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Topic: Complete binary tree

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	PlanetMath: complete binary tree
		A complete binary tree is a binary tree with the additional property that every node must have exactly two “children” if an internal node, and zero children if a leaf node.
		The property of being “complete” is preserved if, at each step, we expand the tree by connecting exactly zero or two individual nodes (or complete binary trees) to any node in the tree (but both must be connected to the same node.)
		This is version 4 of complete binary tree, born on 2002-02-28, modified 2002-03-08.
	planetmath.org /encyclopedia/CompleteBinaryTree.html (131 words)

	Binary tree - Wikipedia, the free encyclopedia
		The height of a node n is the length of the path from the node n to its furthest leaf.
		In order for a tree to be the latter kind of complete binary tree, all the children on the last level must occupy the leftmost spots consecutively, with no spot left unoccupied in between any two.
		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.
	en.wikipedia.org /wiki/Types_of_binary_trees (1471 words)

	Glossary - GNU libavl 2.0.2
		(see binary tree) are adjacent if one is the child of the other.
		(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 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)

	Complete Trees
		Notice that the left subtree of node 1 is a complete binary tree of height three; and the right subtree is a perfect binary tree of height two.
		Theorem The internal path length of a binary tree with n nodes is at least as big as the internal path length of a complete binary tree with n nodes.
		Theorem The internal path length of a complete binary tree with n nodes is
	www.brpreiss.com /books/opus8/html/page353.html (785 words)

	A complete binary tree based system for activation of concurrent processes (abstract only)
		The main purpose of this paper is to create a complete binary tree (CBT) system to activate processes concurrently.
		One of the routines is called nrouter.c which is a recursive program used to create a complete binary tree structure to activate user processes simultaneously.
		The advantages of using complete binary tree structure to activate user processes are that the user processes can be activated almost simultaneously and the redundant leaves will not be created.
	portal.acm.org /citation.cfm?doid=320599.320737 (186 words)

	Exercises
		Devise an algorithm to determine whether a given binary tree is a heap.
		Devise an algorithm to determine whether a given binary tree is a leftist tree.
		Prove that a complete binary tree is a leftist tree.
	www.brpreiss.com /books/opus8/html/page383.html (406 words)

	Binary tree (Site not responding. Last check: 2007-10-26)
		Stern-Brocot Tree in Disguise: a problem for a binary tree that somehow relates to Stern-Brocot tree.
		Binary trees of this type are called complete.
		A binary tree is a tree which is either empty, or one in which every node:.
	www.wonsecurity.com /binary+tree.html (336 words)

	Sample Data Structures Questions - Chapter 10
		Then draw an array with six components and show where each of the six node values would be placed in the array (using the usual array representation of a complete binary tree).
		* root_ptr) // Precondition: root_ptr is the root pointer of a binary tree.
		Consider the node of a complete binary tree whose value is stored in data[i] for an array implementation.
	www.cs.colorado.edu /~main/questions/chap10q.html (1737 words)

	[No title] (Site not responding. Last check: 2007-10-26)
		But if there are other entries in the tree, then the tree must be rearranged because a heap is not allowed to run around without a root.
		Moreover the left side still represents a complete binary tree which is almost a heap.
		When the unsorted side of the array is once again a heap, the heapsort continues by exchanging the largest element in the unsorted side with the rightmost element of the unsorted side.
	www.mathcs.sjsu.edu /faculty/lee/cs146/23FL20heap[1].ppt (718 words)

	[No title]
		The solution to these problems is to go ahead and insert like a complete binary tree, but then reheapify upwards starting with the new data.
		To reheapify upwards --- Example Removing From a Heap Tree Since heap trees are used to find the biggest value fast, when removing from a heap tree you are always removing the biggest value.
		The solution to this problem is to save the root data in a temporary variable, move the last value in the array up to replace the root value, then reheapify downwards starting with the new root value.
	www.cs.iastate.edu /~freeman/CS228-Sum03/HeapTree.doc (318 words)

	perfect binary tree (Site not responding. Last check: 2007-10-26)
		Definition: A binary tree with all leaf nodes at the same depth.
		A complete binary tree may be seen as a perfect binary tree with some extra leaf nodes at depth n+1, all toward the left.
		This kind of tree is called "complete" by some authors ([CLR90, page 95], Leighton) and "full" by others (Budd page 331, Ege, [HS83, page 225]).
	www.itl.nist.gov /div897/sqg/dads/HTML/perfectBinaryTree.html (150 words)

	COMSC 3613 Data Structures (Site not responding. Last check: 2007-10-26)
		Therefore whenever a complete binary tree is called for, we can completely manipulate it using an array, moving up and down the tree by subscript calculation.
		Heap (Binary Max Heap) A heap is a complete binary tree in which every node has a value that is greater than or equal to that of its children.
		Sometimes a heap is known as a priority queue.
	www.comsc.ucok.edu /~stockwel/cbt.html (323 words)

	[No title] (Site not responding. Last check: 2007-10-26)
		[Basis] A single node r is a complete binary tree of height 0 with root r.
		[Inductive step] If T1 and T2 are complete binary trees of height h-1 with roots r1 and r2 respectively, a complete binary tree of height h can be constructed by taking T1, T2, and a new root vertex r, and adding edges (r, r1) and (r, r2).
		A complete binary tree of height h+1 consists of a root node plus two trees of height h (plus some edges).
	csr.uvic.ca /~wendym/courses/225/01/1notes/5notes.html (185 words)

	complete binary tree (Site not responding. Last check: 2007-10-26)
		Definition: A binary tree in which every level, except possibly the deepest, is completely filled.
		At depth n, the height of the tree, all nodes must be as far left as possible.
		This kind of tree is called "complete" by authors that mention it (Budd page 332, Ege, Carrano and Prichard page 427, Goodrich and Tamassia page 302, [HS83, page 226], [Knuth98], [Stand98, page 249]).
	www.nist.gov /dads/HTML/completeBinaryTree.html (198 words)

	PHP: Downloads
		Regular source and binary snapshots are available from snaps.php.net.
		PEAR packages, PECL hosted PHP extensions, PHP-GTK source and binaries, and Smarty sources are available on their own pages.
		See the ChangeLog for a complete list of changes, or the release notes for more information on this particular release.
	www.php.net /downloads.php (339 words)

	Heaps - CMPSCI 187
		A heap is a complete binary tre in which every node has the `heap property'.
		First, it is a complete binary tree, and second, every node has the heap property.
		It is because of our desire to use an array representation that we insist on the completeness of the binary tree.
	www.cs.umass.edu /~utgoff/cs187/lectures-spring-96/21-heaps.html (2096 words)

	full binary tree (Site not responding. Last check: 2007-10-26)
		Definition: A binary tree in which each node has exactly zero or two children.
		See also complete binary tree, perfect binary tree.
		For efficiency, any Huffman coding is a full binary tree.
	www.itl.nist.gov /div897/sqg/dads/HTML/fullBinaryTree.html (141 words)

	Heaps and Heapsort
		Recall that in a binary tree each node can have a left child node and/or a right child node.
		An almost complete binary tree is a binary tree in which the following 3 conditions hold: all the leaves are at the bottom level or the bottom 2 levels, all the leaves are in the leftmost possible positions, and (except possibly for the bottom level) all levels are completely filled with nodes.
		Definition: A minimal heap (descending heap) is an almost complete binary tree in which the value at each parent node is less than or equal to the values in its child nodes.
	cis.stvincent.edu /swd/heaps/heaps.html (2379 words)

	[No title]
		ª, A&ó ¨Trees 2¨mFor a complete binary tree, which node is the first node for a preorder traversal?
		ó¨Trees 2¨mFor a complete binary tree, which node is the first node for a postorder traversal?
		ª? &ó ¨Trees 2¨¡For a complete binary tree, which node is the first node for a levelorder traversal?
	www.cs.fsu.edu /~awang/courses/cop4530_f2003/review_for_final.ppt (276 words)

	Graph
		This vertex is the root of the tree
		) of the tree is the maximum depth of all vertices.
		is a binary tree if each vertex has an out-degree of at most 2.
	www.inf.fh-flensburg.de /lang/algorithmen/grundlagen/graphen.htm (236 words)

	Graph
		This vertex is the root of the tree
		) of the tree is the maximum depth of all vertices.
		is a binary tree if each vertex has an out-degree of at most 2.
	www.iti.fh-flensburg.de /lang/algorithmen/grundlagen/graphen.htm (236 words)

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