Pascal Triangle | Finding nCr in minimal time

[@takeUforward]

Please watch our new video on the same topic: kzbin.info/www/bejne/mIOanoSdrLaSpZo

[@arpitbhavsar6020]

Recursion without a base case 😁😁

[@KurumiddeKezia]

Bro one dout my code is executed in codestudio but not executed in leetcode y😢

[@the_avii_7]

@@arpitbhavsar6020 🤣🤣

[@takeUforward]

Please do like the video, it won't cost you anything, but it will highly motivate me :)

[@shra1]

Did this problem move to easy from hard?

[@ankushprajapati519]

Ofcourse we do...... But not only for motivation,but also for your efforts.......😊 Such type of free content is very helpful for those persons who are not capable to buy an expensive course......👍✨

[@newsbuster2194]

done bhaiya

[@divyareddy7622]

your videos actually got me out of depression and gave me aa hope at becoming better at DSA!!!!

[@chandan1s2]

got better?

[@shashankgsharma0901]

What's the status now champ?

[@codewithtejaswi]

What's the update on your depression champ🎉

[@hellsterkun8764]

lol

[@TasneemMohammad-oj3ie]

lol update bro?

[@md.ualiurrahmanrahat2400]

used to solve this problem by myself but the solution was brute force method. Never have I ever thought this problem can be solved by such observation. Hats off to the effort Striver puts in his video. Incredible!

[@swacharahman5084]

I always amazed the level of intelligence you have brother, Thank you for this playlist, Trust me your playlist is making thousands/millions of students better coder.

[@p1xel3434]

nCr = nC(n-r) so, we can take i < min(n, n - r) it is more efficient

[@chiraggill2940]

will not affect complexity though so no need

[@naveensaicremsiyadlapalli3769]

#include using namespace std; class PascalsTriangle{ private: int Ncr(int n,int r) { int ans=1; for(int i=1;i

[@akashkumarmaurya2319]

very very easy solutoion ..every time i can think about only brute solution but u gived both the solution at same time which is fantastic ...amazing love the way you teach

[@sarthakjain1824]

450 questions will need many months of continuous hard work. Hats off bhaiya

[@takeUforward]

We have already covered > 60%, trees : 56, graphs: 56 dp: 56 ;)

[@AdityaSingh-in6ce]

there is no good playlist for string on KZbin only one or two videos and its and important topic please start with string@@takeUforward

[@ashutoshsahu5567]

Frankly speaking I am not able to understand Pascal triangle problem until I watched this video, Earlier I see almost 5-7 videos on KZbin , from those videos I Get what is the pascal triangle, but didn't able to solve the problem. After watching this video, I have confidence to solve any problem based on pascal triangle.

[@HansrajSinghShekhawat-s3u]

I computed it using memoization. I didn't think of the combinations formula whilst coding it. The video was very helpful. Thanks!!

[@mirishfaqhussain6168]

His involvement while he delivers the lecture is motivational ❤

[@parasarora5869]

That was fabulous. I didn't know about nCr unfortunately, but I learned it separately from other videos. Thanks for the great video. ❤

[@chethanprabhu4475]

Finally I was able to solve a problem before looking at your solution. That too hard one 😎 All thanks to your foundational videos on Arrays ♥ Watched the video anyways. Just to look at your approach

[@priy9491]

We can reduce the time complexity to (n^2/2) by running the inner loop only for row/2 times and assigning values symmetrically because the pascals triangle is symmetric. Thank you for the videos!

[@RajNamdev_19]

that's what I was thinking

[@Gurunat16]

To add symmetry to the result, you need to run a loop right? Or is there any other ways?

[@priyankasoni5537]

Can you please explain Space complexity of both the approaches of variation 3? Like how come it is O(1)(Written in the sheets notes and also strivers mentioned in the video

[@AnkitKumar-su1yi]

@@priyankasoni5537 yes its O(1) because we are not using any extra space like we are asked to print the pascals triangle so we are just using a list to store and print it that's it

[@priyankasoni5537]

@@AnkitKumar-su1yi thank u understood

[@amansayyad7286]

i think best teacher present is this man. Please try to motivate him and support him. Love you bro

[@cinime]

Understood! Super awesome explanation as always, thank you very very much for your effort!!

[@ishanraghuvanshi3283]

I just did a[ i ][ j ]= a[ i-1 ][ j-1 ] + a[ i-1][ j ] keeping first and last element of the arrays 1, takes O(n^2) compexity but works fine

[@NikitaSingh-kz2ii]

APPROACH TO THIS PROBLEM IS SUPER SE V BHT BHT BHT ZYADA UPAR🔥🔥🔥🔥🔥🔥🔥🔥🔥

[@RaunitJaiswal-s9v]

- [00:02](kzbin.info/www/bejne/mIOanoSdrLaSpZo) 🧠 Overview of the DS Algo course and problem statement of Pascal's triangle - The course is extensive and covers over 400 problems in DS algo - Introduction to Pascal's triangle and its structure - Explanation of three types of problems related to Pascal's triangle - [03:53](kzbin.info/www/bejne/mIOanoSdrLaSpZo) 🧮 Calculating nCr using brute force method - Discussing the traditional brute force method to calculate nCr - Explaining the formula for nCr and line-by-line code implementation for nCr calculation - Detailed explanation of time complexity considerations and space complexity - [10:55](kzbin.info/www/bejne/mIOanoSdrLaSpZo) 🖨 Optimizing the calculation of nth row of Pascal's triangle - Introducing the optimization to calculate the nth row more efficiently - Deriving a formula based on observations to calculate elements of the nth row - Implementing the optimized code for generating and printing the nth row - [19:30](kzbin.info/www/bejne/mIOanoSdrLaSpZo) 🪙 Generating the entire Pascal's triangle efficiently - Explaining a naive brute force approach to generate the entire Pascal's triangle - Describing a more optimized method using the second type of problem solution - Discussing the time complexity reduction strategy for generating the complete Pascal's triangle with improved efficiency - [22:02](kzbin.info/www/bejne/mIOanoSdrLaSpZo) 🧮 Solution complexity analysis - Optimal time complexity for type 3 problem is O(n^2) - Generating each row has a time complexity of O(n) - Using long long data type is recommended due to potential large number calculations - [24:24](kzbin.info/www/bejne/mIOanoSdrLaSpZo) 📝 Coding the solution - Write a function to generate a row based on the row number - Use the function to generate the entire triangle structure - Code quality is important in interviews, focus on readability and structure - [26:04](kzbin.info/www/bejne/mIOanoSdrLaSpZo) 📚 Final notes and channel engagement - Encouragement to like the video to support content creation - Importance of subscribing for more content - Follow links in the description for further engagement on social media platforms

[@AshutoshVerma-d4z]

instead, for the first problem, the loop should run for min(r, n-r) and not 'r' because if it is 10C7, r is bigger than n-r

[@harshsinha7642]

I tried solving ncr problem with this approach but still test cases are failing for ex 69c43 You can search ncr problem gfg ... Can you try solving with first approach along with min(n-r, r) modification and let me know?

[@prajwalnakure]

00:04 Pascal's Triangle - A pattern of numbers where each number is the sum of the two directly above it. 02:05 Finding element at a specific row and column in Pascal Triangle. 06:48 Shortcut for finding nCr in minimal time: multiply numbers from n to n-r+1. 09:11 The numerator in nCr calculation keeps getting multiplied and then divided with the value of i+1. 13:39 Pascal Triangle formula is used to find nCr in minimal time. 15:59 Pascal Triangle for finding nCr 20:22 Generate Pascal Triangle row in minimal time 22:16 Optimal solution for finding nCr in minimal time 26:16 The KZbinr encourages viewers to subscribe and engage with their content.

[@prabhatkumarsingh3073]

3:40 4th type question can be asked is sum of nth row ans :simple left lift 1 by (n-1) that is 1

[@deokumarjnu]

Thanks Striver, my code is not passing because of spacing issue in between digits😌 we can do in more way, pascle is nothing but power of 11, so if it's asking for N, then just run a loop from 1 to N and calculate the power(11, i), push into the vector if spacing is not considered. Stuck with spacing.

[@aakarshshukla8364]

congrats striver for 700k and happy Diwali🎆🎆🎇🎇🧨🧨

[@mehulthuletiya497]

Timestamps 00:51 What do you mean by Pascal's Triangle? 02:27 3 Types of problems that might be asked to you 03:52 1st Type Problem Statement 06:56 Formula shortcut 07:49 Code 09:46 Complexity 10:31 recap 10:54 2nd Type Problem Statement 11:38 Brute force 12:18 Complexity 12:37 Optimal solution & Deep dive into formula and observation 15:11 Minor changes and formula 17:27 Pseudocode 19:06 Complexity 19:21 3rd Type Problem Statement 20:00 Brute force 20:07 Pseudocode 21:17 Complexity 21:50 Optimal Solution 22:19 Code 25:16 Interview Tip : Code Quality

[@takeUforward]

Just a suggestion, don’t add ‘-‘ in timestamps, its 00:05 Intro Just a space :) it becomes easier for me to copy paste. Thank you for always adding it up 🫶

[@priyotoshsahaThePowerOf23]

Thanks for taking us forward,, Striver❤

[@infinitecodes]

Thank you very much for this amazing course 🎉❤

[@souvikbiswas292]

You are the GOD of dsa

[@habeeblaimusa4466]

Your explanation is superb ❤️❤️.. Ride on Striver.

[@depthsoffacts3651]

🔥🔥 love your teaching 🤗 you are my inspiration

[@ARYANGUPTARA]

Python code for 1st variant def pascal(n,r): res = 1 for i in range(r): res = res * (n-i) res = res/(i+1) print(res) n = int(input("Value of N")) r = int(input("Value of R")) pascal(n-1,r-1)

[@Manishgupta200]

It's a very tricky problem based of math nCr.. approach by you is really good

[@arnavjain6038]

class Solution(object): def pascal(self, numRows): pt=[[1]]*(numRows) pt[0]=[1] for i in range(1,numRows): pt[i]=[1]*(i+1) for j in range(1,i): pt[i][j] = pt[i-1][j-1]+pt[i-1][j] return pt for generating entire pascal's triangle.

[@Shakti_singh96]

00:04 Pascal's Triangle - A pattern of numbers where each number is the sum of the two directly above it. 02:05 Finding element at a specific row and column in Pascal Triangle. 06:48 Shortcut for finding nCr in minimal time: multiply numbers from n to n-r+1. 09:11 The numerator in nCr calculation keeps getting multiplied and then divided with the value of i+1. 13:39 Pascal Triangle formula is used to find nCr in minimal time. 15:59 Pascal Triangle for finding nCr 20:22 Generate Pascal Triangle row in minimal time 22:16 Optimal solution for finding nCr in minimal time 26:16 The KZbinr encourages viewers to subscribe and engage with their content. Crafted by jai rajputana

[@artitech6668]

Amazing explanation. thanks a ton. Working harder to make u proud.

[@SumitMishra-rb8zo]

For Part 1- 3:51 to 10:52, part 2- 10:56 to 19:14

[@suyashshinde2971]

SDE Sheet: Day 1 Problem 2 Done!

[@sathvikreddy4807]

so how many have you done till now>?

[@venup2813]

Excellent 👌

[@shaktijain8560]

Each row is binomial expansion coefficient for certain power. We can directly use combination formula to get it .

[@kj5215]

1st -> 3:51 2nd -> 10:55 3rd -> 19:21

[@bharathis7890]

verrry good explanation and even the methods of solving the given problem😇

[@Mohit-s9c2v]

understood, Thankyou Striver

[@bilalahmedkhan5876]

Loved it, very well explained!

[@reddygopichand2002]

We can use ncr=nc(n-r) when r>n/2 10:44

[@ganeshjaggineni4097]

NICE SUPER EXCELLENT MOTIVATED

[@rahuljmd]

Understood brother, Thanks for this amazing amazing explanation...

[@psrs985]

Or you could use the previously stored values to generate the lower rows which will take O(n*n) TC

[@sainallajarla7022]

UNDERSTOODDDD STRIVER !!!

[@sukhpreetsingh5200]

Awesome explanation as usual💗

[@sourabhsoni5065]

Very Nice Explanation

[@akshatmalviya8563]

I did the last part with dp. Complexity was O(n^2)

[@anitha8562]

Striver!!Please upload videos on binary search.

[@jatinsareen7771]

Hey striver, I was having a doubt that will you cover up some competitive programming concepts in this course or not?? Because covering all cp topics will make this course legendary and no one will be able to surpass this level in generations.

[@Bababahahabwhwh]

😂😂😂lol

[@shrutisrivastava7174]

Really amazed by ur Intelligence but i don't know why i am not think this kind of solution on my own why 😭😭😭

[@poojakumarisingh5506]

Awesome video. Thankyou striver ❤❤

[@AjeyaKumaraK]

superb explanation

[@ishaanrejra1084]

You are the best !

[@culeforever5408]

understood 😇

[@PogalaHarshitha]

thank you striver

[@torishi82]

Samaj aa gaya!!

[@dishaparwani6711]

class Solution{ public: vector generateRow(int row) { long long ans = 1; vector ansRow; ansRow.push_back(1); //inserting the 1st element //calculate the rest of the elements: for (int col = 1; col < row; col++) { ans = (ans * (row - col))); ans = (ans / col)); ansRow.push_back(ans); } return ansRow; } vector nthRowOfPascalTriangle(int n) { // code here vector ans; //store the entire pascal's triangle: for (int row = 1; row

[@vigneshkumarganesan1529]

I don't get the point where he bring the formula. How did he arrive that formula will give the output? anyone knows the answer?

[@AS-gf3ci]

Q.2 Code in C++ #include using namespace std; void printRow(int n) { // T.C --> O(n) S.C --> O(1) int ans = 1; cout

[@vanamadinarendra2974]

Keep doing great 👍🎉

[@inspiringzone12]

Excellent👍👏

[@AshishSahu-ef9rl]

Maja aagaya 😊

[@shanks5719]

Understood, sir.

[@yamini436]

understood :) thankyou striver

[@complexcat6329]

understood, thank you!

[@rishabhgupta1222]

Understood very well

[@arnavsaha3631]

This is great...I hope you earn enough from all this 😊

[@vamsikrishnagannamaneni912]

7:22? I didnot understand part? 10/3 will give me nothing? what does that mean ? it will give 3.333 or 3 if rounded right?

[@Shivi32590]

understood. Respect!

[@kabilm8040]

TRIED MYSELF class Solution { public: vector generate(int numRows) { vector ans(numRows); for(int i=0;i

[@heyanikethere]

Great work....

[@YourCodeVerse]

Understood✅🔥🔥

[@harshverma9675]

Bhaiya, Combination wale question ki bhi list bana do please, Ya phir Combination ke concept ke baare mai ek acchi video bana do.

[@ashishpradhan6250]

understood ..Thanks🙂

[@nitinchandrasahu1774]

Try This. 😁😁 vector generate(int numRows) { vector ans; for(int i = 0; i

[@hxgaming8886]

good video ... understood

[@mainakdasgupta7130]

Thank you

[@shivamjain1811]

whats the intiution behind (n-1)C(r-1) ? can someone plz tell

[@adirohilla]

I am also looking for its intuition, thanks for raising this , but nobody has still answered on it yet

[@tarunrajput6865]

12:43 yaha se dekh Bhai agr phir bhi na smjh aye TB btayio

[@prerakhere]

Look at this step by step: The rows and columns of Pascal's triangle starts from r=0 and c=0. r=0, c=0: What are the number of ways to choose 0 items from 0 items = 1 r=1, c=0: What are the number of ways to choose 0 items from 1 item = 1 r=1, c=1: What are the number of ways to choose 1 item from 1 item = 1 r=2, c=0: What are the number of ways to choose 0 item from 2 items = 1 r=2, c=1: What are the number of ways to choose 1 item from 2 items = 2 r=2, c=2: What are the number of ways to choose 2 items from 2 items = 1 r=3, c=0: What are the number of ways to choose 0 items from 3 items = 1 r=3, c=1: What are the number of ways to choose 1 item from 3 items = 3 r=3, c=2: What are the number of ways to choose 2 items from 3 items = 3 r=3, c=3: What are the number of ways to choose 3 items from 3 items = 1 ... goes like this i got this intuition from wiki: en.wikipedia.org/wiki/Pascal%27s_triangle

[@thebestofyoutube4810]

Thanks a lot my ninja.....

[@yasaswiv2030]

we can use recursion right ?? generate the answer for N-1 and the add another row by with the help of last row of generated answer and add this row and return the final answer

[@NazeerBashaShaik]

Understood, thank you.

[@trsk]

thank you Anna

[@akashverma5756]

We personally call it Parallel computing or Stacking method.

[@konankikeerthi]

Thanks bro. Understood

[@introvert9112k]

Just a small improvement for the nCr calculation. int findNumber(int n,int r) { long long res = 1; for(int i = n; i > max(r,n-r); --i) { res*=i; res/=(n-i+1); } return res; } Time Complexity : O( min(r, n-r) )

[@heyOrca2711]

Understood! sir

[@meghnakhaitan2495]

Can you pls pls plsssss do strings before binary search next plsss🙏 ?

[@gautamsaxena4647]

understood bhaiya

[@codeman3828]

Wonderful

[@AniketKumar-hf2bo]

understood 👌👌👌👌❤❤❤❤

[@her_soulmate]

Understood 🎉

[@anshulrai6058]

understood👍

[@nishant4595]

understood!!

[@akhilmittal2762]

can we do it with that apprach as we have seen them as the square , cube and quadraple of 11 as 11,121,1331....and so on so we first convert that no . to string and then string to that vector and then print:) this will take as overall complexity of O(N) in worst case

[@abusufyanmalik]

Python Solution from typing import * def pascalTriangle(n : int) -> List[List[int]]: def generateRow(row): ans=1 ansRow=[] ansRow.append(1) for col in range (1, row): ans=ans*(row-col) ans=ans//col ansRow.append(ans) return ansRow res=[[1]] for i in range (2, n+1): res.append(generateRow(i)) return res