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PlanetMath: quicksort Quicksort is a divide-and-conquer algorithm for sorting in the comparison model. The behavior of quicksort can be analyzed by considering the computation as a binary tree. This is version 10 of quicksort, born on 2003-10-07, modified 2006-08-06. planetmath.org /encyclopedia/Quicksort.html   (231 words)

Quicksort Quicksort is a sorting algorithm which, on average, needs Θ(n log(n)) comparisons to sort n items. Quicksort is usually faster, but needs lots of extra care to avoid the worst-case behaviour problems. quicksort :: Ord a => [a] -> [a] quicksort [] = [] quicksort (h:t) = (quicksort [y www.ebroadcast.com.au /lookup/encyclopedia/qu/Quicksort.html   (789 words)

Quicksort - Wikipedia, the free encyclopedia Quicksort is a comparison sort and, in efficient implementations, is not a stable sort. When quicksort is used in web services, for example, it is possible for an attacker to deliberately exploit the worst case performance and choose data which will cause a slow running time or maximize the chance of running out of stack space. Quicksort is usually faster, though there remains the chance of worst case performance except in the introsort variant. en.wikipedia.org /wiki/Quicksort   (4294 words)

Cprogramming.com - Sorting Algorithms - Quicksort That is why beginning programmers often overlook quicksort as a viable option because of its T(n^2) worst-case running time, which could be made exponentially unlikely with a little effort. In fact, quicksort is the currently fastest known sorting algorithm and is often the best practical choice for sorting, as its average expected running time is O(n log(n)). Quicksort is a relatively simple sorting algorithm using the divide-and-conquer recursive procedure. www.cprogramming.com /tutorial/computersciencetheory/quicksort.html   (618 words)

Understand Quicksort with DDD CAR Hoare described the Quicksort algorithm in a much-cited 1962 paper, and it is still in common use 40 years later. The divide-and-conquer approach of Quicksort is probably where it got the prefix quick; by segregating smaller elements from larger elements it eliminates the need for many comparisons. Because this is a recursive quicksort, this test is necessary to end recursion when an array with one element is passed in (more on this later). www.linuxjournal.com /node/6258/print   (1190 words)

Developing for Developers : Efficient selection and partial sorting based on quicksort Quicksort is a compelling example of how algorithms with poor worst-case behavior but good average-case or expected behavior can be highly practical. Quicksort is fundamentally based on the efficient partition operation, a linear-time operation which divides a list into two parts: the elements less than a value, and the elements greater than or equal to a value. In efficient implementations of quicksort, partitioning is usually implemented as an in-place operation that just shuffles elements of the array around as it scans over it. blogs.msdn.com /devdev/archive/2006/01/18/514482.aspx   (959 words)

Quicksort   (Site not responding. Last check: 2007-10-05) QUICKSORT IS OPTIMAL Robert Sedgewick Jon the quicksort cheerleader paper. A variant of quicksort which attempts to choose a pivot likely to represent the middle of the values to be sorted. Quicksort Quicksort is one of the fastest and simplest sorting algorithms [Hoar]. www.softpanorama.org /Algorithms/Sorting/quicksort.shtml   (429 words)

Quicksort Quicksort is one of the fastest and simplest sorting algorithms [Hoa 62]. In the average case a partitioning as shown in Figure 2 b is to be expected. Quicksort turns out to be the fastest sorting algorithm in practice. www.iti.fh-flensburg.de /lang/algorithmen/sortieren/quick/quicken.htm   (546 words)

Quicksort Quicksort is one of the fastest known sorting algorithms for evenly distributed data and is not difficult to implement. As we run quicksort on these two partitions, they'll both in turn be split into partitions of their own. The most common method is to have 2 pointers - one that initially points to the start of the array (call this pointer L for left) and another that initially points to the end (call this pointer R for right). goanna.cs.rmit.edu.au /~stbird/Tutorials/QuickSort.html   (696 words)

Quicksort — Oberlin College Computer Science Quicksort, on the other hand, starts by partitioning the array into two parts in such a way that when recursive calls are made to the parts, the result is a sorted version of the entire array. Then apply quicksort to the part of the array before the median and to the part of the array after the median. Then apply quicksort to the part of the array before the pivot and to the part of the array after the pivot. occs.cs.oberlin.edu /classes/fall2004spring2005/cs151/lecture28.html   (431 words)

Quicksort   (Site not responding. Last check: 2007-10-05) The quicksort algorithm works by partitioning the array to be sorted, then recursively sorting each partition. Each recursive call to quicksort would only diminish the size of the array to be sorted by one. Due to recursion and other overhead, quicksort is not an efficient algorithm to use on small arrays. epaperpress.com /sortsearch/qui.html   (651 words)

Quicksort   (Site not responding. Last check: 2007-10-05) recursively apply quicksort to the part of the array that is to the left of the pivot, and to the part on its right. More careful versions of quicksort pick a pivot that is more likely to belong near the middle of the array. Quicksort is most effective on large arrays of random numbers. www.cs.princeton.edu /~ah/alg_anim/gawain-4.0/QuickSort.html   (322 words)

4 Cache-Effective Quicksort Instead of saving small subarrays to sort in the end, the memory-tuned quicksort sorts these subarrays when they are first encountered in order to reuse the data elements in the cache. We also found that the performance of quicksort and its cache-optimized alternatives are very sensitive to the types of the data set being used. By combining the advantages of flashsort and quicksort, we present a new quicksort alternative, flash quicksort, where the first two steps are the same as in flashsort and the last step uses quicksort to sort the elements in each class. www.jea.acm.org /TURING/Vol5Nbr3/node4.html   (801 words)

4GuysFromRolla.com - Sorting Arrays (VBScript Implementation) Quicksort uses a divide and conquer approach, dividing the total array in half, then recursively dividing each half info halves, and those halves into halves and so on and so on. You can also, as this code shows, use your Quicksort algorithm with client-side scripting as well (although if you choose to use client side scripting, I would highly recommend a JavaScript implementation, which can be found here). Kevin Moon is an accomplished ASP developer, who translated the Quicksort algorithm from JavaScript to VBScript, and also coded a two dimensional version of Quicksort. www.4guysfromrolla.com /webtech/012799-2.shtml   (423 words)

GameDev.net - Understanding the QuickSort Algorithm The QuickSort is a recursive function that works using a "divide and conquer" method. The partition element is then at its permanent place in the array, and QuickSort calls itself twice: once to sort the upper half of the array, and once to sort the bottom half. A QuickSort function should take two parameters, which we’ll call high and low, that represent the upper and lower bounds of the portion of the array to be sorted. www.gamedev.net /reference/articles/article1073.asp   (803 words)

Lecture 5 - quicksort To justify its name, Quicksort had better be good in the average case. When Quicksort is implemented well, it is typically 2-3 times faster than mergesort or heapsort. Quicksort is good on average, but bad on certain worst-case instances. www.cs.sunysb.edu /~algorith/lectures-good/node5.html   (1385 words)

Heapsort, Quicksort, and Entropy Quicksort is wasteful because it persists in making experiments where the two possible outcomes are not equally likely. Roughly half of the time, quicksort is using a 'bad' pivot - 'bad' in the sense that the pivot is outside the interquartile range - and, once it has become clear that it's a bad pivot, every comparison made with that pivot yields an expected information content significantly less than 1 bit. A simple hack that reduces quicksort's wastefulness is the 'median of three' modification of quicksort: rather than picking one pivot at random, three candidates are picked, and their median is chosen as the pivot. www.aims.ac.za /~mackay/sorting/sorting.html   (2370 words)

Quicksort Quicksort was developed by C.A.R. Hoare and is a widely used sorting technique, based on divide and conquer. Quicksort first selects an element that is to be used as split-point from the list of given numbers. As you can see, quicksort is not an inplace sort, since it needs extra space to store the recursion stack. www.seeingwithc.org /topic2html.html   (897 words)

6.3 Quicksort (supplementary)   (Site not responding. Last check: 2007-10-05) Quicksort is a sorting algorithm originally proposed by C.A.R. Hoare in 1962. In spite of its age, it is still used as a standard method of sorting. Quicksort can rearrange items into ascending or descending order in O(n lgn) time, which is a known theoretical lower bound for comparison sorting. www.ugrad.cs.ubc.ca /~cs260/chnotes/ch6/Ch6Sec03.html   (565 words)

Sorting by divide-and-conquer Quicksort also uses few comparisons (somewhat more than the other two). Quicksort, invented by Tony Hoare, follows a very similar divide and conquer idea: partition into two lists and put them back together again It does more work on the divide side, less on the combine side. Quicksort uses a simple idea: pick one object x from the list, and split the rest into those before x and those after x. www.ics.uci.edu /~eppstein/161/960118.html   (1693 words)

kirupa.com - Fast Sorting with Quicksort: Page 2 I will first provide a simple overview of how quicksort works, then I will provide a more detailed look at how the major parts of the overview work by demonstrating a small example, and I will then conclude with a line-by-line analysis of how our code turns our understanding of quicksort into machine-understandable actions. Quicksort works by initially picking an item in your list of items called a pivot. For example, in quicksort, all items to the left of the pivot value should be smaller, and all items to the right of the pivot value should be larger. www.kirupa.com /developer/actionscript/quickSort2.htm   (509 words)

StringGrid Quicksort If you try an exchange sort on 10,000 rows, be prepared to have time for a meal (and maybe a nap) before viewing the results. For 10,000 items the difference is roughly a factor of 1000 in favor of Quicksort. The trick to applying Quicksort to a stringgrid is to only actually sort an array of row numbers as opposed to shuffling entire grid rows. www.delphiforfun.org /Programs/Delphi_Techniques/GridQuickSort.htm   (546 words)

Quick Sort - CS245 Project By Joseph George Quicksort is based on the divide and conquer approach and inspite of its slow worst case running time, it is often the best practical choice for sorting because it is remarkably efficient on the average. Quicksort works by partitioning the list into two parts. In the worst case, the partitioning routine produces one region with (N-1) elements and one with only one element (this happens when the list to be sorted is already sorted). www.cse.iitk.ac.in /users/dsrkg/cs210/applets/sorting/quickSort/quickSort.html   (446 words)

Quicksort The second exchange sort we consider is the quicksort  algorithm. A divide-and-conquer algorithm solves a given problem by splitting it into two or more smaller subproblems, recursively solving each of the subproblems, and then combining the solutions to the smaller problems to obtain a solution to the original one. This is why quicksort is considered to be an exchange sort. www.brpreiss.com /books/opus5/html/page490.html   (580 words)

kirupa.com - Fast Sorting with Quicksort: Page 1 What this means is, given an input, it divides the input into smaller parts before performing an operation on those parts as opposed to working on the entire input at once. Flash's built-in Array.sort() method is a variation of quicksort, and since it is coded at a lower level, it is also much faster. This tutorial aims to explain how quicksort works, and this will allow you to sort data that may be more varied than the limited set of inputs allowed by built-in sort methods such as Array.sort(). www.kirupa.com /developer/actionscript/quickSort.htm   (276 words)

Quick Sort Quicksort works by "partitioning" the array to be sorted, then recursively sorting each partition. Alternatively, stop early and do a final pass of InsertionSort at the end; this imposes less overhead in cycles than doing lots of separate little insertion sorts, but may interact less well with cache (for moderate datasets) or VM (for immoderate ones). As with quicksort (but even more so), you want to stop "early" and switch to a simpler, lower-overhead algorithm once the pieces are small. c2.com /cgi/wiki?QuickSort   (560 words)

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