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Topic: Binary tree sort

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	Sorting algorithm - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-09)
		Efficient sorting is important to optimizing the use of other algorithms (such as search and merge algorithms) that require sorted lists to work correctly; it is also often useful for canonicalizing data and for producing human-readable output.
		Bubble sort is the most straightforward and simplistic method of sorting data that could actually be considered for real world use.
		For sorting really enormous amounts of data that completely dwarf system memory, even the index may need to be sorted using an algorithm or combination of algorithms designed to perform reasonably with virtual memory, i.e., to reduce the amount of swapping required.
	en.wikipedia.org /wiki/Sort_algorithm (2072 words)

	Binary search tree - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-09)
		Although this operation does not always traverse the tree down to a leaf, this is always a possibility; thus in the worst case, it requires time proportional to the height of the tree.
		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 (1088 words)

	Java Programing: Section 11.4 - Andamooka Reader (Site not responding. Last check: 2007-10-09)
		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 with 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.
		But the binary sort tree property guarantees that the items in the left subtree of "judy" are precisely those that precede "judy" in alphabetical order, and all the items in the right subtree follow "judy" in alphabetical order.
	www.andamooka.org /reader.pl?pgid=javanotesc11s4 (3870 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 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 (2830 words)

	Binary search tree
		In computer science, a binary search tree is a binary tree where every node has a value, every node's left subtree has values less than the node's value, and every right subtree has values greater.
		There is a sort algorithm based on binary search trees, and also a search algorithm.
		There are a variety of schemes for overcoming this flaw with simple binary trees.
	www.brainyencyclopedia.com /encyclopedia/b/bi/binary_search_tree.html (428 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		The internal path length of the tree is ___26___.
		A right pre-threaded binary tree may be traversed efficiently in preorder without the use of a stack.
		The Binary Tree Sort is not in-place because of the space needed for the tree nodes.
	www.unf.edu /public/cop3530/phigbee/exams/exam2.key (1739 words)

	Trees
		is a tree used to illustrate the logical relationships among records in a database.
		is a binary tree T in which data is "stored" in the vertices such that data in the left subtree is less than the data in the right subtree.
		Regardless of the notation, an expression is represented in a binary tree in the same manner all the time.
	www.lv.psu.edu /ojj/courses/ist-230/topics/trees.html (1273 words)

	GameDev.net - Heapsort
		By viewing the array as a complete binary tree, Heap Sort transforms such a binary tree into a heap.
		Sort the complete binary tree (actually an array) so that it becomes a max-heap, thus the first element is always the biggest element.
		Since what we want is exactly the opposite (the last element should be the biggest instead), we swap the first element and the last element.
	www.gamedev.net /reference/articles/article706.asp (262 words)

	[No title]
		It uses a binary sort tree of strings.
		Then the number of nodes in the tree and a list of items in the tree are output.
		Since the tree is a sort tree, the output // will be in increasing order.
	math.hws.edu /javanotes/source/SortTreeDemo.java (869 words)

	[No title]
		You will be provided a binary tree sort program and you will build a bubble sort program.
		As they are placed into the sort tree, the tree is built by the placenode() procedure one node at a time, starting at the root.
		Program Design - Your bubble sort program should be able to access an array, say S() of N values where N is the maximum number of values to be sorted.
	campus.murraystate.edu /academic/faculty/bob.pilgrim/245/lab_07_2.doc (684 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		The intent of the tree class is to provide a dynamic binary search tree that creates and searches a binary tree.
		It should not matter what the representation of the tree is to a user and, in theory, you could totally change it and as long as the user recompiles, the user's code (e.g., your driver program) should work.
		If you have constructed the tree // correctly, this will be sorted order // void binary_tree::sort(void) { } // // WRITE a small driver program as was done on the stack example and insert some integers into the tree to test your code.
	www.rivier.edu /faculty/rgreene/web/cs551/ooprog.htm (326 words)

	Tree Sort (Site not responding. Last check: 2007-10-09)
		Because of its structure records stored in a binary tree are already in sorted order if a traversal of the tree is made using an Inorder search technique.
		If records are to be stored in a binary tree no other data structure is needed.
		Insert each record into the binary tree using the standard binary tree InsertNode() function.
	www.cs.uah.edu /~rcoleman/Sorting/TreeSort.html (267 words)

	Binary Space Partitioning Trees FAQ
		BSP tree construction is a process which takes a subspace and partitions it by any hyperplane that intersects the interior of that subspace.
		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.
	www.faqs.org /faqs/graphics/bsptree-faq (6434 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.
		This is exactly the same as the binary search algorithm, and the result is a similarly efficient algorithm.
		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 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 /swd/bintrees/bintrees.html (2923 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		Most classical sorts have time requirements that range from O(n log n) for the faster sorts to O(n^2) for the slower sorts.
		In the partitioning performed by quicksort, an element "a" of the n-element array to be sorted is placed in a position "j" such that (explain): p.
		337-338 Binary tree sort was accepted as an answer, but it is best when the original data is organized so that approximately half the numbers following any given number a in the array are less than a and half are greater than a.
	www.unf.edu /public/cop3530/phigbee/quiz/quiz6.key (445 words)

	Heapsort Algorithms (Site not responding. Last check: 2007-10-09)
		Sorting, in general, is very important due to “need for sorting arises in many situations” (Data Abstraction and Problem Solving in Java; page 384).
		It is known fact that mergesort and radix sort algorithms are the two of the best in terms of Big-O analysis, according to the textbook of Data Abstraction and Problem Solving with Java, but selecting the best suited sorting algorithm for a particular data size and specific input order is crucial for optimal results.
		Number of comparisons that it makes during run time is very small when compared to some of the other sorting algorithms, such as that of the insertion or quicksort.
	www2.hawaii.edu /~mhackler/heapsort.htm (934 words)

	Computer science department
		C. The binary search tree sort can easily be used as an example use of trees before the other sorts are discussed.
		E. As recursion techniques are particularly useful for tree algorithms, recursion is primarily discussed in conjunction with trees.
		G. At least one order(n squared) sort will be implemented, as well as a version of the quicksort, and a version of the heapsort.
	cs.lamar.edu /curricula.htm (349 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		import java.io.; import java.util.Enumeration; import tree.; // The TreeSort class uses a binary tree to sort** lines in a file and // remove duplicates.
		Each line is inserted into the tree and the tree // is then enumerated to print each line.
		Tree tree = new Tree(); String line; while ((line = in.readLine()) != null) { // Insert the current line into the tree.
	www.fas.harvard.edu /~adm119/lectures/examples/java/day6/TreeSort.java (404 words)

	Lab 7 - Binary Search Tree Sort
		where infile is the name of the file containing the unsorted numbers and outfile is the file to be created and filled with the sorted numbers after duplicates have been removed.
		A binary search tree (BST) has the property that at every node, the data in the node is larger than all the values in that node's left subtree and smaller than all the values in that node's right subtree.
		After that you find the proper place for a value by moving down the tree comparing the value to the ones already in the tree.
	www.mathsci.appstate.edu /~dap/classes/2440/lab9.html (844 words)

	Dynamic Memory Allocation and Dynamic Structures (Site not responding. Last check: 2007-10-09)
		Write a program to sort a sequence of numbers using a binary tree (Using Pointers).
		A binary tree is a tree structure with only two (possible) branches from each node (Fig.
		To sort numbers simply assign the left branch to take numbers less than the node number and the right branch any other number (greater than or equal to).
	www.kongu.edu /~sakthi/C/node11.html (746 words)

	lecture26
		In real world programming you will most often use sorting algorithms that are already included in the libraries with the programming language or an application you will work with.
		As the result, insertion sort is the preferred sort in situations where the input is almost sorted and we expect only a few items to be out of order.
		The total number of operations is the same as for the worst case insertion sort, i.e.
	www.ccs.neu.edu /home/vkp/csu213-sp05/Lectures/lecture26.html (1421 words)

	MCS 360 Lecture Twenty Thirty
		In this lecture we considered sorting using a priority queue and a binary tree.
		The straight selection sort in between can be regarded as a possible implementation of the delete operations in a priority queue.
		For each sort we counted the number of comparisons.
	www.math.uic.edu /~jan/mcs360/lec30.html (128 words)

	100#19
		Binary search tree sort is good if tree is kept balanced
		A pivot element of the vector being sorted is chosen.
		Elements of the vector are rearranged so that elements less than or equal to the pivot are moved before the pivot.
	www.cs.duke.edu /~dr/100.99f/n/L19.html (414 words)

	COS 381 - COMPUTER ORGANIZATION (Site not responding. Last check: 2007-10-09)
		This routine should be a standard recursive algorithm as would typically be done in a high level language.
		Implement a routine which will TRAVERSE a binary tree recursively in inorder to print the element in numeric order.
		Duplicate entries should generate an error message and not be entered in the tree.
	www.css.tayloru.edu /~btoll/f97/381/p5f97.html (478 words)

	Scheme Sorting Examples
		Remember that selection sort works by finding the smallest element and moving it into the first position, then finding the second smallest and moving it into the second position.
		The binary tree sort works by building a binary search tree from the input and then traversing it.
		If we can build such a tree from the input, than a inorder visit finds the elements in the correct order.
	www.tjhsst.edu /~rlatimer/assignments2004/SmalltalkSamples.html (786 words)

	TREE STRUCTURES
		Records with equal keys (if duplicate keys are permitted) maintain their relative position within the sort.
		/* Node - ptr to a node in the tree
		Here is a recursive algorithm to build an ordered balanced Binary tree from the entries in the array.
	www.seasite.niu.edu /cs464/tree2.htm (671 words)

	CIS 250 - Assignment #7 (Site not responding. Last check: 2007-10-09)
		The objective of this assignment is to use a binary tree to sort and obtain a count of all the words in the novel "A Tale of Two Cities" which is available on kermit at /examples/cities.txt.
		The binary tree class and associated Node class must be templated to allow various classes to be used as data in the nodes.
		This shouldn't be difficult since we should be creating one in class.
	kish.cc.il.us /faculty/dklick/cis250/asst07.html (192 words)

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