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Topic: Binary search

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	Binary search tree - Wikipedia, the free encyclopedia
		Searching a binary tree for a specific value is a recursive process that we can perform due to the ordering it imposes.
		Once the binary search tree has been created, its elements can be retrieved in order by recursively traversing the left subtree, visiting the root, then recursively traversing the right subtree.
		A splay tree is a binary search tree that automatically moves frequently accessed elements nearer to the root.
	en.wikipedia.org /wiki/Binary_search_tree (1097 words)

	Binary search - Wikipedia, the free encyclopedia
		An example of binary search in action is a simple guessing game in which a player has to guess a positive integer selected by another player between 1 and N, using only questions answered with yes or no. Supposing N is 16 and the number 11 is selected, the game might proceed as follows.
		The search begins by examining the value in the center of the list; because the values are sorted, it then knows whether the value occurs before or after the center value, and searches through the correct half in the same way.
		Binary search is a logarithmic algorithm and executes in O(log n) time.
	en.wikipedia.org /wiki/Binary_search (895 words)

	Binary numeral system - Open Encyclopedia (Site not responding. Last check: 2007-10-21)
		The binary or base-two numeral system is a system for representing numbers in which a radix of two is used; that is, each digit in a binary numeral may have either of two different values.
		The first known description of a binary numeral system was made by Pingala in his Chhandah-shastra, placed variously in the 5th century BC or the 2nd century BC.
		A binary number can be represented by any sequence of bits (binary digits), which in turn may be represented by any mechanism capable of being in two mutually exclusive states.
	open-encyclopedia.com /Binary_numeral_system (2597 words)

	Topic #9: Binary search trees
		The minimum element of a binary search tree is the last node of the left roof, and its maximum element is the last node of the right roof.
		To delete a given element from a binary search tree, we use two pointers: q and p such that q is always the parent of p.
		Binary search tree property with respect to key: a node must be larger than its left child and smaller than its right child.
	www.cs.mcgill.ca /~cs251/OldCourses/1997/topic9 (2726 words)

	Binary search at opensource encyclopedia (Site not responding. Last check: 2007-10-21)
		Binary search operates by examining the value in the center of the list; because the values are sorted, it then knows whether the value occurs before or after the center value, and searches through the correct half in the same way.
		Binary search is often used together with other algorithms such as insertion sort or data structures.
		Binary search is a logarithmic algorithm and executes in O(log n).
	wiki.tatet.com /Binary_search.html (650 words)

	Binary Search Trees
		Binary search trees store data in nodes that are linked in a tree-like fashion.
		In this respect, the algorithm is similar to a binary search on an array.
		The binary tree algorithm has been implemented as objects, using a module for the algorithm, and a class for the nodes.
	epaperpress.com /sortsearch/bin.html (669 words)

	PlanetMath: binary search
		The binary search technique is a fundamental method for locating an element of a particular value within a sequence of sorted elements (see Sorting Problem).
		If, however, the value we are searching for comes before the middle element, then we repeat the search on the first half of the sequence.
		This is version 11 of binary search, born on 2001-10-07, modified 2004-03-25.
	planetmath.org /encyclopedia/BinarySearch.html (336 words)

	Binary Search
		We represent the binary search process on a list of n elements by a binary tree; the root node of the tree contains the middle element of the list, the left (right) child of the root is the middle element of the top (bottom) 1/2 of the list, and so forth.
		However, the notion of a linked structure that can be searched rapidly can be achieved (potentially) by "imitating" the binary search tree structures which we used as a model for binary search on an ordered array.
		If the linked binary search tree is unbalanced, however, then the treesearch cost to find the insertion/deletion point is high (more than for binary search), and the overall maintenance costs are higher than is desirable.
	www.cs.rutgers.edu /~kaplan/503/binsearch.html (1205 words)

	ASPN : Python Cookbook : Binary search (Site not responding. Last check: 2007-10-21)
		Binary search is a fast algorithm for searching sorted sequences.
		For large lists that you need to search multiple times, it might well be more efficient to sort and use binary search instead of sticking to a linear search.
		Binary search is described in every introductory book on algorithms I have encountered, and is very well documented.
	aspn.activestate.com /ASPN/Cookbook/Python/Recipe/81188 (212 words)

	Binary Search Trees (Site not responding. Last check: 2007-10-21)
		If t is not empty, then t is a binary search tree if its left and right subtrees are binary search trees and all items in the left subtree are less than the root and all items in the right subtree are greater than or equal to the root.
		If t is a binary search tree, and i is an item, we would like an operation to insert i into t and retain the property that t is a binary search tree.
		If t is a binary search tree, and i is an item in t, we would like an operation to delete i from t and retain the property that t is a binary search tree.
	www.cse.ohio-state.edu /~lohse/CIS321/bst.html (772 words)

	Binary Search (Site not responding. Last check: 2007-10-21)
		At each itteration, the binary search establishes a "search zone" where key data might be found.
		If we are only going to search a list a small number of times, it's generally more efficient to use the linear search because sorting the list requires machine time.
		On the other hand, if we are going to search a large enough set of data many times, it is usually more efficient to sort the list first and then use binary search to find our items.
	www.mcs.drexel.edu /~mcs172/Sp01/lectures/2.1_Searching/Binary.html (175 words)

	4.8.2 Binary Search Trees (Site not responding. Last check: 2007-10-21)
		A binary search tree is constructed by inserting the key values 1, 2, 3, 4, 5, 6, 7 in some order specified by a permutation of 1,..., 7, into an initially empty tree.
		Define the optimum binary search tree as the one for which the average number of comparisons on a successful search is minimum.
		Also, assume that successful and unsuccessful searches are equally likely and that in the event of a successful search, it is equally likely that any of the 31 names was searched for.
	lcm.csa.iisc.ernet.in /dsa/node104.html (698 words)

	CS170 C++ Binary Search Lab (Site not responding. Last check: 2007-10-21)
		The main idea of binary search is to divide the array into two equal parts and narrow down the range of the array to be searched either to the low part of the array or high part of the array.
		Sequential search is the intuitive approach of searching an array for a particular element.
		Since binary search requires that the array be sorted in ascending order, when using the random number generator to generate integers, we need to make sure that the integers are sorted.
	www.cs.uregina.ca /Links/class-info/170/bsearch.html (1841 words)

	Binary Search Tree Phone Book (Site not responding. Last check: 2007-10-21)
		A difference in a simple binary tree and a binary search tree is that the binary search tree has the property that the stored data contains a key value such that the key value in the root of the left subtree is less than the key value in the root of the tree.
		This still leaves the problem of searching for a node since the search is based upon a key field not necessarily the entire data.
		Since we are implementing a binary search tree; not simply a binary tree it is logical to define a key within the tree.
	cs-netlab-01.lynchburg.edu /courses/DataStru/BSTPB.htm (1198 words)

	Animated Binary Tree (Site not responding. Last check: 2007-10-21)
		Search for an integer in the binary tree.
		Node comparisons will appear in the bottom panel of the applet, including whether or not the requested node exists within the binary tree.
		Node comparisons will appear in the bottom panel of the applet, including whether or not the requested node can be deleted from the binary tree (i.e.
	www.cs.jhu.edu /~goodrich/dsa/trees/btree.html (118 words)

	Binary search trees
		A binary search tree is a recursively defined data structure that simplifies the process of conducting binary searches by marking appropriate bisection points structurally instead of requiring them to be computed.
		Here's the recursive definition: A binary search tree B either is empty or consists of a datum (typically a record that includes a key field) and two binary search trees L and R, called the left and right subtrees of B.
		It presupposes that the binary search tree is not empty.
	www.math.grin.edu /~stone/courses/fundamentals/binary-search-trees.html (1229 words)

	Binary Trees
		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 (>).
		To be a binary search tree, for every node, all of the nodes in its left tree must be <= the node, and all of the nodes in its right subtree must be > the node.
	cslibrary.stanford.edu /110/BinaryTrees.html (4373 words)

	Balanced search trees - Overview
		Binary search trees (see Figure 1) work well for many applications but they are limiting because of their bad worst-case performance (height = O(n)).
		AVL trees are identical to standard binary search trees except that for every node in an AVL tree, the height of the left and right subtrees can differ by at most 1 (Weiss, 1993, p:108).
		Although searching operations on a 2-3 balanced search tree are guaranteed a very good worst case, this property comes at the expense of sometimes costly insertions.
	www.cs.mcgill.ca /~cs251/OldCourses/1997/topic19 (1230 words)

	Binary Newsgroup Search
		Binary newsgroup search is a way to search Usenet more easily to find the binaries you want to download.
		The problem with this is that when the binary files are uploaded, they are broken down into many smaller pieces that must be found and reassembled if you want to view them.
		Conducting a binary newsgroup search can be a very simple and useful way to find binaries on Usenet, especially with services like bincrawler.com.
	www.usenet.com /articles/binary_newsgroup_search.htm (296 words)

	[No title]
		Binary search is a procedure for searching an element in an array.
		In this case the search is successful and the returns the index (field position) of the element to be found.
		The search is then continued recursively to the left of the element.
	www.animal.ahrgr.de /en/Animation5.html (215 words)

	CS 367-3 - Binary Search Trees
		One property of a binary search tree is that an in-order traversal walks over the nodes in order of their keys (thus the name in-order).
		Unlike a binary tree which is a data structure, a binary search tree is an ADT.
		search --- in the worst case the search key is not found, but would be located next to the deepest leaf in the tree.
	www.cs.wisc.edu /~siff/CS367/Notes/bsts.html (1282 words)

	ongoing · On the Goodness of Binary Search
		On the other hand, binary search is so simple and robust that you can code up five subtly different binary searches for different places in your code, all using optimized direct references into your internal structures, and not suffer any software engineering angst.
		All that said, the core idea of binary search is mind-bogglingly simple; you have a sorted array, you look at the middle element which tells you what you're looking for is in the top or bottom half, then you take that half, rinse and repeat until done.
		Suppose, for example, you want to search for a range in that array; take two input numbers and find the index of the entry that is smaller than the lesser of them, and of the entry that is larger than the greater.
	tbray.org /ongoing/When/200x/2003/03/22/Binary (2007 words)

	The Official Blitz Website
		A binary search is a faster method of searching a sorted array than directly checking each element for a value.
		Binary searches simply check the value of the middle element in an array, check if its value is higher or lower than the target
		The search keeps cutting the "tree" in half, resulting in a very fast search for a value in an array with a large number of elements.
	www.blitzbasic.com /codearcs/codearcs.php?code=279 (91 words)

	binary star
		binary star or binary system,pair of stars that are held together by their mutual gravitational attraction and revolve about their common center of mass.
		True binary stars are distinct from optical doubles—pairs of stars that lie nearly along the same line of sight from the earth but are not physically associated.
		Although most binary stars have distance between them, the components of W Ursae Majoris binaries are actually in contact with each other, their mutual gravity distorting their shapes into teardrops.
	www.infoplease.com /ce6/sci/A0807587.html (528 words)

	Optimal Binary Trees vs. Optimal Alphabetic Binary Search Trees (Site not responding. Last check: 2007-10-21)
		An optimal alphabetic binary search tree can be obtained from an existing optimal alphabetic binary tree by embedding information supporting the binary search procedure in the internal nodes of the tree.
		A given leaf node (a letter from the alphabet) of the optimal alphabetic binary search tree can be located using a binary search procedure.
		On the other hand optimal alphabetic binary search trees are sufficient for both the encoding and decoding process.
	www.cs.rit.edu /~std3246/thesis/node8.html (390 words)

	C++ Notes: Algorithms: Binary Search (Site not responding. Last check: 2007-10-21)
		A fast way to search a sorted array is to use a binary search.
		If the key is less than the middle element, do a binary search on the first half.
		The advantage of a binary search over a linear search is astounding for large numbers.
	www.fredosaurus.com /notes-cpp/algorithms/searching/binarysearch.html (322 words)

	0.2.3 Binary Search Trees
		A binary search tree builds on the concept of the binary search algorithm.
		By comparing each node's value with the one for which you are searching, and then moving in the correct direction (left or right depending on the result of the comparison) it is possible to quickly determine whether a target value is in the tree or not.
		Like comparisons in the binary search, each comparison in a binary search tree (and subsequent traversal) results in a reduction the number of items yet to be searched by one-half if the tree is balanced.
	www.darkridge.com /~jpr5/archive/alg/node14.html (496 words)

	binary search (Site not responding. Last check: 2007-10-21)
		Definition: Search a sorted array by repeatedly dividing the search interval in half.
		If the value of the search key is less than the item in the middle of the interval, narrow the interval to the lower half.
		Paul E. Black, "binary search", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST.
	www.nist.gov /dads/HTML/binarySearch.html (227 words)

	Binary Search Tree
		A binary search tree is a tree that uses binary nodes (nodes with no more then two children) kept in sort order, with smaller nodes on the left and larger nodes on the right.
		In a binary search tree the efficiency of the tree depends on the height of the tree.
		The binary search tree iterator class is used for sort order tree iterations.
	www.datareel.com /docs/classes/general/gxbstree.htm (655 words)

	[No title]
		The search is continued recursively to the right of the element.
		The search is continued recursively to the left of the element.
		The animation demonstrates the process of binary searching and shows the source code.
	www.animal.ahrgr.de /en/Animation3.html (201 words)

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