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Topic: Heapsort

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	heapsort
		Note: Heapsort can be seen as a variant of selection sort in which sorted items are arranged (in a heap) to quickly find the next item.
		David Carlson's heaps and heapsort tutorial and code (C++).
		Comparison of quicksort, heapsort, and merge sort on modern processors.
	www.nist.gov /dads/HTML/heapSort.html (208 words)

	PlanetMath: heapsort
		Heapsort is not quite as fast as quicksort in general, but it is not much slower, either.
		Also, like quicksort, heapsort is an in-place sorting algorithm, but not a stable sorting algorithm.
		This is version 6 of heapsort, born on 2002-03-07, modified 2004-04-02.
	planetmath.org /encyclopedia/Heapsort.html (274 words)

	Heapsort
		Heapsort is one of the good general-purpose sort algorithms, part of the selection sort family.
		Heapsort works by first finding the largest element in the array, putting it in the last position, finding the next largest element, putting that in the next-to-last position, etc. A naive implementation of this idea would result in selection sort.
		Heapsort is more efficient because it uses a data structure called a heap.
	www.ebroadcast.com.au /lookup/encyclopedia/he/Heapsort.html (949 words)

	Heapsort
		Heapsort is one of the best general-purpose sort algorithms, a comparison sort and part of the selection sort family.
		Heapsort also competes with merge sort, which has the same time bounds, but requires Ω(n) auxiliary space, whereas heapsort requires only a constant amount.
		Heapsort relies strongly on random access, and its poor locality of reference makes it very slow on media with long access times.
	www.brainyencyclopedia.com /encyclopedia/h/he/heapsort.html (886 words)

	Heapsort, Quicksort, and Entropy
		He says `I suspected that heapsort should do better than its poor reputation and I think these results bear that out.' In his tests, the best compiler (for either heapsort or quicksort) produced a heapsort that was about 20% faster than quicksort, in total CPU time.
		Heapsort is inefficient in its comparison count because it pulls items from the bottom of the heap and puts them on the top, allowing them to trickle down, exchanging places with bigger items.
		After all, Heapsort's starting heap is rather like an organization in which the top dog has been made president, and the top dogs in divisions A and B have been made vice-president; a similar organization persists all the way down to the lowest level.
	www.aims.ac.za /~mackay/sorting/sorting.html (0 words)

	Heapsort
		Heapsort does not have a locality of reference advantage and thus might runs quicker then alternatives on CPU architectures with small or slow data caches.
		Heapsort is an internal sorting method which sorts an array of n records in place in O(n log n) time.
		Note: Heapsort can be seen as a variant of selection sort in which sorted items are arranged (in a heap) to quickly find the next item.
	www.softpanorama.org /Algorithms/Sorting/heapsort.shtml (2253 words)

	Heapsort
		Heapsort is one of the best general-purpose sort algorithms, and is part of the selection sort family.
		Heapsort also competes with mergesort, which has the same time bounds, but requires Ω(n) auxilary space, whereas heapsort requires only a constant amount.
		However, mergesort is simpler to understand than heapsort, is a stable sort, parallelizes better, and can be easily adapted to operate on linked lists and very large lists stored on slow-to-access media such as disk storage or network attached storage.
	www.xasa.com /wiki/en/wikipedia/h/he/heapsort.html (657 words)

	OS/2 e-Zine! - The REXX Files
		Heapsort is much more efficient than the bubble sort or the insertion sort, which you will recall from last month, are N-squared algorithms meaning that they require of order NxN comparisons to sort N items.
		Heapsort is perhaps not as well known as Quicksort, which is another Nlog2(N) algorithm that in most cases is the fastest known algorithm.
		The name Heapsort comes from "heap" which is a set of N numbers (let's call the set "a") defined in a specific way mathematically.
	www.os2ezine.com /v3n01/rexx.htm (1016 words)

	Sorting revisited
		The inner loop for heapsort has an opportunity to perform conditional computation rather than an unpredictable conditional branch (a big no no on modern microprocessors) and these flags allow the Intel compiler to exploit this situation while the other compilers were unable to do this.
		Furthermore, heapsort has very poor data locality, while Quicksort has excellent locality, which means the read/write penalties will be worse for heapsort than Quicksort.
		Introsort is just a quicksort that calls itself recursively as normal until it detects that its stuck in one of its worse case scenarios and just switches to heapsort for such bad partitions.
	www.azillionmonkeys.com /qed/sort.html (2194 words)

	Wanginator.de - Heap Sort
		HeapSort is a very efficient comparison sorting algorithm invented by Robert W. Floyd and J. Williams in 1964.
		Bottom-Up HeapSort is a variant by Ingo Wegener in 1990 which reduces the comparision overhead for great data sets.
		HeapSort is not better than other sorts when encountered with an already sorted list.
	www.wanginator.de /studium/applets/heapsort_en.html (681 words)

	Technical Reports :: Princeton Computer Science
		Heapsort is a classical sorting algorithm due to Williams.
		In Williams's original Heapsort, the new root is sifted down by repeatedly comparing its two children, and swapping it with its larger child if a comparison shows the child to be larger than the key being sifted.
		For both versions of Heapsort, it is shown that these best and worst case numbers can be found in heaps that also require the best and worst case numbers of key comparisons.
	www.cs.princeton.edu /research/techreps/TR-370-92 (330 words)

	man: heapsort
		The qsort() and heapsort() functions sort an array of nmemb objects, the initial member of which is pointed to by base.
		The algorithms implemented by qsort(), qsort_r(), and heapsort() are not stable, that is, if two members compare as equal, their order in the sorted array is undefined.
		The heapsort() and mergesort() functions return the value 0 if success- ful; otherwise the value -1 is returned and the global variable errno is set to indicate the error.
	www.hmug.org /man/3/heapsort.php (576 words)

	Heapsort
		Heapsort relies on creating a certain kind of data structure called a HEAP.
		A heap is an array (or binary tree) which has the property that for every element at location K, it is greater or equal to the elements at 2K and 2K+1.
		The next picture walks you through the Siftdown process, as the main Heapsort algorithm swaps new large keys with new "last" positions, and calls on Siftdown to "re-heapify" the array.
	www.seasite.niu.edu /cs464/heapsort.htm (650 words)

	Koders Code Search - HeapSort.java - Java
		1998 Dec 28 This simple heapsort demonstrates the use of a delegate object to implement a callback.
		A heapsort works much like a cutthroat bureaucracy with underlings constantly challenging their bosses for dominance.
		RadixSort is faster than HeapSort which in turn is faster than QuickSort.
	www.koders.com /java/fidC213180CAF275B32EB3DA5E97E94857BFB30BBD6.aspx (0 words)

	Heapsort
		Der folgende Algorithmus Heapsort konstruiert zunächst mittels buildheap aus den zu sortierenden Elementen einen Heap.
		Heapsort ist damit optimal, da es die untere Schranke erreicht.
		Heapsort wurde 1964 von Williams in der Rubrik Algorithms der Zeitschrift Communications of the ACM angegeben [Wil 64].
	www.iti.fh-flensburg.de /lang/algorithmen/sortieren/heap/heap.htm (1056 words)

	Class 1: Introduction (Site not responding. Last check: )
		There is a wide variety of sorting algorithms, and they use a rich set of techniques.
		Heapsort algorithm sorts in place and its running time is O(nlogn).
		Hence the running time of heapsort is O(n) + O(nlgn) = O(nlgn).
	cs.gmu.edu /syllabus/syllabi-fall03/cs483-kaznachey/04/Heapsort.htm (828 words)

	CIS Department > Tutorials > Software Design Using C++ > Heaps and Heapsort
		Heapsort is performed by somehow creating a heap and then removing the data items one at a time.
		Heapsort is Theta(n * lg(n)), either average case or worst case.
		The other main component of heapsort was described earlier: to repeatedly remove the root item, adjust the heap, and put the removed item in the empty slot toward the end of the array (heap).
	cis.stvincent.edu /html/tutorials/swd/heaps/heaps.html (2425 words)

	Heapsort
		The function heapsort is not called by any function of the algorithm.
		Because of the data structure implementation the array appears to the algorithm as a heaptree.
		This is the entry function of the heapsort algorithm.
	olli.informatik.uni-oldenburg.de /heapsort_SALA/english/Funktionen/heapsort.html (547 words)

	Heap Sort - CS245 Project By Joseph George
		The heapsort algorithm uses the data structure called the heap.
		Consequently, the Heapify algorithm is recursively applied to the appropriate subtree rooted at the the node whose value was just swapped with the root and the process continues until either a leaf node is reached, or it is determined that the heap property is satisfied in the subtree.
		In the Heapsort algorithm, Heapify is used (N/2) times to construct the initial heap and (N-1) times to sort.
	www.cse.iitk.ac.in /users/dsrkg/cs210/applets/sorting/heapSort/heapSort.html (607 words)

	Sorting by divide-and-conquer
		Heapsort uses close to the right number of comparisons but needs to move data around quite a bit.
		It also uses even fewer comparisons than heapsort, and is especially suited for data stored as linked lists.
		This is simpler than heapsort (so easier to program) and works pretty well.
	www.ics.uci.edu /~eppstein/161/960118.html (1693 words)

	7.4 The Heapsort Algorithm (Site not responding. Last check: )
		The heapsort algorithm then repeats this process for the heap of size n-1 down to a heap of size 2.
		Each heap is shown at the beginning of an iteration of the for loop in line 2.
		The HEAPSORT procedure takes time O(n lg n), since the call to BUILD-HEAP takes time O(n) and each of the n-1 calls to HEAPIFY takes time O(lg n).
	www.cs.uml.edu /~skaminen/ALGO/sec74.html (193 words)

	Information Structures
		Another nlogn sorting algorithm is known as heapsort.
		Heapsort is based on a hierarchical tree structure.
		heapsort is guaranteed to finish in time O(n log n) with minimal storage, so on large lists it performs better than mergesort (which requires a copy of the data) and quick sort (which has a worst case runtime of O(n
	www.louisville.edu /~ecrouc01/CECS302/Lecture22.htm (918 words)

	Heapsort
		The data structure of the heapsort algorithm is a heap.
		As shown later, in the implementation no pointer structures are necessary to represent the tree, since an almost complete binary tree can be efficently stored in an array.
		Using this array representation of the heap, heapsort can be implemented as an in-place sorting algorithm.
	www.inf.fh-flensburg.de /lang/algorithmen/sortieren/heap/heapen.htm (0 words)

	Heapsort
		This method cannot be used until the student implements
		The main method illustrates the use of a heapsort to sort a small array.
		Sort an array of integers from smallest to largest, using a heapsort algorithm.
	www.cs.colorado.edu /~main/docs/Heapsort.html (0 words)

	The External Heapsort
		The N elements to be sorted are stored in a memory of M pages, with room for S elements per page.
		The heapsort algorithms seen so far are not very well suited for external sorting.
		The expected number of page accesses for the basic heapsort in a memory constrained environment (e.
	www.diku.dk /forskning/performance-engineering/Jesper/heaplab/heapsurvey_html/node23.html (0 words)

	Digg - Sorting algorithms: Heapsort
		Surely those CS people have already seen many implentations of a HeapSort, and the rest of people don't care to see one.
		What this means is if you sort (for example) by date, and then by time, heapsort will have the dates scrambled, but mergsort will have both dates and sorted correctly.
		Or maybe some relevance, I think the postgresql guys might be experimenting with replacing qsort in the index routines because the worst cases with quicksort are fairly common; I know I saw that on the mailing list at one point.
	www.digg.com /programming/Sorting_algorithms_Heapsort (0 words)

	heapsort() -- perform heap sort on array
		If two members compare as equal, their order in the sorted array is unspecified.
		function is an implementation of J.W.J. William's heapsort algorithm, a variant of selection sorting.
		The algorithm is taken from Algorithm H in D.E. Knuth's Sorting and Searching.
	www.mkssoftware.com /docs/man3/heapsort.3.asp (0 words)

	CodeGuru Forums - Heapsort or Quicksort??
		Which type of sorting would you prefer??Quicksort or HeapSort?Even though both of them have complexities of (N log(N)), quicksort in some situations degenerates to O(nn).But however heapsort* is known to be less efficient than quicksort!!So which one to use in practice?Under what criteria would you choose between those 2??An example would be??
		This kind of question is what Google is good at: QuickSort or HeapSort?
		One can think effectively only when one is willing to endure suspense and to undergo the trouble of searching...
	www.codeguru.com /forum/showthread.php?t=374454&goto=nextnewest (0 words)

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