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Topic: Inorder tree walk

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	551-0318 (Site not responding. Last check: 2007-10-09)
		A tree is a data structure in which every node, except one called "root", has exactly one predecessor (and zero or one or several successors).
		A binary tree is a tree where each node can only have a left successor and a right successor.
		The path the algorithm following is from the root to where a node is or should be in the tree, therefore the running time is proportional to the length of the path, and the worst case running time is proportional to the height of the tree.
	www.cis.temple.edu /~pwang/551-PT/Lecture/551-0318.htm (880 words)

	CS 4521 Assignment 4
		The 'c' command creates an empty tree on which subsequent commands are to be performed.
		You can use recursion to display the structure of the tree if the tree is oriented on the page (or screen) with the root at the far left and children to the right.
		is (a pointer to) the root of the tree.
	www.d.umn.edu /~hudson/4521/assignments/assignment4.html (727 words)

	CS 14: Programming Assignment 6 (Site not responding. Last check: 2007-10-09)
		The binary search tree you coded in assignment 5 is limited in that it can only hold integer values.
		The binary search tree class you created for assignment 5 should be modified so that each binary search tree node contains a separate data member for the key and the data being stored.
		It should search the tree for a node with a key that matches the passed in value and return the data from the matching node, if found.
	www.cs.ucr.edu /~gusta/cs14f99/cs14_as6.html (581 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		the node y that is "spliced out" from the tree is the successor[z] node, not z itself as in the first two cases; here we need to reattach the child of the successor[z] and simply replace the key of z with the key of its successor.
		The key idea for the RB structure: we start with a basic structure that is a complete binary tree, and mark all its nodes as fl nodes indicate their belonging to the basic structure: obviously the fl height is log(#fl nodes).
		Any other tree with the same fl height bh will have more nodes as it will retain all the fl nodes of the smallest RB tree and add some red nodes in-between the fl nodes and some fl leafs for the red nodes where needed.
	metcs.bu.edu /~zlateva/cs566/SearchTrees.doc (1425 words)

	Lecture 8 - binary trees
		A binary tree is a rooted tree where each node contains at most two children.
		A binary tree can be implemented where each node has left and right pointer fields, an (optional) parent pointer, and a data field.
		Tree predecessor/successor both run in time proportional to the height of the tree.
	www.cs.sunysb.edu /~algorith/lectures-good/node8.html (1067 words)

	Class notes CS251B -- Winter 1997 : Topic#20 : Augmented Data Structures
		Running time: to maintain tree sizes in the Phase 1 of insertion or deletion we have to increment or decrement size[x] for each node x on the path from the root down toward the leaves.
		Interval tree is a binary search tree for intervals which are efficient for the dictionary operations and overlap.
		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)

	Binary Search Trees (Site not responding. Last check: 2007-10-09)
		(h) time, where h is the height of the tree.
		Given a pointer to a particular node, the node containing the successor value can be found.
		Tree is a pointer to some data type that represents an entire tree.
	homepages.ius.edu /JHOLLY/c455/notes/Chapter12/BinTrees.htm (438 words)

	4.8.2 Binary Search Trees
		successor(x) as the key which is the successor of x in the sorted order determined by an inorder tree walk.
		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.
	lcm.csa.iisc.ernet.in /dsa/node104.html (698 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		In other words, show a set of points S and another point p, not in the set, such that sorting the points relative to p (using the angles from p to the points in the set) and then applying Graham's scan does not lead to the correct convex hull.
		Thus, the set operations are fast if the height of the search tree is small; but if its height is large (i.e., it is unbalanced) their performance may be no better than with a linked list.
		Thus, for example, an inorder tree walk of the data structure lists the intervals in sorted order by low endpoint.
	www.nada.kth.se /~rand/ak97/ovning6 (605 words)

	Binary Search Tree
		During this type of walk, we visit the root of a subtree between the left subtree visit and right subtree visit.
		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)

	CS 14: Programming Assignment 5 (Site not responding. Last check: 2007-10-09)
		If the value was found and removed from the tree, the method returns 1; if the value was not in the bst table, the method returns 0.
		This method determines whether or not the integer value passed to it is in the tree or not.
		Finds and returns the largest value in the tree (or 9999999 if the tree is empty; make sure and declare 9999999 as a constant).
	www.cs.ucr.edu /~gusta/cs14f99/cs14_as5.html (405 words)

	Class 1: Introduction
		Binary search tree is a binary tree that stores keys and satellite data.
		It takes Q(n) to walk an n-nodeBST, since the procedure is called exactly twice for each node of the tree (left and right child) + printing the node.
		The nodes encountered form a path downward from the root of the tree, hence the running time of search is O(h), where h is the height of the tree.
	cs.gmu.edu /syllabus/syllabi-fall03/cs483-kaznachey/09/BinarySearchTrees.htm (676 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		So, if find_node() finds that the value n is already in the tree, the function does nothing else.
		Additionally, however, check to see if tn is the root of the tree since we must do things slightly differently if so during each step of going throught the tree.
		This is due to the fact that in a binary search tree, if a node has two children, its successor has no left child.
	mrl.nyu.edu /~harper/code/binsearchtree.c (509 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		Inorder tree walk produces a sorted order of number.
		Inorder -> the root is printed BETWEEN the values in its left subtree and those in its right subtree.
		h=lgn iff the tree is a balanced tree.
	www.cs.tufts.edu /~sanpawat/al/chap13.txt (132 words)

	Intro to Algorithms: CHAPTER 13: BINARY SEARCH TREES
		A binary search tree is organized, as the name suggests, in a binary tree, as shown in Figure 13.1.
		As an example, the inorder tree walk prints the keys in each of the two binary search trees from Figure 13.1 in the order 2, 3, 5, 5, 7, 8.
		Given a node in a binary search tree, it is sometimes important to be able to find its successor in the sorted order determined by an inorder tree walk.
	www.personal.kent.edu /~mlu3/CSCourses/AdvAlgorithms/CLR-BOOK/books/book6/chap13.htm (4783 words)

	CS 4521 Assignment 5
		In the first part, you implement and demonstrate the red-fl tree operations.
		As described in the text and in class, red-fl trees are a specialization of binary search trees which guarantee balance (within limits) so that searches, insertions, and deletions are O(lg n).
		Note that since the nodes are inserted in key order, a straight BST implementation would link the nodes linearly in the equivalent of a linked list, not a balanced tree.
	www.d.umn.edu /~hudson/4521/assignments/assignment5.html (406 words)

	prog3 (Site not responding. Last check: 2007-10-09)
		For this programming assignment, you are asked to implement a variation of the binary search trees, which are slightly different from the binary search trees described in the book.
		Each node of your search tree has three components only: 1) a left child, 2) a right child, and 3) a real number for a key.
		That is, your tree node does not contain a parent pointer.
	lambda.uta.edu /cse2320/prog3 (265 words)

	Trees
		Height of a tree is the height of the root
		If we have an n-ary tree (each node has at most n children), each node could contain links to all its children (could be null)
		Binary Search Tree: every node is no smaller than any value in its left subtree and no larger than any value in its right subtree
	www.cs.umbc.edu /courses/undergraduate/202/spring02/bb/202.webnotes.trees.spring02.htm (697 words)

	C++ Annotations Version 4.0.0 (Site not responding. Last check: 2007-10-09)
		When processing a binary tree containing objects, the tree is recursively descended and a given operation is performed for each object.
		When scanning inorder first the left subtree is scanned, then the leaf itself is processed and finally the right subtree is scanned.
		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.cc.gatech.edu /data_files/classes/cs6390/burks/cpp/cpptut/cpp15.htm (5464 words)

	[No title]
		Little is known about the height of a binary tree build with insertions and deletions If built by insertion alone, and also built in a random way such that the n keys give rise to a tree from an empty tree in which the keys are inserted in random order.
		However, since the modify the tree, it is at least possible if not likely that the result may violate the red-fl properties described in section 13.1 We must restore these properties: we must possibly change the colors of some nodes and change the pointer structures.
		No more than two rotations are performed.¡ªP5:º%/óJ)¨Treapsª¨If we insert a set of n items into a standard binary search tree, the resulting tree may become horribly unbalanced This leads to long O(n) search times Randomly built binary search trees tend to be balanced.
	www.vancouver.wsu.edu /fac/wade/pub/cpts450/fall2004/slides/slides201-300.ppt (840 words)

	Review: Inorder Tree Walk (Site not responding. Last check: 2007-10-09)
		An inorder walk prints the set in sorted order:
		Preorder tree walk: print root, then left, then right
		Postorder tree walk: print left, then right, then root
	www.cs.virginia.edu /~luebke/cs332.fall00/lecture10/tsld004.htm (36 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		It holds * a key and a payload object (the containees) and has some housekeeping * pointers for maintaining a binary search tree.
		These are all * static to keep the size of the node object to a minimum.
		/ /* * This method does an inorder tree walk and prints * out the results to the passed in printstream.
	www.mcmanis.com /chuck/java/javaworld/src/dec96/v2/BSTNode.java (352 words)

	BinaryTree (JUtil 1.0 documentation)
		Sometimes you want to expose the fact that you're working with a Tree, instead of abstract it into a Set or what-have-you.
		Returns the successor of x in the sorted order determined by an inorder tree walk.
		Subclasses are expected to swap any data derived from the positions as well.
	cag.lcs.mit.edu /~cananian/Projects/JUtil/jutil-1.0/doc/net/cscott/jutil/BinaryTree.html (337 words)

	[No title]
		[10] Encouraged by the nice amortized cost analysis showing that a heap of n elements can be built in O(n) time, your friend, Bob, has designed an algorithm of building a binary search tree from any given set of n elements, and claims that his algorithm takes only O(n) comparisons.
		Your other friend, John, says that Bob's claim must be flawed because any comparison-based sorting algorithm takes at least Omega(n lg n) comparisons.
		If Bob's claim were true, then his tree building algorithm followed by an inorder tree walk would be able to sort n elements with only O(n) comparisons.
	www.deas.harvard.edu /courses/cs124/cs124-midterm-97.html (893 words)

	Ovning 17 for INDA Winter 99 (Site not responding. Last check: 2007-10-09)
		There are a variety of ways to implement what are generally referred to as height balanced or self-balancing binary search trees.
		An interval tree is an AUGMENTED height balanced binary search tree that is used to support operations on dynamic sets of intervals of real numbers.
		VLSI databases commonly represent an integrated circuit as a list of rectangles.
	www.nada.kth.se /kurser/kth/2D1340/inda98/ov17.html (579 words)

	COT 4400 Exam 2 Review (Site not responding. Last check: 2007-10-09)
		Hash tables: Basic concept, collisions, collision resolution by chaining, asymptotic run-time for search in hash table with chaining, properties of a good hash function, how open addressing works
		Binary search trees: definition and binary-search-tree property, proof of run-time for inorder-tree-walk (details), tree-search algorithm, insertion and deletion processes for binary search trees.
		Red-Black trees: definition with 5 properties, lemma 13.1 on height and it's proof (details), max run-time for operations
	www.cse.fau.edu /~roy/cot4400.04s/exam_2_review.html (197 words)

	Introduction to Algorithms \| Glossary
		defined on n keys as one that arises from inserting the keys in random order into an initially empty tree, where each of the n!
		We define the total path length P(T) of a binary tree T as the sum, over all nodes x in T, of the depth of node x, which we denote by
		Any use is subject to the Terms of Use and Privacy Policy.
	highered.mcgraw-hill.com /sites/0070131511/student_view0/chapter12/glossary.html (258 words)

	[No title]
		/************************************************************* This defines red-fl trees, a balanced version of binary trees**.
		See pp263 of Corman, Leiserson, and Rivest, "Introduction to Algorithms" for more details.
		left), k, z)); else return(tree_search_return(&((x)->right), k, z)); } /****************************************************/ /left rotates the tree about the node x ******/ int left_rotate (tree, x) struct rb_tree tree, x; { struct rb_tree y; y = (x->right); x->right = y->left; if ((y->left != NULL) && (key(y->left)
	marathon.csee.usf.edu /~sarkar/cgeom_code/red_black_tree.c (124 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		Binary search imposes an implicit tree organization on the data set.
		The tree structure is what allows operations to be fast.
		left); x->print(); Inorder-Tree-Walk(x->right); } }¡T~ª6ó¿¨Exercise¨dFor the set of keys {1, 4, 5, 10, 16, 17, 21}, draw binary search trees of height 2, 3, 4, 5, and 6.¡eeóÀ¨Searchª óÁ¨Insertª óÂ¨Insertion at the rootª óÃ¨Insertion at the rootª óÄ¨ Rotationsª /ðó
	www.eg.bucknell.edu /~csci311/F03/lectures/lecture23.ppt (742 words)

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