2.2 Masters Theorem Decreasing Function 

Angel has come down and explains the impossible things.....

I can't explain to you how helpful these videos are to me. Thank you.

When u said “this is masters theorem” after writing few conditions.....even master theorem itself in shock, I made this look so complex to even university professors and this guy is making fuN of me.....lol. GOD BLESS U....

Wow!.. Never seen someone explain master's theorem so beautifully and passionately

Greetings from America, and thank you very much! Your videos are some of the best I've seen. 🙂

You english is so fluent and easy going👍

Sir, massive respect to you. I have never understood Master's Theorem in my college class. But thanks to you. Regards, Saurav

Guys video dekho to 1 like bhi kardo.. it's sad to see that there are 2lakhs+ views and just 3k likes 🥺..

This guy is a GOD level teacher lol. Big thanks to U

Thank you my friend , LOVE FROM ROMANIAA !!!!

Our teacher took 3 hours to teach these topics, but also after that no one was able to understand these clearly. But here you made it clear within a 8 minutes of lecture. I can't thank you enough.

For t(n)=2t(n-1)+ n solution comes out to be O(2^n) and not as the formula predicted

I was almost crying from how much work I had to do for my class and my professor didn't explain this topic that much and it's a crucial topic we need to understand. This video has helped me so much THANK YOU!!!

This made Master's theorem make sense!! Thank you, thank you!

nothing short than legendry explanation. this series is the benchmark of algo teaching

Hats off sir !!! for your simplicity and explanation, I had never seen some explaining like this.

I have never seen anyone dedicating 30 odd videos for explaining the complexity of the algorithms. Thanks to you sir, this is the best use of youtube I have ever done till date.

Thank you, sir! I've been recommending my friends to watch your videos, You're excellent!

thank you so much sir . this is just what we need .its my last subject to prepare for gate 2021 and i can say its going well thanks to you..

@Abdul Bari Thanks a lot professor for the amazing videos. I have a question, if you could answer me please. In master's theorem you mentioned f(n) is in the order of O(n^k); WWhen the time function is T(n)=T(n-1)+logn, we have that f(n)=logn. How can "logn" be expressed as O(n^k). Am I missing something? Thanks a lot in advance!

Thanks for the explanation Sir - One question while generalizaing the below 6 statements you created --> "aT(n-b) + f(n)" which I understand. but how can we say that f(n) = O(n power K), because we also had T(n-1) + log n , log n doesnt come in O(n power k) class . please correct me otherwise.

The moment I realise my childhood was a lie 🤥🤡 06:36 😭😭😭 Now it's 12 mid night and I don't know whom to I can share my eureka moment. After writing multiple exam over this same topics now only I realise that masters theorem is this simple🎉😢

Its most simplified video exist on Master Theorem first observation then going through making the cases is just Lit i remembered very easily by writing on myself in the first go tysm

Master's theorem by one of the masters' of the subject !! #GOD_LEVEL

😮this is my reaction when i saw it♥️

You sir are amazing! You're making these computer science stuffs very easy. Please continue making these videos. Thank you!

Why? why, why, why the hell O(n) = f(n^k) ????? How in hell did you get that result?

Thank you very much. You are a genius. 👍👍🙏🙏👌👌🔝🔝

wtf suddenly i got it

Never come across such a Simple and Beautiful explanation so far. Further, the way to memorize the formulae is Fantastic.

You are the boss and best teacher i have seen on this topic..Lots and lots of love and respect 💚💚💚💚🙏🙏🙏🙏🙏🙏

I can say it's the MOST complete and easy to understand playlist. Just couldn't understand this Master Theorem before but with you I got it. Respect to you sir

am i watching a movie or studying ? i am enjoying it so much

6:08 as far as I know it is illogical to have a < 1. It might be mathematically be correct but it is not possible. So if someone asks you such questions, rather than solving it prove it and them wrong.

dhanyawad sir ji aapka dm sahu

Thank you Abdul you're a fantastic teacher! Way better than my own teacher that just reads the slides...

Sir, your videos are amazing. Truly high quality stuff. Many Thanks

how I can write a program to make T(n)=a T(n-b) +f(n), and 'a' is less than 1?? thanks

Thank You very much sir🥳🥳🥳🥳🥳🥳🥳

How does f(n) = log n fit master theorem? Theorem says f(n) should be of form O(n^k) where k>=0. But log n does not look like n^k form. Are there restrictions on value of n too that can make k >= 0 when f(n) = log n? On a side note, the way i think about the big O is 1. number of times executed x 2. # steps in each loop). So the a > 1 case would be more consistent with a = 1 case if written the other way as O(a^(n/b) * n^k). Also, it seems like if a=1 and b>1, the formula can be generalized too to n/b * f(n), which makes n^(k+1) a less general formula.

Sir, you're true genius in teaching. Some people will only ignore it because of the thumbnail or your get-up. Your contents are gem.

Sir, This Master theorem definition is different than other definitions available on the Internet? :O

After watching one recurrence relation video i thought of skippin the rest ...but you explained each and every concept like our teachers do in our elementary school(spoon feeding) which made me not to skip atleast one lecture on this. Thanks for last minute preparation.

Its easy to understand this video because you related masters theorem with previous videos very nicely winded up recurrence relation. Thank you sir.

Sir I have a real doubt that when there is 2power n then that is O(2pow n) But why log n! Has no upper bound as 2 long! Kindly help sie

Your teaching skills are God level 🙏.

Sir, You made us Master this theorem!

Thank you so much sir. I do not know how to appreciate you, have no words to mention.

Great Knowledge i achieved sir. Thankyou so much sir☺🙌

why in class it's seems like finding the Holy Grail and with you it's so simple. Next time i'll stay home and study by myself on YT

No one has explained masters theorem better this :D

I dont have any word to say how good i feel from your lecture

U made MASTER Theorem a piece of CAKE.. Just loved it.💖💖

in coreman the theorem is sth like this t(n)=aT(n/b)+f(n) and your's is little different.. so does it alters?

in case 2. a=1, what happens when b ≠ 1? is O((n/b)*f(n)) the ans???

Hello sir !!! Thanks for your videos and it's great way to learn algorithms from this channel. May God bless you with good health and wealth.. I have a doubt in solving the relation T(n) = T(n-1)+T(n/2)+n where n >0. Here should the f(n) be taken as n or as T(n/2)+n. How to solve this relation? Thanks in advance.

6:35 this is master's theorem. MIC DROP

Very Precise ! Nice Lectures Sir :) Doing A Grt Job

thank u very much sir

6:56 masters's theorem notes;

Mind-blowing explanation!! I used master's theorem for over an year, but never observed these subtle things. Wonderfully proved with examples.

Your videos are a lifesaver for computer science students. Thank you sir for this wonderful explanation. 🙏🙏🙏

Thankyou so much sir

Thank you very much sir. Even our university teachers also follow you.

This is the best explanation of Masters theorm I have ever seen

No any other can explain as you can...👌👌👌👌🙏🙏🙏🙏

Thank you sir but what if a=1 and b is not equal to 1..is there any updation in formula??

Thank you so much sir... i had pretty much hatred on DS & Algo .. but after watching your video everything is much easier and fun to learn ... thank you so much from bottom of my heart ... you are my saviour

This is awesome !!!

Master the Blaster !

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🙏🙏 thanks a lot .

If I am understanding this correctly from this video, something like T(n) = T(n-2)+n would just be O(n^2) still because a=1 which follows O(n*f(n))?

Hello Dr, Abdul Bari, Can you please confirm that the solution for T(n) = nT(n-1) where n > 1 and when n=1 T(n) = 10 is O(n^n)?

Thank You !

Great explanation sir. Just one question from the last part of the video. How can "a" (the coefficient) be less than one. From my understanding a is the number of times a function is calling itself in one iteration, so how can it call itself less than one times. Any explanations are welcome and once again Thank You.

at 7:19 , should the f(n) be multiplied by n? similarly when he used the f(n)=n^k for that same explaination, he didn't multiplied it by n i.e, (n^k * n). Can anyone explain??

here are many guides but you are excellent .. thank u so much sir..bt there is 1 req plz upload the playlist on programming & data structure

Hero!

The world is a much better place with professors like you!!

watching in 2024, with paper in the morning. . . .very helpful

I love you😂

you have saved our life..may god bless you sir.

5:00 for a=1, O(n^k+1) doesnt prove right in the case of t(n)= T(n-1) + logn, whereas O(n*f(n)) is true.

you are best teacher on youtube, you make difficult consepts easier.

Sir, you are the great Algos tutor that I have come across so far. I am greatly inspired by your humility and patience.

Salute you sir. I have not seen a teacher in DS like you. Superb.

I have a lot of confusion while solving coding problems, but after seeing this video all doubt clearly related to time complexity in dynamic programming.

So simplified. Thank you!

excellent video sir! tomorrow is my exam and you cleared all the 5 mark questions of masters theorem at one go!

There's a logic behind it. a simple logic of multiplication theorem from permutation.

The more times you see his videos the clearer and concise it becomes hats off

In this master theorem why f(n) =O(n^k) as fn is also log(n)? Can any explain thanks in advance!

at 3:18 you are saying a>0 and then at 6:13 you are saying case 1: if a less than 1 then T(n)=O(f(n)). I think a should be not equal to zero.

This video is the world`s best explanation of reccurence relations! Thanks to you!

Great job😍

what would be the answer of T(n)= 2T(n-1)+T(n-1)+n

Is there any reasoning behind the formulae for condition a

Thanks, If I made it to Jane Street, I will make a donation to your uni.

_"Just by watching you can not remember this one"_