1.10.1 Comparison of Functions #1

[@heilaal-mogren5828]

Literally AMAZING. Calm, comfortable, tidy and step-by-step explanation and reaching the point in a short time! this is what a perfect teacher means 👍🏼 MANY THANKS!

[@pradyumnsingh6278]

wish i had watched this series in lockdown...

[@devildemon7511]

we are currently in lockdown only dude

[@diveshsisodia7029]

@@devildemon7511 😂😁🤘

[@mayankuniyal1829]

So true bro

[@Stuzard-s8j]

2024 almost feels the same as lockdown :(

[@asishraz6173]

On behalf of the CBSE students, THANK YOU Abdul Sir. Very fortunate to get to know about this channel of yours. Thank you once again.

[@indianitguru]

I have been going through your videos and am pretty much impressed with the way you ease up the subject. Hats off. That is truly a talent. Will keep watching your videos.

[@zyro9922]

The last two questions are of GATE and I was so frustrated as I could not solve it. I just searched how to compare functions asymptotically and sir your video came up. Such a perfect explanation. Sir thanks a lot.

[@sejalsyed5119]

lol ...bhai ..

[@health.upgradedbyscience.7309]

Truely amazing!! All your tutorials are a tremendous help in understanding correlations that seemed so hard to decode - but with your explanation all becomes logical and cristal clear! Thank you so much!!

[@nattaphumjampalee206]

thanks a lot sir, you did give me a lot of knowledge than the professor at my university did ! you deserved a big thumb from the bottom of my heart!!

[@wirito]

I like how you left this blooper in 1:34 Lol Thank you for these amazing videos. I am learning a lot :)

[@oliverchen4079]

bug or feature?

[@humbleguy9891]

@@oliverchen4079 depends on the user :)

[@sachinbansal4622]

this was necessary to give you in-person class experience! hahaa

[@sushantgupta1564]

I wish I had found these tutorials a few months ago. I could have done far better in my first test. Simply you are a genius. You know how to explain these things well.

[@umairgillani699]

It shows that sub-continent has some of the best teachers on planet. I'm from Pakistan, and I remember I had teacher with a same name "Abdul Bari" and a master of his subject (Mathematics). Learn a lot from your videos sir, please keep helping us absorb that complex knowledge making it simple enough. Huge respect from Pakistan!!

[@dwaipayanroy3232]

☺☺

[@vaibhavkumar912]

rupees and paise great way of explaining

[@qvikk333]

but large number of paisa can become rupee

[@just-wild-life]

@@qvikk333 Yes even for n = 8 and base 2 wont hold

[@036karan]

@@qvikk333 but that large number would be on both sides

[@KiyoGam1]

No? That power 10 was only on one side. ​@@036karan

[@omerakcan3991]

The best instructor I have ever seen in my life

[@shobhitkumarpatkar5468]

Your teaching style is really very simple and easy to understand. Thanks a lot for the best lectures.

[@devildemon7511]

Sir in the previous problem u have comapred 2logn and logn and said that 2logn is greater(they have just different coefficient) but not in the last question

[@sujalchoudhary5206]

6:55 rupees and paisa perfect explanation

[@simranvedpathak7112]

Best content on youtube 🙌🏼👍🏼

[@aadarshbishen7078]

dividing f(n) and g(n) and apply limit n -> ∞ will be more easy to estimate.

[@manhazehra8823]

Tomorrow is my exam. If your videos would not been on KZbin I would definitely fail. Thank you so much Sir. Rise and shine...May allah bless you abundantly. Kindly increase your playlists 🙏

[@Egli]

You are the most amazing tutor!

[@hemantbhangale9505]

Excellent progression and crystal clear content. Thanks!

[@shreyavinchankar5643]

Do we not ignore the coefficient for logarithmic terms as well? Ex. 3logn > 2logn but 3n = 2n, why is it so?

[@cubangeorge]

comparison at 1:40 wont hold when n=1 or 0

[@sumandas201]

Thank you, sir, for this amazing video series............

[@silviupavel6966]

7:00 is the comparison correct? loglogn^10 isn't equal to log10logn?

[@Nameiscantsay]

What sir said is wrong. What you have written in the comment is correct

[@kimanh6922]

In 7:03 sir said that f(n) is greater than g(n) without explain why loglogn is ignored, then I need to find the answer: 1. When we divided f(n) by g(n), got n/logn^9 which tends to zero when n is increasing: when the value of n is small, the value of this function is large but when it increases, the value of the function gets smaller (asymptotic to zero) 2. So that with the small value of n: f(n) is greater than g(n); but with the large value of n: g(n) is greater than f(n) 3. I drew a graph in desmos with 2 functions and I saw which I said at 2 So I want to ask that with ambitious value of n, can we compare 2 functions? or something I misunderstood about compare 2 functions?

[@kimanh6922]

hehe after watching the next video i found out my mistake, we ignored smaller expression because we're comparing functions in time or space complexity which is not important in smaller value

[@shiroshinomiya5714]

You're a life saver sir!

[@Han-ve8uh]

So when comparing functions, are we using asymptotic behaviour or actual values? I don't understand the logN > loglogN so you can ignore the contribution of the 10 loglogN and focus only on 2logN. My example is n^2+n vs 7n. According to the video's argument, no comparison n^2 wins. But if we compare actual values (like the end of video says), 7n is bigger for n = 1,2 and only loses when n > 2, so which values are we comparing?

[@thegloriousgoldeneagle]

Sir thanks for these amazing videos

[@wirito]

Professor, I see why 2logn > logn but why is 10log(logn) less than log(logn)? Shouldn’t it be also larger just like 2logn > logn?

[@HarshJain-vv3yg]

I also have the same doubt. I can only add that perhaps logn is a increasing f. while loglogn is a decreasing f.( by sampling), not sure about the overall nature of loglogn . What do you think?

[@debrajadhikary7734]

Yeah man ....its embarrassing 2nd function is greater

[@Onomandah]

He did not say that 10log(logn) is less than log(logn). But we are comparing the bigger n of the two functions. logn is more than log(logn), so we can ignore the log(logn) and instead compare the logn with the highest n of the other function, which is 2logn.

[@saroj_kumar]

Forget about the first example, lets talk about the second. In the first example f(n) is greater than g(n), but in second case sir said, we are ignoring 2 and f(n) = g(n). I have a doubt on that. If anyone reading this, can explain.

[@humengineerhaijholalekarni8408]

no one replied so I am commenting. log(logn) is much smaller than logn why? consider n = 16 then log(log16) = log(log(2^4)) = log4 = log(2^2) = 2 and logn = log16 = 4 hence we can say logn is larger than log(logn) now suppose i travel a distance say 3km and 10m and you travel say 2km and 50m we compare the bigger unit right? so I travelled more 3km>2km we ignore the 10 and 50m because they are smaller units. The same applies here

[@user-w87b7egvss]

Your videos are amazing, you actually make Algorithms fun 😄

[@KhaledAhmed-cs8rv]

for the second example. shouldn't the left hand side equation greater than the right one starting from n= 28,1?

[@monicaj3878]

i spent hours look for an explanation of this... thank you so much !!!

[@somyagupta2527]

sir in the example n^2(logn) and n(logn)^10 the first function is greater for some values and after that the second function is greater .I checked it by putting values in both the functions.

[@animerank4907]

Yeah, you can check in desmos, second function becomes greater after x = 28 or something like that.

[@swplogic4158]

@@animerank4907 No worries, sir. The professor's got it right. Just remember, "n" is a natural number, so it's gotta be "n >= 1." And for any value of "n," "f(n)" is always gonna be more than "g(n)." Plot it on a graph and take a look from "n >= 1."

[@sajalrastogi3904]

@7:00 sir how would we know that log(logn) should be ignored because it has lower value on both sides. if we dont know its value.

[@arizablozki9370]

I think that g(n) is greater than f(n) in the first example 4:42, I think Prof. Bari mistakenly says f(n) is bigger.

[@swplogic4158]

No worries, sir. The professor's got it right. Just remember, "n" is a natural number, so it's gotta be "n >= 1." And for any value of "n," "f(n)" is always gonna be more than "g(n)." Plot it on a graph and take a look from "n >= 1."

[@SRNR_PODCAST.]

a gold mine in youtube

[@RavinderRam]

awesome Sir Make a series of programming tutorial for non-programmer I am data analyst currently using R programming

[@subramaniyanvg6367]

Nicely explained with examples. Thank you sir.

[@viveksaxena7376]

0:00 first method 1:39 sec method

[@ujjwalgupta8945]

sir, if the value of log is greater than 1 it will be always greater than g(n) please reply example 2 {time: 4:43}

[@stevenbooke8594]

At 7:05 where you say f(n) > g(n) I don’t believe this is the case. If you graph both of those functions we can see g(n) approaches infinity faster than f(n) so isn’t f(n) < g(n)?

[@kera2403]

You probably have taken log with a base 10 while graphing. Here the base is 2.

[@nicksidiropoulos802]

@@kera2403 It's still true for base 2.

[@crickfever100]

i was making the same mistake,zoom out the graph and you will see f(n) >g(n)

[@learningchannel274]

I respect this man

[@vishalkeshri9695]

Superb sir u keep continue thnx sir

[@supamdeepbains5172]

6:45 kya bat hai kya cheez hai paisa paisa lol

[@narendrasriram]

Your videos are too awesome. In this video around 7m time, you are comparing two functions, how f(n) can be bigger compared to g(n) as , let say n=4, f(n)=32, but g(n) will be 4*2^10; if we are considering log base 2

[@himadrimukadam6459]

Sir, I have a question. If your last question (the one with the root) has both functions asymptotically same, then why not the second one? Both functions have log n + log log n... Just different coefficients. So can they be said asymptotically same??

[@the_humble_lazy]

At 6:37....why 2logn is greater than logn....they are assymptotically same naa!

[@the_humble_lazy]

@@abdul_bari thanks a lot sir!

[@mohamednaufal719]

because 2logn signifies n^2 and logn signifies n.

[@tjsm4455]

Date - 17/6/22 Imp note - a raise to log c base b == b raise to log c base a.

[@adipratapsinghaps]

OMG I never knew how to compare functions in 4 years of industry experience.

[@mdaffansajjad3294]

great comeback at 1:38 sir sir sir

[@MrLazini]

an excellent lesson

[@sergeyshestakov4936]

Спасибо Мистер

[@mohammedadel8948]

Thank you for your efforts

[@divyachaudhary1154]

Very clear explanation... Thanks

[@rnjnmhta.catomato]

2:58 log formulae

[@alibabarahaei2229]

Perfect👌

[@Rob-J-BJJ]

thank u sir, u r godsend!!!

[@codekalavya1843]

Great examples

[@Arvy565]

why is the base by default 2? shouldn't it be 10?

[@Arvy565]

@@abdul_bari oh I see. thanks for answering

[@MuhammadAsif-fj5ox]

Great Effort Sir!

[@prateekkumar6426]

Sir aap ne c++ ka course q nhi banaya Bana dejiye premium hoga to chalega

[@vaibhavdiwan517]

Sir if you take n=100 then g(n) will become greater

[@saptarshisahoo5075]

Great..

[@jessesinger4790]

How do I derive rule 4?

[@manhazehra8823]

Plesse include all subjects of CS🙏

[@saikumarchennu1791]

Nice explanation sir

[@debolinasihi9967]

Thankyou so much sir,

[@nuzhatul596]

f(n) is big omega of g(n)... @2

[@smitfultariya5984]

7:04 answer is maybe wrong

[@chamangupta4624]

Sir, Comparison question at 7:05 is not correct, you can check yourself using calculator, beyond 2.7 for any value the g(n) will be larger than f(n) , rupees and paisa explanation fails at least here , just a suggestion

[@chamangupta4624]

Okkk sorry sir i got it, u were not talking about the value but the order was being compared.. Right na?

[@AnujKumar-tt5md]

Thanks🌹

[@cybershrajal]

sir dark mode use kijiye na

[@91-ritikjain36]

thank you so much sir today is my exam

[@selinbaris7822]

What is the base of the logarithm that you are taking Sir ?

[@subhrapaladhi5888]

it doesn't really matter on which base you take the log. it should just be any valid base.

[@subhrapaladhi5888]

it doesn't really matter on which base you take the log. it should just be any valid base.

[@selinbaris7822]

@@subhrapaladhi5888 but why

[@subhrapaladhi5888]

as we are only going to compare. just make sure you take both of them on the same base

[@036karan]

can 'n' be ever negative?

[@RavinderRam]

make a tutorial of computer fundamental and basic programming concept e.g data structure & algorithm

[@loading757]

Very helpful

[@reyy9220]

TYSM

[@ShivamShrivastava35]

where it helps in DAA

[@bhanupratapmudgal4831]

Fed up of this Coding Blocks Advertisement,LOL

[@jihanIT]

Thank you

[@hometvfirestick]

thanks

[@humbleguy9891]

I watched it in 2017 and also in 2022.

[@HappyKitya]

8:43

[@shabeerahamed2129]

1:34 😄

[@donfeto7636]

4- law is -> a^log(c) is c^log (a) not as you wrote it also first example is not correct. from section 3.2 in introudction to algorithms book

[@okbagaming7564]

الهندي تاعنا

[@ciaravlogs6202]

Do a iready lesson

[@arizablozki9370]

actually I am wrong for n > 10000000000000000 f(n) is bigger!

[@manavnagrani8338]

Your way of explaining is very much similar to Khaleel sir ❤

[@dakshpatel1769]

He was student of khaleel sir😊

[@swplogic4158]

Who is Khaleel?

[@cybershrajal]

black bord , black t shirt

[@GamingWithRaghu650]

haters guna hate.

[@ragedragon33]

math sucks

[@qauattan2416]

Which book you follow sir? Please tell me the book name you follow? @abdul bari