The Quicksort algorithm is one of the very popular sorting algorithms in programming, often used to sort a large array of numbers. Though there is numerous algorithm available to sort a list of objects, including integer, string, and floating-point number, quicksort is best for general purpose. It's a divide and conquers algorithm, where we divide the given array with respect to a particular element, known as 'pivot' such that the lower partition of the array is less than the pivot and upper partition elements of the array are higher than the pivot. The Quicksort is also one of the best examples of recursion, a key programming technique to solve Algorithmic problems. This algorithm is naturally recursive because it sorts the large list by dividing it into smaller sub-list and then applying the same algorithm to those. The base case of recursion is when a list contains either one or zero elements, in that case, they are already sorted. Quicksort is well ahead with primitive sorting algorithms like Insertion sort, selection sort, and Bubble sort. The average time complexity of quicksort is O(N log N), while in the worst case its performance is similar to bubble sort, I mean O(n^2). Apparently, the worst case of quicksort is the best case of insertion sort, where they have to sort an already sorted list. In this article, we will learn how to implement a quicksort algorithm in Java using recursion. We will also learn how quicksort works, and how it sorts a large list of unsorted numbers. In the last section, we will revisit some important things about quicksort. Btw, if you are new to the Data Structure and Algorithm field and not familiar with essential searching and sorting algorithms like Quicksort, I suggest you take a look at the Data Structures and Algorithms: Deep Dive Using Java course on Udemy. One of the better courses to master algorithms and data structure in quick time. 1. How do the QuickSort Algorithm works? An old saying is, a picture is worth more than a thousand words. This is completely true in the case of understanding how the sorting algorithm works. In the past, I have understood Insertion sort, Bubble sort, and Radix sort much better by following a diagram rather than reading about it. That's why I am sharing this diagram which explains how the quicksort algorithm works, how it sort a list of integers. It's similar to a flowchart but doesn't use the notation flowchart uses, instead it practically shows how sorting happens. Once you go through this diagram, read the explanation, it will make more sense. As I told before QuickSort is a recursive algorithm, it divides the big list into smaller list around pivot until those lists are individually sorted. The first step of the Quicksort algorithm is to determine pivot, it's general practice to choose the middle element of the array as a pivot, but you are free to choose any index. Now you have two lists, the next step is to ensure that the left partition only contains numbers less than the pivot and the right partition only contains numbers greater than the pivot. We start the pointer from the left and right of the pivot, and as soon as the left pointer encounter 4, it stops because 4 is greater than 3. Similarly, the right pointer stops at 3 because all numbers on the right side of the list are greater than 3. Now it's time to swap, so 3 takes place of 4 and vice-versa. Now, we move the pointer to one more step, since 2 > 3, the left pointer shifts but since 4 > 3, it stopped. Since the left point is also past the right pointer it stopped. Now if we repeat this process one more time, the list will be sorted. If you still don't get the algorithm then I suggest you join the Visualizing Data Structures and Algorithms in Java course on Udemy. A special course that will teach you data structures and algorithms in Java through animations and implementations. 2. The Concept of Pivot and Partition Though we often select a middle element of the array as a pivot, there is no such rule and pivot can be an element of the given array. You can even consider the first element as the pivot in every partition. It's experienced that choice of pivot affects the distribution of the elements in partitioning and affects the complexity of the quicksort algorithm. As per the rule of partition, numbers in the lower partition should be less than the pivot and upper partition numbers should be higher than the pivot. The running time of partition logic is linear. 3. The complexity of Quicksort Algorithm Explained On average Quicksort Algorithm has the complexity of O(NlogN) and in the worst case, it has O(n²) when the elements of the input array are already sorted in ascending or descending order. The good thing about Quicksort is that it's an in-place algorithm, which means it does not take any additional space, except those used by method stack. By the way, there are some tricks to improve the performance of quicksort, even in the worst case. As suggested in one of the best algorithm design books, The Algorithm Design Manual, by Steven Skiena, you can apply the following recommendation to improve your quicksort algorithm implementation. 3.1. Randomization You can avoid the worst-case performance of O(n²) when sorting nearly-sorted data by random permutation of keys. Though it incurs some cost of permutation still gives better performance than O(n²) 3.2. Leave small sub-arrays for Insertion sort finish Quicksort recursion and switch to insertion sort when fewer than 20 elements: There is a drawback of using recursion to implement a quicksort algorithm, It will not scale because JVM has no tail call optimization, it will simply grow the method call stack to something proportional to the array to sort, and it will fail for the very large array. Btw, if you have trouble understanding how we calculate the time and space complexity of an algorithm or solution, I suggest you check out Algorithms and Data Structures - Part 1 and 2, a two-part series in Pluralsight to learn how to calculate time complexity. It's an excellent course for beginners. 4. Java Program to Sort Integer Array using QuickSort Algorithm Here is our recursive implementation of the QuickSort sorting algorithm. We have used it to sort an array of randomly distributed integers. We have two sets of inputs, one which doesn't contain any repeated numbers and the other which contains duplicates. The Logic of quicksort is encapsulated in method recursiveQuickSort(int[] array, int startIdx, int endIdx) and partition(int[] array, int left, int right), which implements partitioning logic. In order to hide implementation details, we have only exposed a convenient static utility method called quickSort(int[] array), which takes an integer array and sorts that in place. package test; import java.util.Arrays; /** * Java program to Sort integer array using QuickSort algorithm using recursion. * Recursive QuickSort algorithm, partitioned list into two parts by a pivot, * and then recursively sorts each list. * @author Javin Paul */ public class QuickSort{ public static void main(String args[]) { int[] input = { 23, 31, 1, 21, 36, 72}; System.out.println("Before sorting : " + Arrays.toString(input)); quickSort(input); // sort the integer array using quick sort algorithm System.out.println("After sorting : " + Arrays.toString(input)); // input with duplicates int[] withDuplicates = { 11, 14, 16, 12, 11, 15}; System.out.println("Before sorting : " + Arrays.toString(withDuplicates)); quickSort(withDuplicates); // sort the array using quick sort algorithm System.out.println("After sorting : " + Arrays.toString(withDuplicates)); } /** * public method exposed to client, sorts given array using QuickSort * Algorithm in Java * @param array */ public static void quickSort(int[] array) { recursiveQuickSort(array, 0, array.length - 1); } /** * Recursive quicksort logic * * @param array input array * @param startIdx start index of the array * @param endIdx end index of the array */ public static void recursiveQuickSort(int[] array, int startIdx, int endIdx) { int idx = partition(array, startIdx, endIdx); // Recursively call quicksort with left part of the partitioned array if (startIdx < idx - 1) { recursiveQuickSort(array, startIdx, idx - 1); } // Recursively call quick sort with right part of the partitioned array if (endIdx > idx) { recursiveQuickSort(array, idx, endIdx); } } /** * Divides array from pivot, left side contains elements less than * Pivot while right side contains elements greater than pivot. * * @param array array to partitioned * @param left lower bound of the array * @param right upper bound of the array * @return the partition index */ public static int partition(int[] array, int left, int right) { int pivot = array[left]; // taking first element as pivot while (left <= right) { //searching number which is greater than pivot, bottom up while (array[left] < pivot) { left++; } //searching number which is less than pivot, top down while (array[right] > pivot) { right--; } // swap the values if (left <= right) { int tmp = array[left]; array[left] = array[right]; array[right] = tmp; //increment left index and decrement right index left++; right--; } } return left; } } Output: Before sorting : [23, 31, 1, 21, 36, 72] After sorting : [1, 21, 23, 31, 36, 72] Before sorting : [11, 14, 16, 12, 11, 15] After sorting : [11, 11, 12, 14, 15, 16] 5. Things to know about QuickSort Algorithm in Java As I said, QuickSort is one of the most popular sorting algorithms between programmers, maybe just next to Bubble sort, which is ironically the worst algorithm to sort a large list of numbers. But one thing is common between QuickSort and Bubble Sort, do you know what? In the worst case, both have the complexity of O(n^2). 5.1 QuickSort is a divide and conquers algorithm, which means it sort a large array of numbers by dividing them into a smaller array and then individually sorting them (conquer). 5.2 Average case complexity of Quicksort is O(n log(n)) and the worst-case complexity of Quicksort is O(n²). 5.3 Quicksort is a comparison sort and, inefficient implementations, it's not a stable sort, which means equal numbers may not retain their original position after sorting. 5.4 Quicksort algorithm can be implemented in-place, which means no additional space will be required. This makes it suitable to sort a large array of numbers. 5.5 The Arrays.sort() method in Java uses quicksort to sort an array of primitives like an array of integers or float and uses Mergesort to sot objects like an array of String. That's all about how to implement a QuickSort algorithm in Java. QuickSort is one of the fast and efficient sorting algorithm, perfect for sorting large arrays, but some programmer finds it extremely hard to understand. One reason for this could be that because quicksort is an in-place algorithm due to which programmers find it a bit confusing, but it's very efficient. Otherwise, if you choose simplicity you can always implement it in other ways. Other Data Structure and Algorithms You may like My favorite free courses to learn data Structure in-depth (FreeCodeCamp) 50+ Data Structure and Algorithms Problems from Interviews (list) 5 Books to Learn Data Structure and Algorithms in-depth (books) How to reverse an array in Java? (solution) 75+ Coding Interview Questions for Programmers (questions) How to remove duplicate elements from the array in Java? (solution) How to implement a recursive preorder algorithm in Java? (solution) How to implement a binary search tree in Java? (solution) Post-order binary tree traversal without recursion (solution) How to print leaf nodes of a binary tree without recursion? (solution) Recursive Post Order traversal Algorithm (solution) Iterative PreOrder traversal in a binary tree (solution) How to count the number of leaf nodes in a given binary tree in Java? (solution) Recursive InOrder traversal Algorithm (solution) 10 Free Data Structure and Algorithms Tutorials (free courses) 100+ Data Structure Coding Problems from Interviews (questions) Thanks for reading this article so far. If you like this Java Array tutorial then please share it with your friends and colleagues. If you have any questions or feedback then please drop a comment. P. S. - If you are looking for some Free Algorithms courses to improve your understanding of Data Structure and Algorithms, then you should also check these free Algorithms courses on Udemy. It's authored by a Google Software Engineer and Algorithm expert and it's completely free of cost.

While most plural nouns follow a standard rule of adding an "s" or "es" to the end of the singular form, there are some irregular plural nouns that do not

A 5 page list of common themes in literature. The first page has a list of word or phrase themes common in literature - particularly children's literature. The last four pages are lists of common themes in sentence form. Some of the themes in sentence form are sorted based on commonalities: themes about family and friends themes about growth mindset themes about being kind / doing the right thing themes about equality / acceptance themes about honesty themes about emotions themes about power themes about hard times These lists are geared towards teaching theme to upper elementary (primarily 4th and 5th grade students). The preview shows everything included in this resource. You might also like: Determining Theme - Reading Passages, Activities, and More Kalena Baker, Teaching Made Practical

Free world history resources Middle Ages to Modern Times (Classical Conversations CC Cycle 2 history). Activities, videos, coloring sheets, and more!

Ready to help your students move beyond "nice" and "mean" when describing characters? Here are 6 ways to build their character traits vocabulary!

A teaching resource that includes dozens of free printables and helpful website links to use in the classroom for elementary and middle school students.

Kali Linux commands cheat sheet. All basic commands from A to Z in Kali Linux has been listed below. Also Read: How to run Kali on your Android device A apropos : Search Help manual pages (man

Overview of C++'s standard sequence

When you join my email list, you’ll gain access to my subscriber-only resource library with tons of free printable teaching resources that you can use in your classroom right now.

Englishbix will help kids to learn new words and improve their vocabulary. This time we have prepared an alphabetically sorted words list for spelling bee

NOTE: This post is sponsored by HarperCollins.Lottie Pumpkin has spent her life obsessed with fairytales, livi

Collective Nouns! What is a collective noun? Learn extensive list of collective nouns with examples and ESL printable worksheets to increase your vocabulary.

Dependent prepositions help ESL students construct whole language phrases with 150 of the most common combinations, organized alphabetically with gap fills for students to check their current level of knowledge. INCLUDES: -50 Verb + Preposition Phrases -100 Adjective + Preposition Phrases -Gap Fill Sentence Worksheet -Sorting Worksheet -Answer Key for All Worksheets PLEASE: Enjoy this lesson to the fullest extent of the law. Check out some of my other lessons and activities in my store. Recommend other ESL-related topics you'd like to see in my store. Visit my website at talkintownenglish.com. Be the best teacher you can be. I'll do the same. :)

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Opposite Of Lazy, Antonyms of Lazy, Meaning and Example Sentences Kind means; having or showing a friendly, generous, and considerate nature, gentle, polite, delicate, affable; type, species, sort, genre, sort of Opposites of Kind; pitiless bad nasty cold bitter heedless impolite mean inhumane hateful indifferent malignant uncivil brutal savage cruel aloof disagreeable Example Sentences with Kind; My teacher is very kind. Please be kind to others. What kind of car is that? What kind of music do you play? Here are 400 Important Opposite Words List boy – girl brave – cowardly break – fix broad – narrow brother – sister build – destroy busy – lazy

You've taken a DNA test and now it's time to work out who's related to who.The Leeds Method is a great way of clustering your matches together to see groups of matches that may indicate your grandparents or great grandparents lines. You can read more about the method on Dana Leeds' website:  www.danaleeds.com/leeds-method-dna/ These worksheets have been developed for those that prefer to do things by hand, rather than use spreadsheets. The DNA Matches - Leeds Method Worksheet comes in multiple sizes A4/Letter/Legal (20 matches) or A3/Ledger (50 matches). List your matches, Shared cM and if they have a tree, then the fun begins as you colour in your shared matches.The DNA Matches - Leeds Method Match Surnames Worksheet comes in A4/Letter/Legal size and allows you to focus on a group of matches and explore the shared surnames at the great grandparent (4th generation) level. We have two blog posts showing how we completed the charts. Find Part 1 here and Part 2 here.If you're a worksheet sort of person, have a look at our downloadable DNA Match Chart, it's perfect for building matches family trees to try and work our how you're related (and it keeps you organised). Print as many as you need for your own use and then use multiple charts for groups of shared matches. Spread them out and look for similarities in family trees. Solve those mysteries.Completed samples do not use real names for DNA Matches.   Do you want some help understanding your DNA Matches? Why not book a Understand Your DNA Results Workshop.

👻 So on top of doing #Drawlloween this year I will be participating in my own prompt list for #Kinktober over on @krovav-nsfw👻 The prompts are based off of my own interests and Patreon requests so...

Fun With Firsties, probability, math lesson, worksheets, assessment, activities

Boy was it a cold start back after winter break. I can take a few days of this weather, but I'm just about over it. Of course the cold did not slow us down in class. We made the most out of the 3 days and 5 hours that we had this week. (Monday was an admin. day and Thursday was a delayed start.) My goals for this week were to introduce our January math and literacy centers (all 21 of them), to do a little Daily 5 retraining, to launch Rocket Math (addition fact drills), to teach all about Y as a vowel, and to work in some fun New Year's activities. Quite a list for a short week. I'm happy to report that we fit everything in. :) My students are all about getting new centers. I change them out each month. I intro all of them over a day (or two) during a few mini lessons. After I explain and model all the centers, they are up and running. I love the year long review these centers provide. They also free me up to meet with students to do a little reteaching. In math this month we are working out of my Baby It's Cold Outside {10 Math Centers for January}. This packet includes work with addition, subtraction, number comparisons, number order, nonstandard measurement, time to the half hour, missing addends, and more. You can get a closer look by clicking on the picture. Below is a FREE center from this packet, Snowman Comparisons. With this center students will practice comparing numbers with the greater than and less than signs. Click on the picture for your own FREE copy. As for our literacy centers, we'll be working with the companion packet, Baby It's Cold Outside {10 Literacy Centers for January}. This packet includes work with rhyming words, long and short a discrimination, sentence sorting, contractions, synonyms, antonyms, compound words, sight words, and more. You can check it out by clicking on the picture. You can have a FREE center from this packet by clicking on the picture below. Hot Chocolate Blends provides your students practice with initial blends. After matching all the initial blend picture cards with the word cards, students will write their answers on the recording sheet. Besides our work with literacy centers and math centers, we also spent a bit of time practicing Y as a vowel. We started off by going over our anchor chart and brainstorming words that end with y. If you would like this anchor chart to use with your students, click on the picture. We talked about how most one syllable words that end with y have the long I sound. While most two (or more) syllable words that end with y have a long E sound. Students applied their vast knowledge of Y as a Vowel by doing various sorts, reading, and writing activities. We primarily worked out of my Words at Work {Seven Word Work Activities for Y as a Vowel}. You can learn more about this packet by clicking on the picture. If you would like a free copy of one of the activities from this packet, click on the picture below. It's a word sort with Y as long E and Y as long I. With all of this learning going on, we had to fit in some time for a little creativity. Plus, my walls were bare after all of our Christmas craftivities went home. We really needed some student artwork to liven the classroom. So . . . after reading some favorite New Year's themed books, we discussed resolutions. Students thought about personal resolutions and wrote them down. Then we made our New Year's Resolution Kids. Using the party blowout was certainly not an original idea, but I love it. The kids love using them too. I'm a little worried that the blowouts will be ripped on the Resolution Kids as soon as I send them home. For first graders, blowouts can be just too fun to resist. Maybe I need to get another set of blowouts to give my students when they take their projects home. We had a great week. Everyone seemed to be rested and ready to get back to our routine. Next week we'll be celebrating our 100th Day of School. I cannot believe we are already at the 100th Day point in the year. Time flies when you're having fun. Time also flies when you are super busy. Thanks for stopping by.

The ballpoint pen, looks pretty simple when you look at a basic BIC for example. But no way this was a major technological advance.

View the comic strip for Basic Instructions by cartoonist Scott Meyer created March 09, 2012 available on GoComics.com

Last week, we posed this question to our GenealogyBank friends on Facebook: “What’s the funniest name or surname you’ve ever come across?” Well, your respo

In stories and books, the names of characters are super important. They help make the story interesting and connect the readers with the main characters. A character's name can tell you about their identity, where they come from, and even give hints about their personality.

Profanity, expletives, curse, we all do it sometimes. But do you know what the expletives words means. Lets look at profanity and their meanings

Item description This Word Sorts For Big Kids resource will help students learn suffixes that make the “shun” sound. They will sort the words according to which suffix each should end with. Definition cards are included to help build vocabulary and reinforce the meaning of each suffix. Includes: TION, SION, and CIAN heading cards 23 Word Cards for sorting and adding the correct suffix 23 Definition Cards Recording Sheets Cut & Paste Worksheet – Students add the correct suffix to each word and glue in the corresponding definition. Answer Keys These can be used for just learning the spelling patterns or for reinforcing word meaning as well.

In stories and books, the names of characters are super important. They help make the story interesting and connect the readers with the main characters. A character's name can tell you about their identity, where they come from, and even give hints about their personality.