Quick Sort Using Recursion (Theory + Complexity + Code)

[@KunalKushwaha]

DSA + interview preparation playlist: kzbin.info/aero/PL9gnSGHSqcnr_DxHsP7AW9ftq0AtAyYqJ

[@mokka_comedy]

Hi kunal, u are the best, could you pls complete entire topics on DSA

[@hc-dc7043]

One of the best explanations I've seen for Quick Sort. The way he broke the concept down to its nuts and bolts is really amazing.

[@nishantsingh8477]

There's this merge sort and quick sort, people say its hard to understand this and so I left them and proceeded further in my DS journey. But I was damn sure you will make it easy and so listened to you and Now I know this . Thankyou KK Bhaiya 🤩

[@Sillysmiles76]

Such a blessing to learn DSA with your videos.😇 Please complete the series.🙂

[@sagarmore9425]

I have tried to understand merge sort and quick sort literally a thousand times. In college, classes, some time by me. I was not able to visualize how it is actually working with recursion, although I knew the code. But the way, you are simplifying the things and the way you have had the first recursion video done is just awesome. That first recursion video is quite important and on top of this you explained this sorting so well, kudos man!

[@kishorevb8331]

With the code you provided, it will not place the pivot at the right spot after one pass, but still it works!!! It doesn't place the pivot in the right index due you incrementing and decrementing the start and end after each swap. We must increment and decrement only when provided that the value in that index is lower than or higher than the pivot

[@mk_ahmar]

Hey Kunal, your lectures are valuably explained, and covers everything one should know sooner or later. For example after watching this QuickSort lecture, all I've to do is practice some question, I don't need to watch any more concept of this anywhere, and this is amazing. You and your video lectures are underrated, if this quality of lectures are provided by any EdTech they would have charged that course extravagant. Hope I'll be able to get ₹7Lakh/month 😂(Joking).

[@KunalKushwaha]

you wont get 7 lakhs per month with dsa, it happens with dev

[@zainabfahim8714]

The confidence you have in your work, is empowering!! Keep that going

[@Tomharry910]

I remember plucking out my hair on recursion and sorting algos before stumbling on your videos. You explain it very well and its very intellectually satisfying to watch your videos as well.

[@karthikpm9669]

this is good...i mean its good that you didnt advertise your videos in a humble way , because people wont know how good your videos are. PS i didnt realise how fast time went , the way you taught was very smooth and seemed like a story to me.

[@rohitchilhorkar8114]

I can't even express how much value it is providing us...hats off kunal bhai!

[@vidhijain2945]

The way you have explained is great Kunal!

[@KunalKushwaha]

Thank You!

[@VinodKumar-fn2iq]

Kunal is very quick now 🔥 Thanks for the course ❣️

[@AshishKumar-ys7rj]

best lecture on yt for quick sort because it is the most efficient i have seen, but first watch the quick sort algorithm by striver, he will clear all the doubts if you have got any by watching this lecture , since i had lot of doubts . Once you understand the algorithm u can follow the code here . The concept will be crystal clear then .

[@tejasvijain1077]

Before watching this vid, i was on gfg and javapoint understanding what quick sort was and my god, kunal has explined it so well and he hasnt copied what they did and I was blown by how easy he has made this!! Kudos bro,

[@shantahiremath7313]

Thank you Kunal Sir. You are always the best teacher. I never learned this sort by fearing the complexity. But now you made it a cakewalk. Always grateful.

[@Helly_Patel]

Thanks for teaching us like no one did till now!! One small request, please make lectures on dynamic programming as well!!

[@vinaykrishna747]

Please Use Black Background for writing on the screen It doesn't affect eyes much 😊😊 Consider this Man

[@Mohit_Gupta24]

As always brilliant explanation. I used to be scared of quick sort in my college days, but this video makes it seem really easy. Moreover, I was able to relate Step: placing pivot at the correct index with Binary Search step. In binary search, we search for a target element, assuming the array is sorted, and use the start and end indexes as pointers to the virtual array. Here we have to just place the pivot at the correct index, so instead of searching the target, we already have the target(i.e. pivot), we have to put at correct index and in this process we are ensuring elements less than pivot are on LHS, and elements greater than pivot are RHS.

[@rakeshkumarmaurya8265]

Best DSA COURSE on EARTH 🔥🔥 THANKU @kunal kushwaha

[@shikhamaurya4453]

Ohh damn, This was so well explained 45 minutes is totally worthy

[@KunalKushwaha]

Thank You!

[@twi4458]

Can anyone help me in understanding 24:50, How we got O(N^2). It is Linear Recurrence Relation, Right?

[@ritviksaran6199]

after each pass how does it ensure that pivot will end up in the correct position ?

[@VishalKumar-pk9ek]

In the merge sort video , I was little confused in the concepts of sorting algorithm through recursion but by this video , the previous confusion also got cleared . Thank you so much 😍😍😍

[@KunalKushwaha]

You're very welcome!

[@vikassk1308]

@@KunalKushwaha little confused, when you say pivot would be in the correct position after swaps if I have below array and I choose 4 as pivot {8,6,1,4,2,12} after swaps, ill end up having {2,4,1,6,8,12} where 4 is at index 1 but it should be at index 2 right ?

[@anshulgoel1940]

An alternative approach is to swap the pivot with the last index before we start in each recursive call and then start comparing left and right. Once index cross over, we swap pivot with left pointer. Works out much cleaner at code level.

[@pratheeeeeesh4839]

The approach which you told above does that calculate the pivot using the same mid concept?

[@anshulgoel1940]

@@pratheeeeeesh4839 No. Pivot can be picked in any way. It won't make any difference at complexity level. This approach I suggested just keeps the code clean. Hope it helps

[@sravansunkara]

I feel very confident whenever I learn from you, Thank You for existing, God bless you!!!

[@SochtaHoonMain]

Kunal Kushwaha : "Your start is low , Your End is going to be high" :)

[@charaiveticharaiveti8414]

Kunal, your tutorials are gems. I can pay for such quality content. But you choose not to. Love and Regards. Tweeting for better reach.

[@piyush9266]

U knw bro..i think u r inborn Guru not a professional teacher.may god bless u with all Happiness of this universe.🙏

[@nishu0766]

i request you to please upload all the remaining topics of this complete DSA bootcamp as soon as possible

[@devanshgaur1747]

Bhaiya ,aap sachii mein bohot achaa padhatee hoo. Thanks bhaiya for such a course

[@abhirajchatterjee6965]

This partitioning algorithm seems to be incorrect, say we take the same example provided in the video wherein the last element is always selected as the pivot - 10, 80, 30, 90, 40, 50, 70 | p = 70, s is at 10, e is at 70 now, s moves till 80 where it finds a violation (element at s should be less than 70, here it is > 70), e stays at 70 since it is also a violation(element at e should be greater than 70, here it is = 70 ), swapping happens -> array after first swap -> 10, 70, 30, 90, 40, 50, 80 -> s moves to 30, e moves to 50 notice that the new part of the array which is going to be partitioned now is 30,90,40,50 and the rest is assumed to have been placed correctly w.r.t the pivot that is 70, which is wrong as 70 is clearly not at the position where it is supposed to be.

[@ritviksaran6199]

Kunal bro this is a doubt. After a pass of the outer while loop, how can we confirm that pivot will end in correct index? For the array {1, 4, 2, 5, 7, 6, 3} after one pass changes to {1, 4, 2, 3, 7, 6, 5}. 5 was the chosen pivot but it does not end in correct position. The whole algorithm is correct at the end it will give the sorted array, but for this version I think we cannot confirm that after each pass pivot will end up in correct index.

[@harcharansingh1997]

Yeah bro having same doubt

[@ritviksaran6199]

@@harcharansingh1997 This method ensures that in each pass the pivot ends up in the correct index public class Main { public static void main(String[] args) { int [] arr = {1, 4, 2, 5, 7, 6, 3}; quickSort(arr, 0, arr.length - 1); for(int i : arr){ System.out.println(i); } }public static void quickSort(int [] arr, int low, int high){ if(low >= high) return; int s = low; int e = high - 1; int pivot = arr[high]; while(s pivot){ e--; } if(s

[@MohamedElsayed-pb3oj]

The reason you are having doubt is because the algorithm is incorrect. Tried it manually and tried it with the debugger and it still gave the first pass answer. Meaning the algorithm doesn't put the pivot in its intended location.

[@takenbysac]

@@MohamedElsayed-pb3oj exactly Elsayed , this algo is wrong, I tried with negative numbers as input and it failed . Tried with {2,5,3,0,8,22,9,-1,-3,-5} as input . @Kunal

[@takenbysac]

@@ritviksaran6199 even this got failed @ritvik for input as {2, 5, 3, -3, -1, -22, 0, 8, 22, 9}

[@Cloud-577]

thank you I actually like this implementation better than other ones I have seen. this will stick with me, no doubt

[@harshaggarwal1821]

@36:05 you mentioned swapping doesn't happen if array already sorted. But taking {1,2,3,4,5} it does call swap with same indices.

[@chennayaianjc3306]

I think he said , swap will not happen if it is already sorted .how? in while(s

[@karanbadhwar4113]

The problem is I did not understand the Time and space Complexity After recurrence relation, as I am do not understand the Maths that you did, it took me more than a week to any how complete the video, but now my question is how can I do that, as I did not understand them Maths you taught, any other way to solve it ?

[@KshitizAnand-xr1wj]

I really loved this sorting algorithm

[@randheerkumargautam6433]

will you make video on dynamic programming as well?

[@vikaspanwar5194]

thanks for uploading at this frequency. Hope that you will cover dp really soon. 👏🙌

[@baap6382]

Wow, you are so good. Wish you to solve complex algorithms down the lane

[@Content_creater_entertainment]

Best vedio❤

[@shivamrana4633]

You are boosting my confidence day by day..🎉😊

[@prashantmishra9220]

@kunalKushwaha Bhaiya aapne to book follow krke pdhai ki hogi....to hmlog sirf is playlist ko follow krenge kya sach me utna hi knowledge gain kr paenge...kya is playlist me jitna pdhaya gya hai utna hi pdhne se sach me acchi job crack kr paenge? pls reply

[@requisits]

Thank you kunal finally understood the concept deeply.

[@jyotiprakashnayak1123]

best course till date in any platform

[@924_aradhyapatro5]

This is by far the simplest explaination of Quick Sort that i have found

[@sravanakirtana2787]

Awesome. You make everything very easy. (In your words easy peasy 😅)

[@firdoshansari2757]

Hey Kunal, what is the possibile time you take to complete dsa and start with Opps??

[@akashpradhan7908]

I have tried some udemy courses, watched some KZbin tutorials on DSA ... But damn.. Kunal is a teacher of another league.

[@yourmentor8242]

Hey kunal please bring some leetcode sorting questions problem videos,and yes Thank you so much for this Awesome content bro ❣️

[@gitansh194]

00:05 Quicksort is a crucial sorting algorithm frequently asked in interviews. 02:11 Quick sort uses pivot to divide elements into smaller and larger groups. 06:22 Quick Sort uses recursion to position the pivot element correctly after each pass. 08:20 Quick sort uses recursion to sort arrays efficiently 12:24 Understanding how to identify violations while sorting using Quick Sort. 14:35 Moving the pivot to the correct position using recursion 18:43 Picking the pivot element in quick sort 20:34 Understanding time complexity and recurrence relation in Quick Sort. 24:23 Quick sort's time complexity is O(n^2), covered in detail 26:22 Recurrence relation of merge sort explained with time complexity formulas. 29:36 Hybrid sorting algorithms combine merge sort and insertion sort for efficiency. 31:26 Exploring new approaches to solve problems is recommended. 34:59 Moving elements according to pivot and violating conditions 36:36 Explanation of the swapping process and recursion call in Quick Sort using recursion. 40:23 Quick sort is a hybrid sorting algorithm 41:58 Quick Sort using recursion is a common sorting algorithm.

[@anjalithakur_12]

Very good explanation just loved it

[@akashnagar4862]

Before starting this course, i was like ''Java is very tough language'', but after dig into this course till now, I am like ''Java is Fun'', Thankyou man for providing such great course. And I would like to request you that please make a course of Collection framework also. And you will be boom on KZbin....trust me the way you transfer your thoughts is really amazing. Cheers to the hard work 🥂

[@NavanshK]

@kunal Please continue this course...

[@absingh773]

13:14 pivot at correct position❌every element at correct position✅

[@spdwivedi5925]

Great video kunal

[@civuasdev5532]

Hey kunal, Thanks for this course.

[@NilavraPathak]

I think quick select is also a closely related technique that can be used to solve many problems.

[@RaviPatel-rj1re]

this quick sort algorithm not given correct ans for (5,4,1,2,8,7,6,3) can you explain it why?

[@amine_fadssi]

use variable int pivot = arr[mid] not just compare with arr[mid] directly

[@anukritisingh4479]

pls upload dp series soon

[@Dekh_rha_hai_vinod.]

Bro amazing hetric👌👌

[@ayushmaheshwari809]

Hey Kunal , why pivot element not place correct index after one recursion call ? Although the array is sorted in the end .

[@sangamsaini138]

bhaiya if conditon lagana ka koi jarurat nahi tha uska binna bhi ho jata becouse loop me bhi same conddition hai or isliya if condition likhna ki koi jarurat nahi thi

[@immortalji]

Hey bhaiya, How to stay away from -ve people? and stay focused toward own goal(SDE OR DATA SCIENTIST).

[@prashantgoswami1491]

Kunal i am waiting for some other topic vedio please kindly upload it I am going to have my placement in next sem

[@mohammedsaad0761]

The video explains the quicksort algorithm in detail, covering its theory, complexity, and coding implementation, while comparing it with other sorting algorithms like merge sort and discussing internal sorting functions in Java and Python. Detailed Summary for [Quick Sort Using Recursion (Theory + Complexity + Code)](kzbin.info/www/bejne/kGnWp4KnltKUnZo) by [Monica](monica.im) [00:04](kzbin.info/www/bejne/kGnWp4KnltKUnZo&t=4) Understanding the importance of Quicksort in sorting algorithms - Introduction to Quicksort and its significance in interviews} - Covering the complexity, time, space, code, advantages, and disadvantages of Quicksort} - Exploring internal sorting algorithms and hybrid sorting techniques} [05:15](kzbin.info/www/bejne/kGnWp4KnltKUnZo&t=315.199) Explanation of quick sort using recursion - Explanation of partitioning elements based on a pivot} - Role of recursion in sorting process} - Unique aspect of pivot placement in quick sort} - Recursion's role in sorting the left and right partitions} - Selection of a new pivot element for further partitioning} [10:33](kzbin.info/www/bejne/kGnWp4KnltKUnZo&t=633.44) Explanation of how to perform quick sort using recursion - Explanation of selecting the pivot element} - Identifying violations in the elements compared to the pivot} - Fixing violations by swapping elements} - Comparison and handling of elements in relation to the pivot} [15:49](kzbin.info/www/bejne/kGnWp4KnltKUnZo&t=949.04) Explanation of the quick sort algorithm using recursion - Explanation of choosing the pivot and dividing the array} - Demonstration of the pivot at the correct position} - Discussion on picking the pivot element} - Introduction to complexity analysis} - Partitioning the elements based on the chosen pivot} [21:07](kzbin.info/www/bejne/kGnWp4KnltKUnZo&t=1267.12) Understanding the time complexity of Quick Sort using recursion - Explaining the time taken to put the pivot at the correct position} - Discussing the recurrence relation of Quick Sort} - Analyzing the worst-case scenario in Quick Sort} - Illustrating the impact of choosing the smallest or largest pivot element} - Highlighting the consequences of the worst-case scenario in Quick Sort} [26:22](kzbin.info/www/bejne/kGnWp4KnltKUnZo&t=1582.48) Explanation of time complexity and space complexity in Quick Sort - Detailed explanation of time complexity using Akra-Bazzi formula} - Importance of understanding space and time complexity in algorithms} - Best case and worst case complexity of Quick Sort} - Stability of algorithms and the concept of stable sorting} - Previous video covering sorting algorithms and stability in detail} [31:40](kzbin.info/www/bejne/kGnWp4KnltKUnZo&t=1900.48) Introduction to Quick Sort Using Recursion - Starting the coding part for quick sort} - Explaining the concept of low and high indices} - Using pointers to manipulate the object in the array} [36:57](kzbin.info/www/bejne/kGnWp4KnltKUnZo&t=2217.68) Explanation of quick sort using recursion and its implementation - Explanation of the recursion process in quick sort} - Dividing the array into two halves for sorting} - Initialization of low and high variables for sorting} - Discussion on different approaches to quick sort} - Recommendation to try other sorting methods before asking for help}

[@AdarshKumar-xh1ie]

Hi kunal. I tried this array int[] arr1 = {1,9,2,3,5,6,7,8,10} on the above code. In the end the array was sorted. But, after the first pass the 5 was on the 1st index before 2 and 3 after taking 5 as the pivot. So is there any other way around for this? Or its working fine?

[@shyamalm88]

Kunal Facing too much problem with sliding window technique. with strings and other things, it will be very helpful if you can create a video on this with solving some problems, not only the maximum sum problems but other problems also some tips or tricks will be fine. Love your work. your content really helpful.

[@suyashkumar8840]

Love you kunal bhai ♥️♥️

[@poojakatare1497]

A very informative and interesting lecture 😎

[@adilkhan-ft7xv]

Hi kunal, can you tell how long it will take for dynamic programming lecture??? Btw we are very thankful for your great work

[@ashishgaikwad440]

god level explain ❤️

[@bishalbhattacharjee850]

Great teaching please make a video on heap sort as well...

[@KunalKushwaha]

Sure I will

[@amruthaa5876]

Thank you so much, Kunal!

[@itsom5294]

Hey kunal bring some leetcode maximum subarray type questions problem videos

[@KunalKushwaha]

I will

[@talish7714]

good job kunal and never gave up bro keep it up

[@KartiKKaushiKYt]

My profssor seriously needs to learn from this dude, I was stressing about this so much, this titorial is elite. THANK YOU SO MUCH

[@mihirjadhav5642]

why did you delete your old videos?? where do we find them now?

[@programmer6953]

At 23:07 i dont get why we put pivot at middle while showing t(n) calculation ,at t=0 the left will be empty but right will be n-1 element does it mean we picked first element as pivot ?if not why we showing pivot in t(n) calculation why not just t k +t n-k + alfa n supposedly pivot is at the end of the array for better presentation pls enlighten me on this..

[@arijitghosh397]

brother i am not able to solve the linear recurrence relation because the function is f(n) = f(n - 1) + O(n) . When I put a^n for f(n) what to put in place for O(n). I am confuse in that part can anyone help me to understand ?

[@arpitanaik4940]

Did you get the answer??? I tried using akra bazzi formula but the problem was that when I put p=0 the ans is O(N) and when I put p=1 the ans is O(NlogN). How can we get O(N^2)

[@twi4458]

Can anyone help me in understanding 24:50, How we got O(N^2). It is Linear Recurrence Relation, Right?

[@Rahul-nw5rp]

Yes man . For this you have to use substitute method . I checked common algorithms book and there was written that to use akra bazee method bi must be in range of 0 to 1 exclusive

[@Sumit-lr1qj]

Nope

[@vcrohithutagonna2105]

Check out the Time and complexity video, You'll get a whole great idea

[@arpitanaik4940]

​@@vcrohithutagonna2105 Still not able to get it. Can you plz share how to got the ans.

[@joshiomkar1394]

Hey bro, I followed your implementation of quicksort, and the array is sorting fine, but there is a problem. Suppose there is an array [2, 4, 5, 3]. Here pivot will be the middle element at index 1 which is 4. Now, all the elements less than 4 should be on the left of 4 and greater at the right, but using your implementation. The resulting array becomes [2, 3, 5, 4]. 4 will get swapped with 3 because 4 and 3 breaks the violation. Then, start will increment and end will decrement and both point to 5. start will break the violation while end doesn't and keeps moving back until 3. Here further swapping will not take place because start > end. To note that the array becomes sorted in the next step because recursion calls quickSort on [2, 3] and [5, 4] but why didn't the 4 get placed in the right position. Is this a behaviour of quicksort or am I missing something? Please respond because this is really confusing me

[@rishavraj6861]

it works well for 2,4,5,3. it gives 2,3,4,5

[@joshiomkar1394]

@@rishavraj6861 yeah, I noticed that but it works like that only when we are using the high = n instead of n - 1.

[@rishavraj6861]

@@joshiomkar1394 how will u take high = n. n is the size of array so, for last index high = n-1. in this video high is also equals to n-1.

[@nikhilsood6126]

you are right brother......after first pass .....acc. to his theory the left of pivot must be less than pivot but it is not after first pass.......in implementation.......so it was also confusing me.......in actual acc. to his implementation only right will follow the theory not left

[@ritviksaran6199]

True, Actually you said that on the second loop, [2, 3] and [5, 4] will be passed, that is not true, [2, 3, 5] and [4] will be passed. This technique works but it does not ensure that pivot will end up in the correct index. I think he was wrong in that point.

[@geetankarkarmakar378]

Mad stuff ❤‍🔥❤‍🔥 Thanks a ton !!

[@PiyushMishra-tq6cl]

Hey Kunal, How did you do the DSA at your time? Like did you rely on tutorial videos or some book?

[@jacksongeorge4047]

hey can you make a video about how to apply remote jobs ...

[@mrrishiraj88]

Great thanks for very useful content in quite comprehensive form.

[@prikshit_sharma4071]

I Never learnt java. Should I start this course or not?🙏🏻🙏🏻

[@KunalKushwaha]

Yes

[@narendramalapula1260]

I think time complexity O(n^2)

[@dineshmadduru7043]

Thank you sir

[@kirankumar9729]

Fabulous explanation..

[@charon71]

best videos here!

[@vanshsharma2486]

great video bro, thank you so much!!

[@moneshc6887]

Please do something such that if I search for quick sort this videos should come first.... : ) The only video required .Thanks Kunal

[@smilemania5102]

Awesooooooooooooome ❤️❤️

[@parmarkamlesh6493]

Hi Kunal, are you planning to launch any playlist?

[@jk-sm6qr]

Thank you Kunal

[@sourabhkothari7014]

Best explanation

[@gowthamselvaraj7793]

Do a separate series for Dynamic programming bro..

[@gauravgautam5963]

Hey , pls tell me one thing that how the primary condition is working , that break condition , that if(low>=hi) return ;

[@gourabmukherjee4848]

How to find the index of the pivot element by using this algorithm ?

[@GunjanFitness]

Can you please continue this course and complete it soon

[@vigyanta94]

Thanks Kunal

[@rajeshkilladi7124]

How about this 5,1,4,2,3 we take pivot as 2, with your explanation it doesn't put the pivot in the right place for this input,