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Topic: Merge sort

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Sorting algorithm

Radix sort

Bucket sort

Stupid sort

Pigeonhole sort

Comb sort

Merge algorithm

Bubble sort

Insertion sort

Shell sort

Counting sort

Quicksort

Selection sort

Pancake sorting

Bogosort

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	Merge sort
		Merge sort is a sort algorithm for rearranging lists (or any other data structure that can only be accessed sequentially, e.g.
		Merge sort has an average and worst-case performance of O(n log(n)).
		Unlike quicksort, merge sort is a stable sort.
	www.ebroadcast.com.au /lookup/encyclopedia/me/Merge_sort.html (653 words)

	Merge
		In the worst case, merge sort does about 39% fewer comparisons than quicksort does in the average case; merge sort always makes fewer comparisons than quicksort, except in extremely rare cases, when they tie, where merge sort's worst case is found simultaneously with quicksort's best case.
		Merge sort's most common implementation does not sort in place, therefore, the memory size of the input must be allocated for the sorted output to be stored in.
		Merge sort is so inherently sequential that it's practical to run it using slow tape drives as input and output devices.
	i-merge.blogspot.com (698 words)

	Merge Sort Introduction
		The strategy behind Merge Sort is to change the problem of sorting into the problem of merging two sorted sub-lists into one.
		Merge Sort is a "recursive" algorithm because it accomplishes its task by calling itself on a smaller version of the problem (only half of the list).
		The basic philosophy of the merge is to determine which sub-list starts with the smallest data and copy that item into the merged list and move on to the next item in the sub-list.
	www.ship.edu /~cawell/Sorting/mergeintro.htm (361 words)

	Merge sort - CodeCodex
		Merge sort's most common implementation does not sort in place, meaning memory the size of the input must be allocated for the sorted output to be stored in.
		Merge sort is much more efficient than quicksort if the data to be sorted can only be efficiently accessed sequentially, and is thus popular in languages such as Lisp, where sequentially accessed data structures are very common.
		Although heap sort has the same time bounds as merge sort, it requires only Ω(1) auxiliary space instead of merge sort's Ω(n), and is consequently often faster in practical implementations.
	www.codecodex.com /wiki/index.php?title=Merge_sort (1776 words)

	Cprogramming.com - Articles - Merge Sort
		heap sort, merge sort requires additional memory proportional to the size of the input for scratch space, but, unlike heap sort, merge sort is stable, meaning that "equal" elements are ordered the same once sorting is complete.
		Merge sort works using the principle that if you have two sorted lists, you can merge them together to form another sorted list.
		The downside of merge sort is that it usually does require a scratch array to store the the results of a merge.
	www.cprogramming.com /tutorial/computersciencetheory/mergesort.html (986 words)

	Merge sort - Wikipedia, the free encyclopedia
		Unlike some (inefficient) implementations of quicksort, merge sort is a stable sort as long as the merge operation is implemented properly.
		Although heapsort has the same time bounds as merge sort, it requires only Θ(1) auxiliary space instead of merge sort's Θ(n), and is consequently often faster in practical implementations.
		As of Perl 5.8, merge sort is its default sorting algorithm (it was quicksort in previous versions of Perl).
	en.wikipedia.org /wiki/Merge_sort (1385 words)

	Merge Sort
		Merge sort divides the array into two halves which are sorted recursively and then merged to form a sorted whole.
		It is interesting to compare quick sort with merge sort; the former has a pre-order structure the latter a post-order structure.
		Merge sort is stable if written carefully, it is a matter of a `<=' versus a `<'.
	www.csse.monash.edu.au /~lloyd/tildeAlgDS/Sort/Merge (361 words)

	Merge Sort
		The merge sort is slightly faster than the heap sort for larger sets, but it requires twice the memory of the heap sort because of the second array.
		Like the quick sort, the merge sort is recursive which can make it a bad choice for applications that run on machines with limited memory.
		A sample C program that demonstrates the use of the merge sort may be downloaded here.
	linux.wku.edu /~lamonml/algor/sort/merge.html (249 words)

	Merge Sort Algorithm
		The merge sort algorithm is said to be one of the earliest sorting algorithms created.
		The merge sort algorithm is a divide and conquer algorithm.
		As the battle rages on determining which sorting algorithm is the fastest, merge sort has shown to be one of the best.
	www2.hawaii.edu /~loganh/mergesort.html (880 words)

	Merge sort - Algorithmist
		Merge sort is a sorting algorithm invented by John von Neumann based on the divide and conquer technique.
		Bottom-up merge sort is a non-recursive variant of the merge sort, in which the array is sorted by a sequence of passes.
		Every two adjacent blocks are merged (as in normal merge sort), and the next pass is made with a twice larger value of
	www.algorithmist.com /index.php/Merge_sort (196 words)

	Sorting by divide-and-conquer (via CobWeb/3.1 planetlab2.cs.virginia.edu) (Site not responding. Last check: 2007-10-13)
		Merge sort is good for data that's too big to have in memory at once, because its pattern of storage access is very regular.
		According to Knuth, merge sort was one of the earliest sorting algorithms, invented by John von Neumann in 1945.
		Merge sort worked no matter how you split the lists (one obvious way is to take first n/2 and last n/2 elements, another is to take every other element).
	www.ics.uci.edu.cob-web.org:8888 /~eppstein/161/960118.html (1693 words)

	Merge sort
		Sorting is done by scanning through the array performing 1-by-1 merges to produce sorted sublists of size 2; then scan through the array performing 2-by-2 merges to produce sorted sublists of size 2, then do 4-by-4 merges to get sorted sublists of size 8, etc., until the whole list is sorted.
		Once having implemented a merge procedure, the sorting is trivial: we only have to call the merge procedure with argument 1, 2, 4, 8,...
		In this case, the second call to the merge procedure only copies the values from the temp array to the destination array.
	thor.auto.tuwien.ac.at /~blieb/woop/merge.html (231 words)

	sort
		Sort lines of all the named files together and write the result to the specified output.
		Comparisons shall be based on one or more sort keys extracted from each line of input (or, if no sort keys are specified, the entire line up to, but not including, the terminating ), and shall be performed using the collating sequence of the current locale.
		Restrict the sort key to an initial numeric string, consisting of optional s, optional minus sign, and zero or more digits with an optional radix character and thousands separators (as defined in the current locale), which shall be sorted by arithmetic value.
	www.opengroup.org /onlinepubs/009695399/utilities/sort.html (2083 words)

	sort -- sort/merge utility
		defines a sorting key that extends from the third character of the second field to the sixth character of the fourth field.
		In other words the sorting key extends from the third character of the second field to the sixth character of the fourth field.
		With either syntax, if the end of a sorting key is not a valid position or no end was specified, the sorting key extends to the end of the input record.
	www.mkssoftware.com /docs/man1/sort.1.asp (1402 words)

	Merge Sort
		Sorting is a common and very important problem in computer science.
		Sorting is one of the best studied problems in computer sciences.
		Compared to a sorting method such as the insertion sort, which runs big O of n squared, it is much more efficient to use the mergesort.
	www2.hawaii.edu /~lammicha/MergeSort.html (671 words)

	SparkNotes: Merge Sort: The Merge Sort Algorithm
		To understand the efficiency of the mergesort algorithm it is useful to separate the merging from the sorting.
		This sort of behavior is reflected by the logarithm:
		The merging process is linear each time two lists have to be merged, because it is simply done by doing one comparison for each pair of elements at the top of each sublist.
	www.sparknotes.com /cs/sorting/merge/section1.html (271 words)

	Analysis of Merge Sort
		In order to be correct, the merge function must update the segment lb to ub of A with a permutation of contents, which is in ascending order.
		Looking at the merge code we see that in the worst case there would be order n comparisons of array elements.
		n in the merge algorithm depends on the compiler and the computer the code is being executed on.
	jupiter.clarion.edu /~rsmaby/cis356/mergesort.html (1179 words)

	Sorting Algorithms Demo
		Some of these sorts are very stupid or very slow and should not be used in code.
		Radix Sort Algorithm (by Alvin Raj) LinkedQueue.java and intNode.java
		One of my favorite references to sorting routines is "Sorting" by William A. Martin, in ACM Computing Surveys, Volume 3, Number 4, December 1971, pages 147-174.
	www.cs.ubc.ca /spider/harrison/Java/sorting-demo.html (527 words)

	mergesort() -- perform merge sort
		function sorts an array of nmemb objects, the initial element of which is pointed to by base.
		The contents of the array are sorted in ascending order according to a comparison function.
		If two members compare as equal, their order in the sorted array is unspecified.
	www.mkssoftware.com /docs/man3/mergesort.3.asp (177 words)

	Merge Sort
		Merge sort is especially useful when one wishes to combine two lists into a sorted list.
		A merge sort works by breaking a list into two different lists, sorting each list, and finally combining them together.
		A merge sort can also continue to break a list into new lists until the new lists are of length two.
	home.earthlink.net /~casaburi/class/notes/mergesort.html (130 words)

	Merge Sort (Site not responding. Last check: 2007-10-13)
		This sorting method uses divide-and-conquer technique, which suggests sorting algorithms with the following general structure: if number of elements n is one, terminate; otherwise, partition array into two or more subarrays; sort each; combine the sorted subarrays into a single sorted array.
		Now both subarrays are to be sorted by recursive application of the divide-and-conquer scheme.
		To combine the sorted subarrays we use a process called merge, which combines to sorted sequences into one.
	www.bridgeport.edu /~dichter/lilly/mergesort.htm (168 words)

	sort
		Sort, merge, or compare all the lines from the files given (or standard input.)
		SYNTAX sort [options] [file...] sort --help sort --version OPTIONS sort has three modes of operation: Sort (the default), Merge (-m), and Check(-c) -c Check whether the given files are already sorted: if they are not all sorted, print an error message and exit with a status of 1.
		It always works to sort instead of merge; merging is provided because it is faster, in the case where it works.
	www.ss64.com /bash/sort.html (415 words)

	K-way Merge Sort Algorithm (Site not responding. Last check: 2007-10-13)
		Merge records in the buffers, by transfering to output buffer;
		The files of any previous merge pass become now the input files for the next merge pass.
		A new set of the sorted sequences of records is ready to start the process again.
	pages.csam.montclair.edu /~gutierre/kmergesa.htm (334 words)

	Lecture 7 - Merge Sort (Site not responding. Last check: 2007-10-13)
		Although the general strategy uses MERGE to put the pieces back together, there is a specific version of the general strategy called Merge Sort.
		The defining feature of Merge Sort is that in step (1), the given list is divided into two equal size pieces (or as near equal as possible).
		We proceed until we're down to singleton or empty lists, which are always sorted, then we work our way back up the recursion by MERGING together the short lists into larger ones (which replace the list that we started with at that level).
	www.cs.ualberta.ca /~holte/T26/merge-sort.html (180 words)

	Merge Sort
		A C function to sort a file, using arbitrary read, write and comparison functions and a tape-merge algorithm, which is O(n log n) in all cases.
		The temporary files are then sorted by merging blocks in a number of passes.
		Notice that if this technique is used, the sorted and unsorted files must be different, and the argument passing structure may become a little less elegant because the function call to delete a file usually requires file specifications, not merely a file pointer.
	efgh.com /software/mergesor.htm (1411 words)

	NetLogo Models Library: Merge Sort
		This model is a visual demonstration of a standard sort algorithm called merge sort.
		Since this model aims to demonstrate the sort algorithm visually, the code is more complex than would be needed if the model only needed to sort the numbers.
		The number of steps required to sort n items using this algorithm is the ceiling of logarithm (base 2) of n.
	ccl.northwestern.edu /netlogo/models/MergeSort (627 words)

	MergeSort demo with comparison bounds
		MergeSort is a recursive sorting procedure that uses O(n log n) comparisons in the worst case.
		To sort the left half of the array, the program calls itself recursively, passing the left half of the bars down to a new activation of MergeSort.
		Bars in sorted arrays are coloured green (or light grey on a fl and white screen).
	www.cs.toronto.edu /~neto/teaching/238/16/mergesort.html (1321 words)

	Merge Sort (Site not responding. Last check: 2007-10-13)
		The basic idea behind Divide and Conquer Sorting is to divide the data into two smaller groups, sort these, then combine the two small sorted groups into one larger sorted group.
		Merge Sort is frequently used to sort very large collections of data stored on external devices.
		If the array to be sorted has more than one item in it divide it into two parts.
	www.cs.uah.edu /~rcoleman/Sorting/MergeSort.html (244 words)

	Example: Batcher's Bitonic Merge Sort. Ver 1.0+
		Local sort is designed so that if it is called with its parameter equal to 1, then it does the initial sort so that even indexed element are sorted in increasing order and odd numbers elements are sorted in decreasing order.
		It is designed to merge bitonic sequences of length 2i performing the exchange operation of distance i and then recursively merging* the resulting subsequences.
		The most complex part of the Bitonic merge algorithm is keeping track of where one should generate an ascending sequence and where one must generate a descending sequence.
	www.extreme.indiana.edu /sage/pcxx_ug/subsection3_6_2.html (996 words)

	The xSortLab Applet
		The applet starts in "Visual Sort" mode, in which 16 bars are sorted step-by-step using one of the sorting algorithms Bubble Sort, Selection Sort, Insertion Sort, Merge Sort, or QuickSort.
		For a visual sort, the number of copies and the number of comparisons are recorded.
		For a timed sort, all the statistics that are displayed in the "Timed Sort" panel are written to the log.
	math.hws.edu /TMCM/java/xSortLab (1112 words)

	C For Swimmers - Data Structures - Merge Sort
		Merge Sort (Breadth First, with User Input, Input List size must be a power of 2)
		Merge Sort (Depth First, Input List size is not a power of 2)
		Merge Sort (Depth First, with User Input, Input List size may not be a power of 2)
	www.c4swimmers.esmartguy.com /mergesort.htm (215 words)

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