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Topic: Comparison sort

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	Merge sort - Wikipedia, the free encyclopedia
		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 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.
		Unlike some (inefficient) implementations of quicksort, merge sort is a stable sort as long as the merge operation is implemented properly.
	en.wikipedia.org /wiki/Merge_sort (1255 words)

	Comparison sort - Wikipedia, the free encyclopedia
		A comparison sort is a particular type of sorting algorithm; a number of well-known algorithms are comparison sorts.
		It is defined as a sorting algorithm which can only read the list elements through a single abstract comparison operation (often a "less than" operator) that determines which of two elements should occur first in the final sorted list.
		A comparison sort must have an upper bound of at least Ω(n log n) comparison operations in the worst case.
	en.wikipedia.org /wiki/Comparison_sort (615 words)

	Collation
		Sort key is useful for performance critical operation which requires comparison of a same string many times (e.g.
		Sort keys are generated as an opaque byte buffer and the length indicates a number of bytes.
		Comparison result to be given as an interger (-1, 0, 1) which is identical to strcmp.
	www.mozilla.org /projects/intl/collation.html (442 words)

	Postman's Sort Article from C Users Journal
		To sort a file of records on a social security number in the third field in format 999-99-9999 one could use the command line.
		Comparative analysis of the comparison sorting and the postman's sort is somewhat difficult since the methods are so different.
		Note that this is an example of a sorting method which requires time proportional to the num- ber of records in the file.
	www.rrsd.com /psort/cuj/cuj.htm (2718 words)

	Sorting Algorithms
		Some sorting algorithms are simple and intuitive, such as the bubble sort.
		Since the speed of a sort can vary greatly depending on what data set it sorts, accurate empirical results require several runs of the sort be made and the results averaged together.
		Keep in mind that "best" depends on your situation - the quick sort may look like the fastest sort, but using it to sort a list of 20 items is kind of like going after a fly with a sledgehammer.
	linux.wku.edu /~lamonml/algor/sort/sort.html (696 words)

	Information on Sorting. The best solution to the Sort problem (Site not responding. Last check: 2007-10-22)
		From now on, we use the term sort to mean a process of ranking a set of data values by the method of pair-wise comparisons of data values followed by data move operation(s).
		A sorting method is said to be stable if it leaves a set of equal data values in the same order as they were before at the end of sorting.
		If we were to sort the table of records by their x-coordinate value, we would be careful to ensure that the y-coordinate values remain in the same sequence for a set of images that have the same x-coordinate value.
	www.logiccoder.com /SortingInfo.htm (2106 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.
		Sorting in-place is possible but requires an extremely complicated implementation and hurts performance.
		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)

	UTN #???: Deterministic Collation
		A stable sort is one where two records with a field that compares as equal will retain their order when sorted according to that field.
		This is a property of the sorting algorithm, not the comparison mechanism.
		A stable sort is to be distinguished from a deterministic sort.
	www.macchiato.com /utc/stable_sort_tn.htm (948 words)

	9.1 Lower bounds for Comparison Sorts (Site not responding. Last check: 2007-10-22)
		Comparison sorts can be viewed abstractly in terms of decision trees.
		The worst case number of comparisons for a comparison sort corresponds to the height of its decision tree.
		Heapsort and merge sort are asymptotically optimal comparison sorts.
	www.cs.uml.edu /~skaminen/ALGO/sec91.html (136 words)

	511-07-08 (Site not responding. Last check: 2007-10-22)
		All the previous sorting algorithms belong to "comparison sort", where sorting is done only by comparisons among the values to be sorted.
		The major comparison sorting algorithms are summarized in the following table in their recursive forms.
		If we see each comparison as a node, then a sequence of comparisons forms a binary tree, in which each comparison (except the first one) has one parent (the preceding comparison) and two children (possible consequences).
	www.cis.temple.edu /~pwang/511-PT/Lecture/511-07-08.htm (527 words)

	ITCWeb On-Line Manual Pages
		The type of sort performed by msort is determined by which comparison operators are chosen by the user.
		Once a comparison operator is chosen, it must be applied to a portion of the input lines.
		Reverses the sense of comparisons for all fields specified up until, but not including, the next use of the -s flag (after which, if reversed ordering is again sought, -r must be used again).
	www.itc.virginia.edu /cgi-contrib/manpage.cgi?msort (1930 words)

	Sorting
		As for selection sort, a nested loop is used; however, a different invariant holds: after the ith time around the outer loop, the items in A[0] through A[i-1] are in order relative to each other (but are not necessarily in their final places).
		Quick sort (like merge sort) is a divide and conquer algorithm: it works by creating two problems of half size, solving them recursively, then combining the solutions to the small problems to get a solution to the original problem.
		After partitioning, the pivot is in A[right+1], which is its final place; the final task is to sort the values to the left of the pivot, and to sort the values to the right of the pivot.
	www.cs.wisc.edu /~vernon/cs367/notes/14.SORTING.html (2440 words)

	Howard Kaikow's Sort Performance Comparison program - Information
		Sorting the String data as numbers requires the numbers to be padded and aligned.
		Depending on the sample size, the order of the source data, the data type, and the sorting method, the time to do the sort may be from less than one millisecond to, nearly, forever.
		Otherwise the sorted data needs to be moved from the Excel worksheet to the selected source and the timing component will not be 0.
	www.standards.com /Sorting/SortPerformanceComparison-Info.html (1655 words)

	UTN #9: Deterministic Sorting
		A stable sort is one where two records will retain their order when sorted according to a particular field, even when the two fields have the same contents.
		Whether a sort is deterministic or stable is a property of the sort algorithm, not the comparison function.
		There are some libraries that offer portable comparison, such as [ICU], but in general the results of comparison or sort key generation may vary significantly between different platforms.
	unicode.org /notes/tn9 (1965 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)

	Sorting -- Getting it Straight
		Comparison sorts determine the order of elements based only on comparisons between the input keys.
		Note that comparison counting is a kind of address table sort; that is, the C array infers the position of each element in the sorted list, but no records are actually moved.
		Distribution counting sort is stable: numbers with the same value appear in the output array in the same order as they were in the input array.
	www.cs.fit.edu /~wds/classes/cse5081/Sort/sort/sort.html (5028 words)

	Radix Sort
		It is possible do the sorting on each digit-position in-situ and then only O(log(n)) space is needed to keep track of the array sections yet to be processed, either recursively or on an explicit stack.
		Radix sort in base ten was very natural for humans using the card sorting machine, but any base can be used and base two is natural for computers.
		Sort (recursively) each of the regions of a[ ] associated with a particular digit value.
	www.csse.monash.edu.au /~lloyd/tildeAlgDS/Sort/Radix (667 words)

	Howard Kaikow's Sort Performance Comparison program - Description
		Sort using the SortArray method of the WordBasic object, then copy the sorted data into the array.
		If checked, the data used for the previous set of selected sort methods will be reused, but only if the data type, the number of data items, whether non-numeric, and the order of source data have not been modified.
		If the sorting algorithms are correct, the result should have been the same no matter which algorithms were used.
	www.standards.com /Sorting/SortPerformanceComparison-Description.html (2127 words)

	[Chapter 15] 15.4 Advanced Sorting
		To define a sort of a different color, you need to define a comparison routine that describes how two elements compare.
		comparison routine is defined as an ordinary subroutine.
		Now remember, the less than is according to your meaning of less than; it could be a numeric comparison, according to the third character of the string, or even according to the values of a hash using the passed-in values as keys.
	members.fortunecity.com /adara7053jwnd/learn/ch15_04.htm (1046 words)

	[No title]
		Using merge sort gives fewer calls to the comparison function, but there is greater overhead because the sort routine itself is written in Perl not C. Whether merge sort or ordinary C
		is the comparison function to use, with the remaining arguments being references to the lists to be merged.
		This n-way merge sort works by keeping a 'pool' of the lowest element in each input list, and after the lowest element of the pool is removed and output, the pool is topped up with insertion sort.
	membled.com /cvsroot/Sort-Merge/Merge.pm,v (1023 words)

	Class 2: Lower Bounds on Sorting Algorithms (Site not responding. Last check: 2007-10-22)
		A comparison sort uses comparisons between two elements as the only means of determining the order information amongst the elements being sorted.
		We will abstract any comparison sort as a decision tree, and prove that you need at least nlgn time to sort n elements using a comparison sort.
		Thus, any comparison sorting algorithm that has a worst case performance of O(nlgn) is asymptotically optimal.
	www.mines.edu /Academic/courses/math_cs/macs406.old/node20.html (232 words)

	UTF-16 String Comparison in Code Point Order
		Binary string comparison is a lexical comparison of the code unit values (the base units of a string).
		A comparison of strings in UTF-8 is done entirely as a comparison of the byte sequences.
		In modern CPUs with significant cache and memory latencies and with branch prediction, it is faster to use comparisons for the "fix-up" value rotation than to use a lookup table.
	icu.sourceforge.net /docs/papers/utf16_code_point_order.html (1116 words)

	Globalization Step-by-Step: Sorting and String Comparison
		If you are sorting only a small number of elements, the easiest and quickest solution is to use the string comparison techniques explained previously, and then to sort elements based on the result of those comparisons.
		Elements are sorted based on script (that is, all Greek characters sort together, all Cyrillic characters sort together, and so on); alphanumeric and symbolic characters; diacritics; case; and other special rules, such as two characters sorting as a single character (for example, the Spanish "CH").
		For example, a sort order for Russian would be based on Cyrillic letters and possibly diacritics, but a sort order for Japanese might be based on the number of strokes it takes to draw a character.
	www.microsoft.com /globaldev/getwr/steps/wrg_sort.mspx (2709 words)

	Project 1: Sort Comparison (Site not responding. Last check: 2007-10-22)
		The purpose of this assignment is to make an empirical study of the performance of each of five sort algorithms from Chapter 9 of our Carrano text (selection, bubble, insertion mergesort, quicksort).
		You are to write a program which will carry out each of the sorts on different sized datasets.
		We want to assess the performance of the sorts applied to each of three kinds of test data: pre-sorted data, inversely pre-sorted data, and random data.
	www.csc.calpoly.edu /~dbutler/csc345/projects/proj01_sort_compare.html (280 words)

	Tcl Built-In Commands - lsort manual page (Site not responding. Last check: 2007-10-22)
		The keyword end is allowed for the index to sort on the last sublist element, and end-index sorts on a sublist element offset from the end.
		Note that duplicates are determined relative to the comparison used in the sort.
		The options to lsort only control what sort of comparison is used, and do not necessarily constrain what the values themselves actually are.
	www.tcl.tk /man/tcl8.4/TclCmd/lsort.htm (630 words)

	Sorting
		he objective of the sorting algorithm is to rearrange the records so that their keys are ordered according to some well-defined ordering rule.
		If the file to be sorted will fit into memory or equivalently if it will fit into an array, then the sorting method is called internal.
		Based on the result of this comparison, the sorting algorithm may perform some calculation which we are not interested in and will eventually perform another comparison between two other elements of input sequence, which again will have two outcomes.
	www.personal.kent.edu /~rmuhamma/Algorithms/MyAlgorithms/Sorting/sortingIntro.htm (481 words)

	Dr. Dobb's \| Algorithm Alley \| July 22, 2001 (Site not responding. Last check: 2007-10-22)
		The sort test runs five different sort functions: the array quicksort in Arrays.sort(), the linked-list quicksort in Collections.sort(), a new linked-list quicksort, a new linked-list merge sort, and a nonrecursive version of the linked-list merge sort.
		Thus, it is not true that linked-list sorting must be slower than array sorting, nor is it true that the quicksort is the fastest comparison sort.
		However, this conclusion is generally based on analyzing the merge sort's performance on an array, which is not the ideal data structure for the merge sort.
	www.ddj.com /184410565 (3009 words)

	Natural Order String Comparison
		Computer string sorting algorithms generally don't order strings containing numbers in the same way that a human would do.
		Strings are sorted as usual, except that decimal integer substrings are compared on their numeric value.
		This should probably be a separate function because doing the comparisons will probably introduce a dependency on the OS mechanism for finding the locale and comparing characters.
	sourcefrog.net /projects/natsort (565 words)

	Array.Sort Generic Method (T[], Generic Comparison) (System)
		Sorts the elements in an Array using the specified Comparison.
		The implementation of comparison caused an error during the sort.
		This implementation performs an unstable sort; that is, if two elements are equal, their order might not be preserved.
	msdn2.microsoft.com /en-us/library/cxt053xf.aspx (866 words)

	The Gadgeteer - Palm OS Database Comparison Review
		Which ever field you choose as the first field in the display order is the field that is used to sort the data (alphabetically).
		A menu option to sort the database with secondary and tertiary sort fields is also available.
		The default sort order is to display the records in the order in which they were entered with new records first.
	www.the-gadgeteer.com /databases-review.html (5133 words)

	Sort Hats - Find, Compare, and Buy at Shopping.com
		Sort and snap together by attribute: boys, girls, hats, hair, stripes, buttons or shoes.
		This wickedly witch is more fun than a flying broom gathering or a spell casting party, because her unique personality allows her to bend and pose in all sorts of wacky positons.
		Clausland is a charming woodsy-lumberjacky sort of Santa who looks like he's straight out of the Great White North.
	www.shopping.com /xGS-Sort_Hats (698 words)

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