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Topic: Binary heap

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	Binary heap (via CobWeb/3.1 planetlab2.cs.umd.edu) (Site not responding. Last check: 2007-10-13)
		Binary heaps are a particular kind of heap data structure such that each node only has two children, and the heap property is placed upon elements in the heap, such that internal nodes contain data that is either larger or smaller than elements in its children.
		Heaps can be organized so that the largest element in the heap is at the root of the tree always, or that the smallest element of the heap is at the root.
		Retrieving the maximum/minimum element from a heap is the basis for the heapsort algorithm.
	publicliterature.org.cob-web.org:8888 /en/wikipedia/b/bi/binary_heap.html (882 words)

	Binary heap
		Binary heaps are a particular kind of heap that only has two children.
		Binary heaps are commonly represented by arrays of values.
		The diagram on the left is somewhat deceptive in that heaps are conventionally in decreasing order rather than increasing order because of their use as priority queues.
	www.ebroadcast.com.au /lookup/encyclopedia/bi/Binary_heap.html (312 words)

	Binary Heap - GPWiki
		A binary heap is a useful data structure if you have a collection of objects to which you are adding random objects and need to remove the object with the highest (or lowest, or the extreme of some other ordering) value.
		A binary tree is already better, but a binary heap is more space efficient, and simpler.
		The way a binary heap works is that you have an array (you can use a fixed size if you know the maximum number of elements that are going to be on the heap, otherwise a dynamic array is a better idea) on which elements are organized in a way that resembles a binary tree.
	gpwiki.org /index.php/Binary_Heap (755 words)

	Heap Tickets
		Heaps where the comparison function is mathematical "greater than" are called max-heaps; those where the comparison function is mathematical "less than" are called "min-heaps".
		Note that the ordering of siblings in a heap is not specified by the heap property, so the two children of a parent can be freely interchanged (as long as this does not violate the shape property).
		Binomial heap is implemented as a collection of binomial trees (compare with a binary heap, which has a shape of a single binary tree).
	www.artistbooking.com /trips/75/heap-tickets.html (1723 words)

	Binary heap - Wikipedia, the free encyclopedia
		Binary heaps are a particularly simple kind of heap data structure created using a binary tree.
		Note that the ordering of siblings in a heap is not specified by the heap property, so the two children of a parent can be freely interchanged (as long as this does not violate the shape property, compare with treap).
		It is perfectly possible to use a traditional binary tree data structure to implement a binary heap.
	en.wikipedia.org /wiki/Binary_heap (923 words)

	6.1 Binary Heaps (via CobWeb/3.1 planetlab2.cs.umd.edu) (Site not responding. Last check: 2007-10-13)
		Heaps (occasionally called as partially ordered trees) are a very popular data structure for implementing priority queues.
		Binary heaps are special forms of binary trees while d-ary heaps are a special class of general trees.
		A binary heap is a complete binary tree with elements from a partially ordered set, such that the element at every node is less than (or equal to) the element at its left child and the element at its right child.
	lcm.csa.iisc.ernet.in.cob-web.org:8888 /dsa/node137.html (254 words)

	Heap Overview
		The heap shape: the binary tree must be a complete tree, that is every level of the tree is full/complete except perhaps for the last level which is filled in from left to right.
		Binary trees that are heaps are typically stored in an array/vector.
		This may violate the heap property, so all nodes on the path from the root to the newly added leaf must be checked to see where the new value really belongs, starting from the leaf.
	www.cs.duke.edu /courses/cps100/spring02/inclass/pq (821 words)

	Class 1: Introduction
		The (binary) heap data structure is an array object that can be viewed as a nearly complete binary tree.
		An array A that represents a heap is an object with two attributes: length[A], which is the number of elements, and heap-size[A], the number of elements in the heap stored within the array A. The root of the tree is A[1].
		The height of the heap is defined to be the longest path from the root to a leaf, and it is Q(lgn) since it is a complete binary tree.
	cs.gmu.edu /syllabus/syllabi-fall03/cs483-kaznachey/04/Heapsort.htm (828 words)

	Heaps/Priority Queues
		We define a heap as a heap-structure with keys at each node (say single character keys, for simplicity) where the key at any node is no smaller than the keys of either of its children.
		In a heap, the largest key must therefore be at the root - it can't be anywhere else, otherwise the heap property is not satisfied.
		At each step, the two subtrees of the current node are heaps, we are rooting them at this node, and locating the root in one of its subtrees until it comes to rest - at which point the tree rooted at that original index is now a heap.
	www.cs.rutgers.edu /~kaplan/503/handouts/heaps.html (1692 words)

	Algorithm Repository Home Page (Site not responding. Last check: 2007-10-13)
		The header file heap_info.h defines a common structure type for heaps so that they can be used interchangeably.
		The heap implementation of Dijkstra's algorithm is an example of this.
		The trees in a 2-3 heap can be viewed in two different ways, and this leads to two different 2-3 heap implementations.
	nz.cosc.canterbury.ac.nz /tad.takaoka/alg/heaps/heaps.html (184 words)

	Heap Sort
		Recall that to be complete, a binary tree has to fill up all of its levels with the possible exception of the last one, which must be filled in from the left side.
		Because of the heap property, as we follow that path, the elements are either decreasing or staying the same.
		It could also be that an entire subtree of the heap is the smallest element or indeed that there is only one element in the heap, which in the smallest element, so the smallest element is everywhere.
	www.personal.kent.edu /~rmuhamma/Algorithms/MyAlgorithms/Sorting/heapSort.htm (1529 words)

	CS 367-3 - Heaps
		A heap that is a binary tree is known as a binary-heap.
		A binary tree is completely full if every non-leaf node has exactly two children and all the leaves are at the same depth.
		A binary tree is complete if each non-leaf node has all its children except for at most one which is the deepest, rightmost non-leaf node.
	www.cs.wisc.edu /~siff/CS367/Notes/heaps.html (563 words)

	CSE1XX Heaps
		We will see that a heap's "coarse ordering" provides a sufficient amount of ordering to make it suitable for use as a priority queue, with add and remove operations that are O(log n) and a peek operation that is O(1).
		A binary heap has a uniform shape which is determined by the number of nodes it has (unlike a binary search tree whose shape depends on the values of the keys and the order in which they are added).
		However, a binary heap's strictly uniform structure, when implemented with an array, allows for quick parent/child access via very simple formulas, which is quicker than if a linked structure were used.
	www.seas.upenn.edu /~cse1xx/projects/Heaps (1206 words)

	Dr. Dobb's \| Algorithm Alley \| July 22, 2001 (Site not responding. Last check: 2007-10-13)
		Many heap implementations also allow you to decrease an element already in the heap, and there are a variety of less-common operations.
		Heaps are usually implemented using binary trees, with the property that for every subtree, the root is the minimum item.
		Usually, binary heaps are declared to be of a certain size and don't grow or shrink.
	www.ddj.com /184410119?pgno=1 (2967 words)

	Heap sort visualization: Home page (Site not responding. Last check: 2007-10-13)
		The Heap sort visualization applet is a tool for beginning computer science students to observe the inner workings of the heap sort sorting algorithm at an abstract level.
		The virtue of the heap sort algorithm, lies with the fact that it's complexity always remains proportional to O(nlogn) even in the worst case, given n array elements to sort.
		Ironically, the worst case scenario for the heap sort algorithm happens to be an already sorted array, which is obviously true when one considers the nature of the algorithm.
	www2.hawaii.edu /~copley/665/HSMain.html (178 words)

	Heap (data structure) - Wikipedia, the free encyclopedia
		In computer science, a heap is a specialized tree-based data structure that satisfies the heap property.
		For pairing heaps the insert, decreaseKey and merge operations are conjectured to be O(1) amortized complexity but this has not yet been proven.
		Interestingly, heaps may be represented using an array alone.
	en.wikipedia.org /wiki/Heap_(data_structure) (529 words)

	Binary Heap Insert Algorithm
		It is a data structure designed to keep up with a maximum or minimum value of interest, to return that value of interest, and to be able to have efficient inserts and deletions in that structure.
		More technically, it is a complete binary tree where every node is either less than (Max Heap) or greater than (Min Heap) its parent.
		The root of the binary heap (and consequently the Min or Max value) is always in the Array index 1.
	www.auburn.edu /~brittwr/comp3270/comp3270.html (630 words)

	CS352: Heaps [F'98]
		Leftist Heap Property: for every node x in the heap, the npl of left child is at least (>)as large as that of the right child.
		Operations of leftist heaps perform all the work on the right path, which is guaranteed to be as short as any in the heap (thus minimizing merge time).
		Interfaces for both routines are same as for binary heap implementation.
	www.cstp.umkc.edu /~mullinsj/cs352/lecture15.html (1140 words)

	Generic package: GenBinaryHeaps
		Here, each node in the heap will have a key value for ordering plus a pointer to a generic object (for example, it could be instantiated with pointers to SinSeries items).
		The heap itself is set up as an array in which the nodes are the cells of the array; therefore each cell points to one of these generic items (and could be instantiated as pointing to SinSeries items) and also has a field for ordering on the heap.
		TheHeap is a pointer to a heap which is implemented by an array of 1..
	astrogeology.usgs.gov /Projects/flexible_ga/ss/genbinaryheaps.html (920 words)

	Kelly O'Hair's Blog: Heap Dump Snapshots
		These all use the old and historic HPROF binary heap dump format as the "heap dump snapshot", which is essentially a complete dump of all the objects in the Java heap at a given time.
		By creating "snapshots in time" of the heap, this allows you to browse the data without disturbing a running process, or allows you to do some postmortem processing on a crashed process.
		This format hasn't changed, and in theory HPROF binary format files from JDK 1.2 could still be used as input HAT or the Mustang jhat, not that I'd recommend it.
	weblogs.java.net /blog/kellyohair/archive/2005/09/heap_dump_snaps.html (763 words)

	[No title]
		The id associated with every node must be a positive integer no greater then the capacity of the binary heap, which is specified by the programmer when the binary heap is created.
		Since id numbers are guaranteed to be in the range from 1 to the capacity of the heap, a hash table is not necessary.
		The third is the actual heap, a dynamically allocated array of node structures, where each node contains an id, a key, and a pointer to void that can point to anything.
	www.cooper.edu /~sable2/courses/fall2005/ece165/homeworks/heap/pa2.doc (539 words)

	CS 4521 Assignment 4
		The assignment: consists of two parts: in the first part, you are asked to implement binary heaps, and in the second part you will prove facts about them.
		I suggest that you represent binary heaps by a pair consisting of a 1000-element array of integers and the heap's size,
		It is quite easy to use recursion to display the structure of the heap if the it is oriented on the page (or screen) so that the root is at the far left and it branches off toward the right.
	www.d.umn.edu /~ddunham/cs4521f05/assignments/a4/assignment.html (733 words)

	binary heap (Site not responding. Last check: 2007-10-13)
		Definition: A complete binary tree where every node has a key more extreme (greater or less) than or equal to the key of its parent.
		A binary heap can be efficiently implemented as an array, where a node at index i has children at indexes 2i and 2i+1 and a parent at index i/2, with one-based indexing.
		Merging two binary heaps is O(n): the best you can do is just concatenate two heap arrays and make a heap of the result.
	www.nist.gov /dads/HTML/binaryheap.html (229 words)

	A Heap Based Priority Queue (Site not responding. Last check: 2007-10-13)
		The nodes in the heap are treated as if they were in an array of the max size and are accessed based on an index.
		When such a node is added, it must be moved from its position as the last element in the heap to the first, by tracing a path from its current position to the root of the heap.
		The alternative to the hash table was to maintain a binary search tree of processes, where the key would be the job id and value of a particular key would be the index of the node corresponding to that job id in the heap.
	www.csua.berkeley.edu /~ranga/school/cs161/index.html (1874 words)

	heap (Site not responding. Last check: 2007-10-13)
		Definition: A complete tree where every node has a key more extreme (greater or less) than or equal to the key of its parent.
		Note: Speaking about operating systems, "heap" refers to memory from which chunks can be allocated.
		David Carlson's heaps and heapsort tutorial and code (C++).
	www.nist.gov /dads/HTML/heap.html (139 words)

	BinaryHeap (Apache Excalibur API) (via CobWeb/3.1 planetlab2.cs.umd.edu) (Site not responding. Last check: 2007-10-13)
		The heap is either a minimum or maximum heap as determined by parameters passed to constructor.
		Instantiates a new min binary heap with the default initial capacity.
		Instantiates a new min binary heap with the given initial capacity.
	excalibur.apache.org.cob-web.org:8888 /apidocs/org/apache/avalon/cornerstone/blocks/scheduler/BinaryHeap.html (356 words)

	Binary Heap Benchmark (Site not responding. Last check: 2007-10-13)
		This benchmark implements the heapifying operation to convert an arbitrary binary tree structure into a binary heap in which the value at each node satisfies the heap property - each node's value is greater than the values of both children nodes.
		Heapifying consists of comparing the element at the current node with the elements of its children, determining if the heap property is violated, and swapping the appropriate elements if so.
		Each node of the tree is implemented as a module that can read the contents of its left and right children, compare its own element to these two values, and update its own as well as one of its children's elements.
	www.cag.lcs.mit.edu /raw/benchmark/suites/bheap/README.html (170 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		// heap.h // // This file contains prototype statements for the routines // of the binary heap library that are publically accessible.
		// PHEAP createHeap(int capacity); // // insert - Inserts a new node into the binary heap // // Inserts a node with the specified data pointer, key, // and id number into the heap.
		// void deleteMin(PHEAP, int pKey, int pId); // // delete - delete the node with the specified id from the binary* heap // // If ppData is supplied (i.e., it is not NULL), it is filled in with // the address of the data associated with the deleted node.
	www.cooper.edu /~sable2/courses/fall2005/ece165/homeworks/heap/heap.h (245 words)

	Binary heaps
		Binary heaps -- efficient data structure for priority heaps.
		An opaque data structure describing a binary heap.
		Removes the element at the top of the heap.
	gts.sourceforge.net /reference/gts-binary-heaps.html (79 words)

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