L7. All Kind of Patterns in Recursion | Print All | Print one | Count

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take U forward

take U forward

Күн бұрын

Пікірлер: 644
@manavpatnaik222
@manavpatnaik222 8 ай бұрын
Folks, these are actually very important patterns to keep in mind with respect to recursion. If you understand these then a lot of Binary Tree problems become very simple. I don't think any one else teaches patterns such as these in a separate video. Great work man!
@pralhadmule677
@pralhadmule677 8 ай бұрын
Striver always rocks!🔥🔥 In every video, he explains all the concepts in-depth. His teaching style is very unique. He starts from the basics and gradually moves up to advanced levels of questions, yet you never feel like you're solving an advanced-level question. That's the magic of Striver. I never believed that someone could teach such premium content on KZbin for free. Hats off to this man! 💕🔥🙏
@manashroy9469
@manashroy9469 Жыл бұрын
I'm so grateful that I found this channel. Whoever is here, may be you found this channel late but don't worry whenever you find this channel your life is gonna take change into a new direction. I'm sooo soooo grateful to have this.
@dtu-emgeenear3274
@dtu-emgeenear3274 Жыл бұрын
whats the status brother , is it still grateful ? have you learnt dp or left in midway
@rkdhillon8450
@rkdhillon8450 5 ай бұрын
@@dtu-emgeenear3274 what's your status?
@Maverick-vu9kl
@Maverick-vu9kl 4 ай бұрын
@@dtu-emgeenear3274 what's your status man 😐😐
@3lpme
@3lpme 3 ай бұрын
​@@Maverick-vu9kl Mine just started ,found this video now, im about to check if this helps me to do recursion problems on my own
@Kumkum-n9v
@Kumkum-n9v 4 ай бұрын
After struggling here and there for 2 days on this topic, I understood it all in one go. The best thing about this man is he knows where a beginner might be stuck and thus shows how to think by doing dry runs, coding, and debugging with us.
@VishalGupta-xw2rp
@VishalGupta-xw2rp 2 жыл бұрын
Notes to Self :- All possible patters from *Subsequence* 1. Print All the Subsequence 2. Print all Sq which sums to K 3. Print only 1st Sq which sums to K 4. Print the count of Sq which sums to K *Note In order to understand Printing all subsequence in absolute clear way..... Just take the example which striver gave in previous video Now create a table of all the output and match it with the power set. A magic will happen and you will be totally blown away 🔥🔥🔥
@aniksadhukhan8477
@aniksadhukhan8477 8 ай бұрын
This man is the sachin ramesh tendulkar of coding.
@ADITYARAJ-x8k5w
@ADITYARAJ-x8k5w 5 ай бұрын
@@aniksadhukhan8477 Striver ?
@garh.kumaon
@garh.kumaon 2 ай бұрын
​@@ADITYARAJ-x8k5w this teacher's name is striver.
@abhinavennala9613
@abhinavennala9613 Ай бұрын
@@ADITYARAJ-x8k5w yes
@adityakumar-sp4ki
@adityakumar-sp4ki 2 жыл бұрын
Previously, I never understand the concepts of recursion, and here it got fitted into my mind permanently.
@rabbanimunna6992
@rabbanimunna6992 Жыл бұрын
Before watching this series, I was very poor in recursion. Never understood the concepts in depth. This series helped me to fell in love with recursion. Thanks Striver.
@debajyotideba5001
@debajyotideba5001 2 жыл бұрын
Thanks is not enough for this GIFT , love you Dada❤️
@beginnertopro7265
@beginnertopro7265 2 жыл бұрын
Mera bas chale to 1M like thok du😍😍
@parthsalat
@parthsalat 2 жыл бұрын
Then GIFT him using youtube "Thanks"
@mehrabrafi9496
@mehrabrafi9496 2 жыл бұрын
nobody teaches me like that!! nobody ever explained me in that much deep.. best wishes my brother and Thank you for making this type of quality tutorial for free.
@stith_pragya
@stith_pragya 8 ай бұрын
UNDERSTOOD............Thank You So Much for this wonderful video...........🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻🙏🏻
@gopalgowda9899
@gopalgowda9899 Ай бұрын
Excellent bro...Having studied recursion with backtracking on my own for long time always use to forget the trick.. this one stands out and there is no way we can forget the pattern... Thanks again for the effort!
@abhay9994
@abhay9994 11 ай бұрын
I wanted to send you a heartfelt thank you for your tireless dedication to teaching DSA for free. Your selflessness and passion for helping students with their job interview preparation have made a significant impact on my life and countless others. I am incredibly grateful for the knowledge and confidence you have imparted to us. Thank you for everything you do!❣✨✨
@BharatVaad
@BharatVaad 2 жыл бұрын
Java code for K sum subsequence :- void f(int ind ,int a[] ,ArrayList list, int k,int sum){ if(ind==a.length){ if(k==sum){ System.out.println(list); } return ; } //take list.add(a[ind]); sum+=a[ind]; f(ind+1,a,list,k,sum); list.remove(list.size() - 1); sum-=a[ind]; f(ind+1,a,list,k,sum); }
@MohanaKrishnaVH
@MohanaKrishnaVH 2 жыл бұрын
Few lines of adding and subtracting from the sum can be avoided by doing it as part of the function call. public static void subsequenceSum(int[] nums, int k) { subsequenceSum(nums, k, 0, new ArrayList(), 0); } private static void subsequenceSum(int[] nums, int k, int index, List subsequence, int sum) { if (index == nums.length) { if (sum == k) { System.out.println(subsequence); } return; } subsequence.add(nums[index]); subsequenceSum(nums, k, index+1, subsequence, sum + nums[index]); subsequence.remove(subsequence.size() - 1); subsequenceSum(nums, k, index+1, subsequence, sum); }
@buzunoorrishika8690
@buzunoorrishika8690 2 жыл бұрын
Here can we also write as If ( ind==a.length && k== sum)
@BharatVaad
@BharatVaad 2 жыл бұрын
@@MohanaKrishnaVH yes
@anmolverma075
@anmolverma075 2 жыл бұрын
@@leetcodebaby6680 is it so?
@anuragkumar7710
@anuragkumar7710 2 жыл бұрын
I am little confused, why we list.remove(list.size() - 1); is used instead of list.remove(a[ind]); Also why it gives error.
@Lullurluli
@Lullurluli Жыл бұрын
I used to struggle a lot with recursion while unraveling the code, but thanks to your patient guidance and clear explanations, most of the complexities are clear to me now. I truly appreciate your willingness to help and your ability to break down complex concepts into manageable steps. Your support has been invaluable in my learning journey, and I am grateful for the progress I've made under your mentorship❤
@vish3933
@vish3933 2 жыл бұрын
What a way of teaching striver. I am really loving recursion bcz of you🙏
@Entertainment-hub519
@Entertainment-hub519 2 жыл бұрын
Make more videos or playlist on recursion and backtracking. I searched a lot and finally I get your videos. Your explanation is awesome, the way you teach us using dry run is amazing. Thanks a lot dada.❤️❤️🔥🙏
@ravipatel-xu5qi
@ravipatel-xu5qi Жыл бұрын
wish I could find this channel earlier. No one had ever explained recursion in such a simple manner. Thank you so much.
@amanpreetsinghbawa1600
@amanpreetsinghbawa1600 27 күн бұрын
Just to inform how good is this guy, I watched his print all subsequences vid and attempted this one on my own and now able to solve this with the way he taught in that vid. Awesome stuff champ
@arindammandal1513
@arindammandal1513 2 жыл бұрын
One of the best playlist to understand recursion. Thanks a lot
@gowreeManohar
@gowreeManohar 2 жыл бұрын
printing only once technique is awesome. like i have tried to do in a contest but got wrong by not applying it in second "if" statement. superb solution sir
@shayonchakravarty4503
@shayonchakravarty4503 2 жыл бұрын
i wish i have found this channel in my second year😓😓 it feels so damn motivated to see striver bhaiya's confidence❤️
@ankittjindal
@ankittjindal 2 жыл бұрын
kon year me ho bhaii?
@rameshap5254
@rameshap5254 2 жыл бұрын
Mine too same feel 😪
@111rhishishranjan2
@111rhishishranjan2 Жыл бұрын
same bro ..now in middle of 3rd year, hope i got to know about this channel in 2nd year, last year january
@consistency_Is_key
@consistency_Is_key Жыл бұрын
me who doing this in first sem feeling proud on myself ,because hardwork never disappoints
@akashnaik6269
@akashnaik6269 Жыл бұрын
@@consistency_Is_key explore bhi karlena first year mai. baaki time bahut hai if rightly use kare toh.
@potatocoder5090
@potatocoder5090 2 жыл бұрын
Another brilliant video! The way you build concepts from the ground up is so helpful and intuitive. Thank you!
@ManishPanda-i2h
@ManishPanda-i2h 10 ай бұрын
one of the best dsa teachers in the world. thank you Striver for your contribution to computer science education.
@sunilkarpe1518
@sunilkarpe1518 Жыл бұрын
Great series so far on recursion.Only thing i will recomment here is to provide a time/space complexity after solving the program.
@lavanya_m01
@lavanya_m01 Жыл бұрын
Striver your priceless contribution to the coding community will be cherished forever. This content is gold
@shiwamsinha7076
@shiwamsinha7076 2 жыл бұрын
U r the one by which I am comfortable at programming right now
@sarth8065
@sarth8065 Жыл бұрын
I am amazed as well as curious about how did you learn this on your own ? Great teaching👌
@Albertrose.24
@Albertrose.24 2 жыл бұрын
No other youtuber is shared... Thanks for all your super efforts for this wonderful video. Please, keep posting many such video bayya
@VinayKumar-ze2ww
@VinayKumar-ze2ww 2 жыл бұрын
One of the most impressive videos of you Everyone should watch it, whether beginner or experienced
@rhythmjayee9707
@rhythmjayee9707 2 жыл бұрын
To all who are learning recursion you all are so privileged that striver has taught all the patterns or ways by which a problem can be solved. When I was learning I have learned all these things by solving random recursion based Qus and lot of Tree problems. I highly recommend if you want to master recursion do lot of tree prblms.
@rhythmpatel5665
@rhythmpatel5665 2 жыл бұрын
hello, fellow rhythm 😄
@dipakixj
@dipakixj 2 жыл бұрын
@@rhythmpatel5665 😆
@TheLearningLab898
@TheLearningLab898 29 күн бұрын
this one video is gem guyz, if you are not confident in recursion during interview time. just watch this video and you will be back to form.🔥
@vikassharma2094
@vikassharma2094 2 жыл бұрын
best video on recursion finally this video gave me confidence in recursion which i never got
@adityaroychowdhury3709
@adityaroychowdhury3709 2 жыл бұрын
After this, recursion feels like such a beautiful topic
@FootClob
@FootClob 10 ай бұрын
You are a legend, I don't know if you're aware how much impact you had on people like me who come from universities and colleges that fail to cover this topic
@prathamvardaan4187
@prathamvardaan4187 2 ай бұрын
amazing series man the depth you are teaching is truly commendable. you covered all the possible questions that can be made on this question.
@parthsalat
@parthsalat 2 жыл бұрын
Code for print all: 11:03 Code for print one: 17:17 Code for count: 32:38
@befantastic3544
@befantastic3544 2 жыл бұрын
👍
@rohitanjane1668
@rohitanjane1668 2 жыл бұрын
Thanks bro 👍🏻
@anonymoushackerar7507
@anonymoushackerar7507 2 жыл бұрын
Thanks Bro ! Great for Revision.
@shivoonone1083
@shivoonone1083 Жыл бұрын
does anybody how to optimize the code for count one it's showing time limit exceeded
@dhananjay5053
@dhananjay5053 Жыл бұрын
for printing one I prefer flag wala method its ez T_T may not be optimized but still
@DeepakKumar-uu3qp
@DeepakKumar-uu3qp 2 жыл бұрын
Bhai one thing i can say for sure that i watch more than 50 videos on recursion and i dont get much.. But now i got your channel and now i Can do any recursion questions... Thanx bhai for your explanation 🙂
@aritra2374
@aritra2374 11 ай бұрын
The only person who could make me love and bring interest into recursion
@rap_like_yash
@rap_like_yash 7 ай бұрын
00:01 Printing subsequences whose sum is k 02:03 Understanding recursion in pattern generation 05:57 Understanding how recursion works in building a tree. 08:03 Recursion with pattern variations. 12:11 Using functional methods to print one answer in recursion. 14:21 Base case is crucial in recursion 18:15 Understanding recursion in a code 20:10 Understanding recursion and returning false on certain conditions 23:48 Implementing a simple structure for counting in recursion 25:41 Implementing recursion with count for subsequences 29:17 Two methods failed to find any subsequence 31:08 Understanding recursion in counting subsequences
@rishikabhati4383
@rishikabhati4383 Жыл бұрын
Absolutely Love the way you educate🔥 May god grant you continued success. Thank you for your efforts
@Kunalmpawar
@Kunalmpawar 2 жыл бұрын
hey, striver thanks a lot man for making this series on recursion. I was not able to understand its concept and looking for a solution from last week but when I came across your channel. in just one day I understand the concept and solved 3 problems on leetcode. Thanks again main thanks you very much. 🙌🙌🙌🙌👏👏
@yuvrajluhach5665
@yuvrajluhach5665 2 жыл бұрын
Moving to L8, Learning a lot👍 thanks for the series
@kaysickishere8010
@kaysickishere8010 Жыл бұрын
What a great video man, all my doubts and concepts of recursion have been cleared, keep up the good work.
@VishalYadav-nz7ie
@VishalYadav-nz7ie Жыл бұрын
In count subsequence problem 23:16 we can take count variable and return count variable everywhere and also in place of l and r use count
@ayushijindal4898
@ayushijindal4898 Жыл бұрын
Took time to understand but finally understood after watching it many times Recursion is not easy to understand I feel it is one of the most complex concept But when it strike into your mind your brain automatically solve the question PS: To understand this video I will say first try to solve very basic recursion questions and slowly build the concept how multiple calls are made then try to watch this video several times in a month or so Only then I can say you can get this concept it will take time but you will get it
@vikassingh-ql7ef
@vikassingh-ql7ef Жыл бұрын
I still can't get recursion if anyone can tell it will be good
@Cool96267
@Cool96267 2 жыл бұрын
Hey Striver, Could you also please attach the link of the respective leetcode questions?
@sanjoythakur7938
@sanjoythakur7938 Жыл бұрын
@Striver yes, this is much needed
@samit840
@samit840 Жыл бұрын
it is always there, since here he is just teaching concepts using his own example so not needed@@sanjoythakur7938
@moharramansari2594
@moharramansari2594 2 жыл бұрын
Best recursion playlist on youtube history
@gnanaphanideep6398
@gnanaphanideep6398 Ай бұрын
I just love your approach of solving the problem ❤🙌
@krishraj1942
@krishraj1942 2 жыл бұрын
I think there is no need to pass the vector ds as pass by reference in formal argument
@abhishekc3556
@abhishekc3556 2 жыл бұрын
why not?
@akshitmangotra5370
@akshitmangotra5370 2 жыл бұрын
Awesome bro. I literally was so dumb before your playlist. Now I am able to think, coorelate pattern and do questions.
@deshnajain2827
@deshnajain2827 2 жыл бұрын
Thank you striver, this is the best explanation I have ever seen , now I am able to correlate between different patterns of a recursion problem. Earlier I used to learn the logics but now I have started building them. Thanks for your efforts 🙂
@Learner010
@Learner010 2 жыл бұрын
Only one thing i have to say and that is Thank You.
@mdbayazid6837
@mdbayazid6837 2 жыл бұрын
Would you please show us how to convert a loop in a recursion and vice versa? Also it would be better if you discuss about various types of recursion such as tail recursion etc.
@lalitbisht8381
@lalitbisht8381 6 ай бұрын
Ive never sol ed subsequence problem tried it 1st time and you made it so simple
@PrakashKumar-ez7vv
@PrakashKumar-ez7vv Жыл бұрын
If i can like this video thousands times I have done that .What an explanation..
@ayankhan-xh8zt
@ayankhan-xh8zt 5 ай бұрын
3 patterns with the same problem which can be applied across various recursive solutions (thankyou striver 😊)
@keertilata20
@keertilata20 2 жыл бұрын
the way you write your code without any error is so awesome
@sanketkulkarni2100
@sanketkulkarni2100 2 жыл бұрын
sirf ladkiyo ko like do :)
@shashwatpriyadarshy7681
@shashwatpriyadarshy7681 2 жыл бұрын
@@sanketkulkarni2100 lmao
@sauravshaw6965
@sauravshaw6965 2 жыл бұрын
@@sanketkulkarni2100 bhai han to banda hi :p
@thegamegoing4320
@thegamegoing4320 4 ай бұрын
I don't usually comment but this is just beautiful explaination
@rupammondal6789
@rupammondal6789 Жыл бұрын
Just🤞🏻🤞🏻🤞🏻🤞🏻🤞🏻 how can i express..... The level of confidence you put in my body
@ayeshasolanki5386
@ayeshasolanki5386 2 жыл бұрын
Not just a human, you're a brand that everyone would move to before anything else :-)
@huzefataj7694
@huzefataj7694 2 жыл бұрын
Python code for K sum subsequence: def f(arr,i,subarray): if i == len(arr): if sum(subarray)==4: print(subarray) else: # include f(arr,i+1,subarray+[arr[i]]) # exclude f(arr,i+1,subarray) arr=[1,2,1,2] f(arr,0,[])
@tanyagupta4247
@tanyagupta4247 2 жыл бұрын
Crystal clear , got all the concepts at once💖
@ishansrivastava598
@ishansrivastava598 Жыл бұрын
Hi
@yaswanthkosuru
@yaswanthkosuru Жыл бұрын
i practice for around 3 months but I don't understand from Kunal Kushwaha but you make clear all concepts
@joya9785
@joya9785 Жыл бұрын
Not to compare Kunal explained recursion in depth about how recursive calls work and returned. After that you can understand striver's videos better
@gautamgrover1087
@gautamgrover1087 Жыл бұрын
Although videos are shorter but still the explaination and different patterns covers almost everything thanks
@sonalsingh7040
@sonalsingh7040 2 жыл бұрын
Recursion was never this easy... thanku raj ❤️❤️
@manishdwivedi5531
@manishdwivedi5531 8 ай бұрын
23:05 you have to add a edge case that if(s>sum)return false; other wise it will give TLE overall very nice vedio bhaiya❤
@surajitdas6555
@surajitdas6555 9 ай бұрын
Super useful, i wish i would have learned this way in my college days ❤
@bhagyashri7729
@bhagyashri7729 2 жыл бұрын
Could not understand pick/ non-pick logic initially and the reason for calling the same function twice. Now it's good.
@pritampadhan5977
@pritampadhan5977 Жыл бұрын
Shandaar,Chamtkaar bhaiya . DSA ka koi v topic ek banda aap se samajh nahi paya toh wo kanhi se v samajh nahi paye gaa
@akankshajain3997
@akankshajain3997 3 ай бұрын
one of the best videos in the series, understood.
@dhirajdeka3675
@dhirajdeka3675 2 жыл бұрын
This is indeed the best recursion series ❤️. Thanks bhaiya ❤️
@zeppelinpage861
@zeppelinpage861 2 жыл бұрын
Hats off to you. God bless you!!!
@ipshitatandon5134
@ipshitatandon5134 3 ай бұрын
Amazing video, really helped me understand recursion patterns in depth! thank youu
@CSBBADRIGAUTAM
@CSBBADRIGAUTAM 2 жыл бұрын
While performing a printS() function can we use stack data structure instead of vector Because for me it totally looks like the vector ds is just being used for push_back() and pop_back() no more. Correct me if I am wrong
@tushargahlaut5812
@tushargahlaut5812 2 жыл бұрын
But if you want to print, It will be better to use vector in place of stack. Otherwise Stack can also be used
@tasneemayham974
@tasneemayham974 Жыл бұрын
When that add about "understanding DSA is difficult " But you are watching THIS LEGENDDD !🔥🔥🔥
@footybit
@footybit Жыл бұрын
Most fascinating thing about this it’s almost identical to a backtracking algorithm, where you have to conduct an exhaustive search to your base case/goal
@ankitbansal7935
@ankitbansal7935 Жыл бұрын
Striver u are jusssst awesome , the questions which i used to take nearly hours to think , i am able to solve in minutes after watching yr series .❤
@anshikagupta5858
@anshikagupta5858 Жыл бұрын
Thankyou Striver, for this great explanation😊
@vigneshwaran3803
@vigneshwaran3803 10 ай бұрын
wonderful lectures thanks for your effort and interest to share your knowledge
@travelnlearn
@travelnlearn 2 жыл бұрын
amazning video System.exit(0) will also work
@rishabh9714-h4v
@rishabh9714-h4v 2 жыл бұрын
Thank u bhaiya 🙌❤️ For this wonderful series on Recursion ❤️🙌
@rishavsingh5568
@rishavsingh5568 2 жыл бұрын
This is what crystal clear teaching is
@sindhumohan1709
@sindhumohan1709 Жыл бұрын
Brilliant video, amazing content and explained in the best possible way! Thanks a lot!! Please keep helping us with continued content in the A2Z DSA course. 🖖
@RoadsInCanada
@RoadsInCanada 2 жыл бұрын
Best backtracking playlist. Thanks a lot.
@mohdalizilani9896
@mohdalizilani9896 Жыл бұрын
maja a gaya bhaiya the way explain is awesome and once you dry run pogram then it makes cocept crystsal clear thank for this beautiful lectures..😍😍
@amandixit8342
@amandixit8342 2 жыл бұрын
thank you so much for such amazing content and teaching style ki toh baat hi na karo ek dum lit , i'm glad ki mene ye ep dekha , bahut time bachega mera :)💥
@ForTech-rt6qi
@ForTech-rt6qi 2 ай бұрын
What a session, amazing. Learned a lot. Thanks striver.
@aradhyapandey1489
@aradhyapandey1489 Жыл бұрын
very well explained... thank you for this amazing course!!
@lakithakare7387
@lakithakare7387 Ай бұрын
The count one might not work if some negative numbers are also present in the array. for example: [1,2,1,-1,1]
@dikshasoni52a98
@dikshasoni52a98 10 ай бұрын
In the question "count the total number of subsequences whose sum = k" Why are we using the left and right method and not directly using the earlier methods where we can use count as variable to count the total subsequences whose sum is sum ?
@VaishnaviNigam
@VaishnaviNigam 2 жыл бұрын
AS ALWAYS U R THE BEST AT EXPLAINING THINGS🔥🔥
@abhinavs2484
@abhinavs2484 9 ай бұрын
for counting sub seq: for [1,1,1] and sum = 2; this might not work for above scenario, since it prints answer as 3, but it s 2
@-BIT-vaishali
@-BIT-vaishali 2 жыл бұрын
Understood evry thing crystal clear
@Rajat_maurya
@Rajat_maurya 2 жыл бұрын
bhai dilse sukriya akpa...bhagwan apko hardam khush rakhe
@Morimove
@Morimove 11 ай бұрын
11:08 you can see charm on his face. he know it is quite rare.
@KarthikNandam-xs4qn
@KarthikNandam-xs4qn Ай бұрын
17:23 at which we can simply make if (sum != currSum) we just dont need to do them nahh if(isum != sum){ v.push_back(mv[i]); isum+=mv[i]; PrintS(mv , v , i+1 , isum , sum , n); v.pop_back(); isum-=mv[i]; PrintS(mv , v , i+1 , isum , sum , n); }
@mdyousufgazi4030
@mdyousufgazi4030 Жыл бұрын
this lecture is like magic. just amazing
@singhsahab9478
@singhsahab9478 2 жыл бұрын
I can see the hard work of your
@yash_jivrajani
@yash_jivrajani 2 жыл бұрын
in JS: //printing sub seq whose sum is K // we will use take and not take function pick(i, a, arr) { if (i >= arr.length) { if (sumOf(a) === auxsum) console.log(a); return; } a.push(arr[i]); pick(i + 1, a, arr); a.pop(); pick(i + 1, a, arr); } function sumOf(arr) { let sum = 0; for (let index = 0; index < arr.length; index++) { sum = sum + arr[index]; } return sum; } // Driver code let arr = [1, 2, 3]; let auxsum = 3; let path = []; pick(0, path, arr);
@swarnabhkashyap5764
@swarnabhkashyap5764 10 ай бұрын
Great explanation with the dry run @Striver. Question: In the print all subsequences with sum=k question, can we have two base cases? if(sum==k): print(arr) return if(ind==n): return Since all the numbers in the array are positive integers, once we find a subsequence with the target sum, we can avoid traversing through the remaining integers. Since if we pick any other integer, the sum will always be >target. Instead we can just return at that point and check the not "picked" condition. Right?
@ThePROestRedn99
@ThePROestRedn99 3 ай бұрын
Actually this should be the correct the code....bcuz not everytime the index == n , and if it's not == n sum will not be calculated in between recurr steps
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