visit all of the nodes of the subtree rooted at the given node.
	cis.stvincent.edu /carlsond/swdesign/bintrees/bintrees.html (2815 words)

	Binary Tree - the source for migration tools and services
		Binary Tree is the leading provider of Messaging and Migration products for Lotus Notes/Domino and Microsoft Exchange.
		Binary Tree’s Common Migration Tool (CMT) family of products has been used by thousands of companies to migrate several million mailboxes as well as to migrate, consolidate, and/or enhance existing Lotus Notes and Domino infrastructures.
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	www.shopbinarytree.com (287 words)

	Binary Tree Traversals
		traverse a binary tree is to examine each of its nodes.
		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.
	nova.umuc.edu /~jarc/idsv/lesson1.html (305 words)

	Binary Search Tree
		Binary Search Tree can be implemented as a linked data structure in which each node is an object with three pointer fields.
		In binary search tree, a node's key is greater than or equal to its child's key but less than or equal to right child's key.
		The TREE-MINIMUN (x) algorithm returns a point to the node of the tree at x whose key value is the minimum of all keys in the tree.
	www.personal.kent.edu /~rmuhamma/Algorithms/MyAlgorithms/binarySearchTree.htm (1216 words)

	One-Time Binary Search Tree Balancing
		The result was a balanced tree — one in which all paths from the root to leaf nodes differ in length by at most one.
		In addition, to eliminate the need for recursion, he generated what is called a "threaded" binary tree, with back-pointers to control the traversal, eliminating the need for a recursive implementation in the traversal.
		Explicit average times were captured for building the tree with random data and emptying it without any balancing (to provide a baseline to subtract, allowing capture of just the balancing time), as well as building the tree, balancing it, and then emptying it.
	penguin.ewu.edu /~trolfe/DSWpaper (2300 words)

	MacDevCenter.com -- Scripting a Binary Tree Using Tcl
		If the binary tree is empty, then we are inserting the first data element into the tree data structure.
		We previously discussed the simplest case for inserting into a binary tree, the case when the tree is empty.
		If the new element to be inserted into the tree is greater than the first element, try inserting the new element to the right node of the tree.
	www.macdevcenter.com /pub/a/mac/2005/01/28/tcl.html (2260 words)

	binary tree
		Definition: A tree with at most two children for each node.
		An early use of the term "dyadic tree" is in Georgii M. Adelson-Velskii and Evgenii M. Landis, An algorithm for the organization of information, Doklady Akademii Nauk SSSR, 146:263-266, 1962 (Russian).
		Paul E. Black, "binary tree", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.
	www.nist.gov /dads/HTML/binarytree.html (160 words)

	binary search tree
		Definition: A binary tree where every node's left subtree has keys less than the node's key, and every right subtree has keys greater than the node's key.
		AVL tree, splay tree, threaded tree, randomized binary search tree, discrete interval encoding tree.
		Note: A binary search tree is almost always implemented with pointers, but may have a variety of constraints on how it is composed.
	www.nist.gov /dads/HTML/binarySearchTree.html (210 words)

	Dictionary of Algorithms and Data Structures
		doubly-chained tree: see binary tree representation of trees
		first child-next sibling binary tree: see binary tree representation of trees
		Data Structures and Algorithms is a wonderful site with illustrations, explanations, analysis, and code taking the student from arrays and lists through trees, graphs, and intractable problems.
	www.nist.gov /dads (662 words)

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