Kwik sort: Sortkwik – Lee Products

cortex-lab/phy: phy: interactive visualization and manual spike sorting of large-scale ephys data

phy is an open-source Python library providing a graphical user interface for visualization and manual curation of large-scale electrophysiological data. It is optimized for high-density multielectrode arrays containing hundreds to thousands of recording sites (mostly Neuropixels probes).

Phy provides two GUIs:

  • Template GUI (recommended): for datasets sorted with KiloSort and Spyking Circus,
  • Kwik GUI (legacy): for datasets sorted with klusta and klustakwik2.

What’s new

  • [7 Sep 2021] Release of phy 2.0 beta 5, with some install and bug fixes
  • [7 Feb 2020] Release of phy 2.0 beta 1, with many new views, new features, various improvements and bug fixes…

Links

Installation instructions

Phy requires a recent GPU and an SSD for storing your data (the GUI may be slow if the data is on an HDD).

  1. You need a recent Python distribution.

  2. Open a terminal and type:

pip install phy --pre --upgrade
# If you plan to use the Kwik GUI, type the following without the leading hash # character:
# pip install klusta klustakwik2
  1. Phy should now be installed. Open the GUI on a dataset as follows (the phy2 environment should still be activated):
cd path/to/my/spikesorting/output
phy template-gui params.py

Dependencies

For your information, here are the Python dependencies of phy (as found in requirements.txt):

phylib
mtscomp
numpy
matplotlib
scipy
h5py
dask
cython
pillow
colorcet
pyopengl
requests
qtconsole
tqdm
joblib
click
mkdocs
PyQtWebEngine

Dealing with the error

ModuleNotFoundError: No module named 'PyQt5.QtWebEngineWidget

In some environments, you might get an error message related to QtWebEngineWidget. Run the command pip install PyQtWebEngine and try launching phy again. This command should not run if the error message doesn’t appear, as it could break the PyQt5 installation.

Upgrading from phy 1 to phy 2

  • Do not install phy 1 and phy 2 in the same Python environment.
  • It is recommended to delete ~/.phy/*GUI/state.json when upgrading.

Developer instructions

To install the development version of phy in a fresh environment, do:

git clone [email protected]:cortex-lab/phy.git
cd phy
pip install -r requirements.txt
pip install -r requirements-dev.txt
pip install -e .
cd ..
git clone [email protected]:cortex-lab/phylib.git
cd phylib
pip install -e . --upgrade

Troubleshooting

Running phy from a Python script

In addition to launching phy from the terminal with the phy command, you can also launch it from a Python script or an IPython terminal. This may be useful when debugging or profiling. Here’s a code example to copy-paste in a new launch.py text file within your data directory:

from phy. apps.template import template_gui
template_gui("params.py")

Credits

phy is developed and maintained by Cyrille Rossant.

Contributors to the repository are:

Kwik Sort Stamp Finder (Canada & USA)

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Obsolete Currency Catalogs- – – – Worldwide Currency Catalogs- – – – Stocks and Bonds Catalogs- – – – Damaged Slightly Cheaper Currency Books- – Close Out Items- – – – Close Out Currency Books and Supplies- – – – Close Out Capital Coin Holders- – – – Close Out Coin Supplies- – – – Close Out United States Coin Books- – – – Close Out Worldwide Coin Books- – – – Close Out Ancient Coin Books- – – – Close Out Stamp Books & Supplies- – Coin Holders- – – – Coin Capsules – Airtite Direct Fit – – – – Coin Capsules – Guard House Direct Fit – – – – Coin Capsules and Capsule Pages – Lighthouse – – – – 2×3’s Snaplock & Harris Frosty Edge Coin Holders- – – – Coin Capsules with Rings – Airtite & Whitman – – – – Airtite Framed Coin Holders- – – – Capital Single Coin Holders & Accessories- – – – Capital Plastics Coin Sets for Cent – Nickels – Dimes – Quarters- – – – Capital Plastics Coin Sets for Halves – Dollars – U.S.Gold & Silver- – – – Capital Slab Type Coin Holders- – – – Capital Plastics Proof & Mint Sets & U. 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Type- – – – Card & Sleeve Coin Holders- – – – Coin World Premier Coin Holders- – – – Euro Coin Holders & Albums- – – – Coin Edge Coin Holders- – – – Cushion Cases & Snap-lock Cases- – – – CLOSE OUT Eagle Brand 2×2 Coin Holders and Albums- – – – Coin Flips – Coin Envelopes – Coin Bags- – – – Coin Display Frames- – – – CLOSE OUT Intercept Shield Coin Holders – 60% off List price- – – – Kointain Coin Holders- – – – Lincoln Bicentennial Cent Coin Holders- – – – Presidential Dollar Coin Holders- – – – Plastic 2×2 Coin Holders- – – – Self Adhesive Cardboard Coin Holders- – – – Slab Type Holders – Do It Yourself- – – – Staple Type Cardboard Coin Holders- – – – Special Occasion Holders- – – – State Quarter – D.C. & Trust Territories Quarter Coin Holders- – – – Proof & Mint Sets Holders- – – – Lighthouse Everslab & Quickslab Coin Holders- – – – Close Out Lighthouse Quadrum 2×2 Coin Holders – 40% OFF List Price- – – – Lighthouse Quadrum Coin Holders with Intercept Shield Protection- – – – National Park Quarter Holders- – – – Westward Series Nickel Coin Holders- – Coin Miscellaneous- – – – Coin Bezels & Money Clips- – – – Coin Novelties- – – – Coin Kits- – – – Lamps- – – – Gold Testing Equipment- – – – Miscellaneous- – – – Staplers & Staples- – Baseball Supplies- – – – Baseball Supplies- – – – Sport Card Books- – Comic Book Supplies- – – – Comic Book & Magazine Holders- – Coin Folders- – – – Harris United States Coin Folders – 35% Off List Price- – – – Close Out Warman’s U. 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Noile dot Net » Kwik Sew K253, Sort Of

So, I’m still staying at home just about 100% of the time, and I never wear shoes anymore. Additionally, for years I’ve longed for slippers that would feel like socks, but would fit less floppily, without slipping on our wood floors or stairs.

It was time to make my own.

Commercial slipper patterns have never worked for me: I have relatively small feet (6.5 USA, 37 UK). They’re slender, but I like a really wide toe box. And I’m no fan of cutesy. I knew whatever pattern I’d  use would require a lot of customization, but I wanted to use a commercial pattern as a base. Enter Kwik Sew K253:

I started by tracing my foot on the K253 sole pattern, since I knew I wanted my slippers to fit the shape of my specific foot. I knew I’d like wearing the slippers better, and also that they’d be less sloppy if they followed my foot contours.

Since I don’t like elastic straps, I also re-contoured the top of the slipper by drawing a curve up to where a strap would probably fall.

Changing the configuration of the sole meant that I had to re-fit the upper piece to fit around the sole accurately, I ran a bit afoul here, but more about that later . . .

My slippers are made of craft felt (these are essentially proof-of-concept, and I knew there would be lots of tweaking before hitting slipper perfection). The lining is cut from flannel scraps. Since I wanted something closer to a sock than a slipper, I didn’t interface the upper, but I did sandwich two layers of batting between the sole and the sole lining.

The soles are a (I hope!) durable synthetic I found on Etsy. I’m not a fan of the ubiquitous dotted “non-slip” fabric used in children’s footies — I don’t think it is particularly effective or long-lasting, and it attracts cat hair like mad — which is messy and also obliterates any non-slip advantage.

Initially I used quilting clips to keep the layers together, but that really wasn’t very effective. In the end, I pinned like mad, and then used a tiny zigzag around all the edges, not only on the sole, but on the upper, too, once the outer felt and inner flannel were sewn together.

The Kwik Sew pattern calls (mostly) for half-inch seams, which I didn’t want, and which I think make construction more difficult. On the one hand, the larger seam allows more room for error — helpful, maybe, when dealing with lots of layers — but, on the other hand, it’s much more bulky to sew. I knew, too, that .25 inch (.64 cm) seams were small enough that they wouldn’t bother my feet inside the slippers.

Using a standard zipper foot made sewing it all together much easier: the edge of the sewing foot was right at the seamline, so the foot didn’t have to battle with excess slipper material as I sewed. The sole is nothing but curves, and this particular economy — along with the smaller seam allowance — made my sewing more accurate, too.

Along with re-drafting the upper, I made several other changes to the style. One was to add a loop to the heel. Mine is made of doubled grosgrain ribbon. It’s sewn to the rear slipper seam, within a half inch of the upper edge of the slipper. The loop is large enough that pulling the slipper on with a single finger is easy.

If you do this, remember to fold the loop back when sewing the upper outer and lining fabrics together! Otherwise you’ll have a useless loop sandwiched between the two — and some seam ripping to do.

The Kwik Sew pattern calls for elastic at the heel. My slippers fit closely enough that this wasn’t necessary, which was another advantage of the more closed style I devised. I love the wrap-around look, and adding a KAM snap to close the wrap gave me exactly the fit I wanted.

The mid-foot opening makes getting the slippers on and off very easy, and the snap snugs up the fit perfectly. They’re very comfortable to wear: as light as socks, but with the protection of a slipper on hard floors.

Overall, I’m very pleased with the results, but I got a few things wrong. First, the heel seam is less than .25 inch  (.64 cm) off center, but that annoys me! Secondly, I didn’t quite fit the upper correctly to the sole, and I need to re-configure it, and double-check my notches. And I may consider curving the center back seam just a little more at the upper edge.

Next time, I’ll look for better quality felt (a lovely wool, I hope — I think there’s some in stash somewhere), and see how much closer to perfection I can get.

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‘The Simpsons’ Kwik-E-Mart ready to open at Broadway at the Beach

MYRTLE BEACH, SC (WMBF) – The longest-running primetime scripted show in television history is bringing a worldwide first to Myrtle Beach.

With millions of fans everywhere, the new attraction is expected to make records of its own. WMBF News got an exclusive first look inside “The Simpsons” Kwik-E-Mart.

“This is the first, world’s first authentic Kwik-E-Mart. Every inch of this store is themed, including bringing products to life,” said Mark Cornell, senior vice president of attractions development with simEx-Iwers Entertainment. “The products that are on the show, you can actually come and experience in the store first hand. Sort of like getting a taste of the show.”

The Simpsons fans can smell, feel and taste their favorite animated convenience store for the first time, even if Apu isn’t behind the counter.

“This store, when you look around, took four years to design and that’s a lot of detail,” Cornell said.

Bart Simpsons Squishee machines, hot lamp hot dogs, Flaming Moe’s energy drinks, Buzz Cola, and the iconic Lard Lad donuts are waiting to tingle folks’ taste buds.

“It’s a magnificent sort of East Coast destination,” Cornell said. “Millions of people vacation here annually and I feel Homer Simpson would vacation here.”

According to Cornell, Myrtle Beach was the perfect place to open a Kwik-E-Mart and Aztec Theatre.  Each, he said, are the first of five future locations like it, and the start of a Springfield he wants to grow at Broadway at the Beach.

“We won’t open the store until it’s perfect, because, you know, that’s what The Simpsons deserve,” Cornell said.

The Aztec Theatre is still under construction with a hopeful opening date later this year.  Inside will be a 4D interactive experience showcasing The Simpsons’ adventure, with your favorite characters coming to life.

The show’s 30th season is now being produced. Cornell said The Simpsons culture will stand the test of time here, with a multi-generational following, iconic characters and genius writing.

Copyright 2018 WMBF News. All rights reserved.

Day 9: Tour of America’s Dairyland p/b Kwik Trip: Cafe Centraal Bay View Classic

By: Sylvi Teich ([email protected] com) | Published June 28, 2019

It was a truly beautiful day for a bike race; by the late afternoon it had cooled down to a great temperature with minimal wind, and the sun was still out. The race didn’t have a delayed start and the women raced for the full hour. Th race started out fast and it only got faster. Harriet Owen (Hagens Berman | Supermint) won yet another stage, beating Peta Mullens (Roxsolt Attaquer) to the line in second and Nat Redmond (Fearless Femme Racing) to the line in third.

One thing that was sort of out of the ordinary was we saw Beck Wiasak (Fearless Femme Racing) riding at the front of the pack for once, not in her usual spot at the back. The course itself was sort of a bow tie shape with six corners. Corner 2 was the worst of them, being over 90 degrees – 120 degrees to be exact. Due to the high pace and the nasty turn 2, riders were shed off the back of the pack from the very beginning of the race. There was a good mix of riders who appeared at the front of the peloton to drive the pace. It wasn’t until about 20 minutes into the race that two riders – Emma Chilton (Roxsolt Attaquer) and Laura Jorgensen (Fast Chance Women’s Cycling p/b THTF) – tried to go off the front, but with Katie Compton (KFC Racing p/b Trek/Knight) driving the chase, they were quickly pulled back to the field. Next, it was Winnie Spoor (Fast Chance Women’s Cycling p/b THTF) who tried to go off the front, but was brought back and it was her teammate, Rachel Langdon who went after her. The bunch was back together again at the halfway point and it was the Lowlands Points leader, Peta Mullens, who won the mid-race point sprint. After the point sprint, at twelve laps to go, it was Pip Sutton (Specialized Wolfpack p/b Jackroo) who tried to take a look off the front. She too was brought back to the bunch as Laura Van Gilder (Mellow Mushroom) jumped off the front to take a $100 prime win. With six laps to go, a group of three containing Laura Jorgensen, Pip Sutton, and Abby Krawczyk (Orion Racing p/b Borah Teamwear) decided that solo attacks weren’t working, so they went off the front as a group.

The sprinters were determined to have the stage end in a bunch sprint and were able to reel the group of three back in. It was Winnie Spoor who tried to jump off the front one more time with three laps to go on the stage – she was brought back in during the next lap. Once again, with one lap to go, the entire group was back together. When it came to the sprint in the end, it was the ever consistent Harriet Owen who took the win ahead of Peta Mullens and Nat Redmond. With the help of the win, Harriet Owen kept her overall lead while Peta Mullens also kept her lead in the Lowlands points jersey and Andrea Cyr (Velocause Centraal) kept her lead in the Oarsman Capital Cat 2 leader’s jersey.

 

As it was for the women’s race, the weather was absolutely great for a bike race, a Bay View certainly does know how to put on a bike race. The crowds were amazing – it was a tunnel of noise coming down the finishing straight. It was the German, Moritz Malcharek (LKT Team Brandenburg) who won in front of the two Pro Racing Sunshine Coast riders, Matthew Rice in second and Taj Jones in third.

On the very first lap of racing, Hayden Strong (Texas Roadhouse Cycling) thought it was a good time to take a look off the front, but with ninety minutes of racing ahead of him and a field determined to catch him, Strong was pulled back in soon after his early attack. Through the early part of the race, we saw two main teams driving the pace up front, the big Australian team, Pro Racing Sunshine Coast, and the team of juniors – LUX/Stradling p/b Specialized. It was a little while before anyone tried another big attack. At about twenty minutes into the race, Stefan Rothe (ELBOWZ Racing) decided to go on the attack along with Seth Callahan (LUX/Stradling p/b Specialized) who won a $50 prime soon after. Once again, the two-man breakaway was brought back by the chasing field. Then again, at thirty minutes into the race, Tobin Ortenblad (Donkey Label Racing), Peter Olejniczak (Project Echelon Racing), and Stephan Hoffman (Team Clif Bar), the guy who forgot his kit, tried to have a go and get away. Once again, a persistent field reeled them back in.

After that, people mostly stayed in the pack, besides sprinting for primes. The eventual third place winner on the stage, Taj Jones, came away with a big $500 prime win close to the end of the stage. As the stage neared its end, both the Aussies and the Germans had a clear presence on the front of the field. Though in the end, it was the German, Moritz Malcharek winning by inches in front of Matthew Rice who took second and Taj Jones who ended up taking third on the stage. Cesar Marte (RCC) stays in his yellow jersey while Lachlan Holliday (Piedmont College) keeps his lead in the Lowlands Points jersey. Travis Wold (New England Devo p/b Cadence Wealth Management) also kept his lead in the Oarsman Capital Cat 2 leader’s jersey.

The riders pick it up again for the penultimate stage of ToAD 2019 on Saturday at Downer – come check it out!

Somerfield orders reshuffle to sort out Kwik Save problem | Business

Business

Nicholas Bannister Chief Business Correspondent

Fri 16 Jul 1999 01. 25 BST

Somerfield, the food retailer, is changing management and converting stores in an attempt to boost its Kwik Save discount chain, which has recently suffered a sharp sales decline.

Earlier this month David Simons, Somerfield’s chief executive, reported problems in integrating the two groups following their £1.26bn merger last year. Somerfield said yesterday that Simon Hughes, the group supply chain director, had been given the specific task of sorting out the “problem” Kwik Save stores. The group said that about 450 Kwik Save outlets were suitable for conversion into full Somerfield stores while the remaining 300 would continue to trade as discount supermarkets.

It is restructuring its management team to concentrate on the Somerfield chain, to improve the performance of Kwik Save, and to develop new formats such as its service station forecourt shops. Separate trading divisions had been created for each business area.

Phil Smith, the group marketing director, is leaving the company. “As marketing will now be the responsibility of the individual trading divisions there is no need for a group marketing function,” a company spokesman said.

Somerfield said it expected its convenience store division to grow significantly as new forecourt stores were added to the 100 already operating. The division includes all those stores where shopping is predominantly supplementary to some other activity.

Under the new management structure, Tony O’Neill, currently group operations director, will be responsible for 1,000 Somerfield stores and those Kwik Save stores which are changed to the Somerfield format.

The group’s buying, finance, systems and supply chain activities will continue to operate centrally while the three trading divisions will be responsible for their own operations, marketing and human resources functions.

Somerfield saw 8% wiped off its share price when it revealed earlier this month that it was having problems with the Kwik Save businesses.

Yesterday its shares closed 5p up at 235.5p.

Just under a year ago Somerfield pulled out of merger talks with Booker, the food distribution and processing business.

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We will be in touch to remind you to contribute. Look out for a message in your inbox in October 2021. If you have any questions about contributing, please contact us.90,000 Quicksort conditions that make it stable

A sorting algorithm is stable if it preserves the relative order of any two elements with equal keys. Under what conditions is mercury resistant?

Quicksort is stable when no item is transferred unless it has a lesser key.

What other conditions make it stable?

sorting

quicksort

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Paradox

April 27, 2011 at 12:29 pm

3 answers


  • Make this QuickSort Java program better

    I have this QuickSort program, I think it might not be the best solution, I need some optimization ideas that I could do.I am planning to run it on about 20 million integers. public static ArrayList quickSort (ArrayList arrayToSort) {…

  • C # QuickSort is too slow

    I am currently researching different types of sorting and found that from a certain point onwards, my QuickSort algorithm was not at all that fast. Here’s my code: class QuickSort {// partitioning array on the key so that the left part is <= key, right part> key private int Partition (int [] arr ,…



13

Well, it’s pretty easy to do a stable quicksort that uses O (N) space, not O (log N), which an in-place unstable implementation uses. Of course, quicksort using O (N) space doesn’t have to be stable, but it can be done like this.

I’ve read that it is possible to do an in-place quicksort that uses O (log N) memory, but is ultimately significantly slower (and the implementation details are pretty awful).

Of course, you can always just look at the array being sorted and add an extra key, which is its place in the original array. Then quicksort will be stable and you just go through it and remove the extra key at the end.

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Justin Peel

April 29, 2011 at 16:37



4

This condition is easy to understand, just keep the original ordering for equal elements.There is no other state that is significantly different from this. The point is how to achieve this.

There is a good example.

1. Use the middle element as the pivot.

2. Create two lists, one for the smaller ones and one for the larger ones.

3. Iterate from first to last and place the items in the two lists. Add an element less than or equal to pivot and before it in the smaller list, an element greater than or equal to pivot and behind it in the larger list.Continue to recursively use the smaller list and the larger list.

https://www.geeksforgeeks.org/stable-quicksort/

The last 2 items are required. The middle element as a pivot is optional. If you select the last element as a pivot, just add all the equal elements to the smaller list one by one from the beginning, and they will keep the original order in nature.

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W.Perrin

03 March 2019 at 14:38



0

You can add them to the list if that’s your approach:

  • When elements are in absolute order
  • When an implementation takes O (N) time to mark relative orders and restore them after sorting
  • When pivot is selected to have a unique key or first occurrence in the current sublist.

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Unknown

April 29, 2011 at 18:32


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: Quick sort :: Exchange Sorts :: Sorts :: Algorithms :: AlgoLab


Easy to implement and very fast way. It is considered the benchmark for speed for sorting algorithms.When it comes to the time complexity of an efficient sorting method, it is usually compared to Quick sort.

The method was developed by Charles Hoare, a 26-year-old graduate student from Oxford. In that distant 1960, he trained in the USSR. At Moscow State University, he studied computer translation, and at Kolmogorov’s school he studied probability theory.

Algorithm

  1. A pivot element is selected (for example, in the middle of an array).
  2. The array is scanned from left to right and searches for the closest element greater than the pivot.
  3. The array is scanned from right-to-left and searches for the nearest element less than the pivot.
  4. Items found are swapped.
  5. Simultaneous two-way scanning continues on the array with subsequent exchanges in accordance with clauses 2-4.
  6. Finally, the left-to-right and right-to-left views converge at a single point, which divides the array into two subarrays.
  7. Quicksort is applied recursively to each of the two subarrays.

Algorithm characteristics

Class

5

n log n )

9029 0

Python quicksort

PHP quicksorts

References

Sorting by exchanges

Quick Sort

Quick sort

Implementation on various YP

90,000 Quick Sort in Python – Another Web Developer Blog

Introduction

Quicksort is a popular sorting algorithm that is often used in conjunction with merge sort.This algorithm is a good example of an efficient sorting algorithm with an average complexity of O (n log n ) . Part of its popularity is also due to its ease of implementation.

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Quicksort is representative of three types of algorithms: divide and conquer (divide and conquer), in-place (in place) and unstable (unstable).

  • Divide and conquer : Quicksort splits an array into smaller arrays until it ends with an empty array, or an array with only one element, and then all is recursively concatenated into a sorted large array.
  • In place : Quicksort does not create any copies of the array or its subarrays. However, this algorithm requires a lot of stack memory for all the recursive calls it makes.
  • Unstable : stable ( stable ) sorting algorithm is an algorithm in which elements with the same value are displayed in the same relative order in the sorted array as before the array was sorted. An unstable sorting algorithm does not guarantee this, of course it can happen, but it is not guaranteed.This can be important when you are sorting objects instead of primitive types. For example, imagine you have multiple Person objects of the same age, such as Dave at age 21 and Mike at age 21. If you were to use Quicksort on a collection containing Dave and Mike sorted by age, there is no guarantee that Dave will come before Mike every time you run the algorithm, and vice versa.

Quick Sort

The basic version of the algorithm does the following:

Divides the collection into two (approximately) equal parts, taking a pseudo-random element and using it as a support (like the center of division).Items smaller than the pivot move to the left of the pivot, and items larger than the pivot move to the right of it. This process is repeated for the collection to the left of the support, and for the array of items to the right of the support, until the entire array is sorted.

When we describe items as “greater” or “less” than another item, this does not necessarily mean larger or smaller integers, we can sort by whatever property we choose.

For example, if we have a custom class Person and each person has name and age , we can sort by name (lexicographically) or age (ascending or descending).

How Quicksort Works

Quicksort often fails to split the array into equal parts. This is because the whole process depends on how we select the pivot. We need to select the support so that it is about more than half of the elements and therefore about less than the other half of the elements. As intuitive as this process may seem, it is very difficult to do.

Think about this for a moment – how would you choose adequate support for your array? In the history of quicksort, many ideas have been presented on how to select a center point — random selection of an item that does not work because “expensive” picking a random item does not guarantee a good selection of a center point; selection of an element from the middle; selection of the median of the first, middle and last element; and even more complex recursive formulas.

The simplest approach is to just select the first (or last) item. Ironically, this results in quicksort on already sorted (or nearly sorted) arrays.

This is how most people choose to implement quicksort, and since it is simple and this way of choosing a support is a very efficient operation, and this is exactly what we will do.

Now that we have selected the pivot element, what do we do with it? Again, there are several ways to do the partitioning itself.We will have a “pointer” to our prop, a pointer to the “smaller” elements, and a pointer to the “larger” elements.

The goal is to move the elements so that all elements smaller than the pillar are to the left of it, and all larger elements are to the right of it. The smaller and larger items will not necessarily be sorted, we just want them to be on the correct side of the axis. We then recursively traverse the left and right side of the axis.

Let’s take a step-by-step look at what we are planning to do, this will help illustrate the whole process.Let’s have the following list.

29 | 99 (low) , 27.41.66.28.44.78.87.19.31.76.58.88.83.97.12.21, 44 (high)

Select the first element as the pivot 29 ) and the pointer to the smaller elements (called “ low “) will be the next element, the pointer to the larger elements (called “ high “) will become the last element in the list.

29 | 99 (low) , 27.41.66.28.44.78.87.19.31.76.58.88.83.97.12, 21 (high) , 44

  • We move towards high that is to the left, until we find a value that is below our pivot.

29 | 99 (low) , 27.41.66.28.44.78.87.19.31.76.58.88.83.97.12, 21 (high) , 44

  • Now that our element high points to element 21, which is less than the pivot value, we want to find the value at the beginning of the array with which we can swap it. It makes no sense to swap a value that is less than the pivot value, so if low points to a smaller element, we try to find the one that is larger.
  • We move the variable low to the right until we find an element greater than the pivot value. Fortunately, low already has a value of 89.
  • We swap low and high :

29 | 21 (low) , 27.41.66.28.44.78.87.19.31.76.58.88.83.97.12, 99 (high) , 44

  • Immediately after that, we move high to the left and low to the right (since 21 and 89 are now in place)
  • Again, we move high to the left until we reach a value less than the pivot value, and we immediately find – 12
  • Now we look for a value greater than the reference value by moving low to the right, and we find such a value 41

This process continues until the pointers low and high finally meet in one cell:

29 | 21,27,12,19, 28 (low / high) , 44,78,87,66,31,76,58,88,83,97,41,99,44

  • We no longer use this pivot so all that remains is to change the pivot and high and we are done with this recursive step:

28 , 21,27,12,19, 29 , 44, 78.87.66.31.76.58.88.83.97.41.99.44

As you can see, we have achieved that all values ​​less than 29 are now to the left of 29, and all values ​​greater than 29 are to the right.

Then the algorithm does the same for collection 28,21,27,12,19 (left side) and 44,78,87,66,31,76,58,88,83,97,41,99, 44 (right side). Etc.

Realization

Sorting arrays

Quicksort is a natural recursive algorithm – split the input array into smaller arrays, move the elements to the desired side of the axis, and repeat.

In this case, we will use two functions – partition () and quick_sort () .

Let’s start with the function partition () :

 def partition (array, begin, end):
    pivot = begin
    for i in xrange (begin + 1, end + 1):
        if array [i] <= array [begin]:
            pivot + = 1
            array [i], array [pivot] = array [pivot], array [i]
    array [pivot], array [begin] = array [begin], array [pivot]
    return pivot
 

Finally, let's implement the function quick_sort () :

 def quick_sort (array, begin = 0, end = None):
    if end is None:
        end = len (array) - 1
    
    def _quicksort (array, begin, end):
        if begin> = end:
            return
        pivot = partition (array, begin, end)
        _quicksort (array, begin, pivot-1)
        _quicksort (array, pivot + 1, end)
    return _quicksort (array, begin, end)
 

After both functions are implemented, we can run quick_sort () :

 array = [29,19,47,11,6,19,24,12,17,23,11,71,41,36,71,13,18,32,26]

quick_sort (array)
print (array)
 

Result:

 [6, 11, 11, 12, 13, 17, 18, 19, 19, 23, 24, 26, 29, 32, 36, 41, 47, 71, 71] 

Since the algorithm is unstable , there is no guarantee that the two 19s will always be in this order one after the other.Although that doesn't mean anything for an array of integers.

Quick Sort Optimization

Considering that quicksort sorts the "halves" of a given array independently of each other, this turns out to be very convenient for parallelization. We could have a separate thread that sorts each "half" of the array, and ideally we could cut the time it takes to sort it in half.

However, quicksort can have a very deep recursive call stack if we are particularly unlucky in pivot selection, and parallelization will not be as efficient as in merge sort.

A simple non-recursive algorithm is recommended for sorting small arrays. Even something as simple as insertion sort will be more efficient for small arrays than quick sort. So, ideally, we could check if our subarray has only a small number of elements (most recommendations say 10 or fewer values), and if so, we would sort it using Insertion Sort.

Conclusion

As we mentioned earlier, the effectiveness of quicksort is highly dependent on the pivot point choice - it can "simplify or complicate" the complexity of the algorithm in time (and in stack space).

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Name Quick sort
Author Sir Charles Antony Richard Hoare
Year Sorting exchanges
Stability None
Comparisons Yes
Time complexity Best O (
Worst O ( n 2 )
Complexity by additional memory Native O

Sedgwick O (log n )