Big Oh(O) vs Big Omega(Ω) vs Big Theta(θ) notations | Asymptotic Analysis of Algorithms with Example
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--------------------------------------------------------------------------------------------- In this tutorial we will understand the 3 different Asymptotic Time Complexity analysis of Algorithms namely -
Big Oh(O)
Big Omega(Ω)
Big Theta(θ)
We will understand each Complexity by taking its mathematical definition as well as example with graph.
Lastly we will understand its practical usage & understand why we really need 3 different time complexity measures.
Big O notation -
Big O notation specifically describes worst case scenario.
It represents the upper bound running time complexity of an algorithm.
Mathematically -
Let f and g be functions of n - where n is natural no denoting size or steps of the algorithm then -
f(n) = O(g(n))
IFF
f(n) less than or = c.g(n)
where n greater than = n0, c greater than 0, n0 greater than = 1
Big Omega notation -
Big Omega notation specifically describes best case scenario.
It represents the lower bound running time complexity of an algorithm.
Basically it tells you what is the fastest time/behavior in which the algorithm can run.
f(n) = Ω(g(n))
IFF
f(n) greater than or = c.g(n)
where n greater than = n0, c greater than 0, n0 greater than = 1
Big Theta (θ) notation -
Big Omega notation specifically describes average case scenario.
It represents the most realistic time complexity of an algorithm.
f(n) = θ(g(n))
IFF
c1.g(n) less than or = f(n) less than or = c2.g(n)
where n greater than = n0, c1,c2 greater than 0, n greater than = n0, n0 greater = 1
Big Ω - Best Case
Big O - Worst Case
Big θ - Average Case
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@aryaman5603
4 жыл бұрын
please make a tutorial on visual basic
@killianjayden3949
2 жыл бұрын
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@chandanakoram9836
4 ай бұрын
How can we imagine the value of g(n) to be n,n2 like that
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@SimpleSnippets
3 жыл бұрын
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@georgikarastoychev1241
3 жыл бұрын
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@convolutionalnn2582
3 жыл бұрын
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@GodOfFools
7 ай бұрын
It's been 3yrs and this saved my life
the most thoroughly and easily explained tutorial I have ever seen. Thank you a bunch!
Thank you very much, after having tried much to grasp what my lecturer explained with no success, yours has just been through. Keep up the good work!
I have not even watched the video yet and I already know this this the best video I have every seen. I legitimately screamed in joy when I realized this was a Simple Snippets video.
7mins into the video, I understood Big Oh better. Well played.
You are amazing! Straight to the point! Nice editting! I truly appreciate it :)
@SimpleSnippets
3 жыл бұрын
Thanks buddy 🤟 glad you liked it 😊
@plumSlayer
Жыл бұрын
nd u look cute :p
Quite exemplary and to the point. Thanks for your work.
Thank you so much for this! Honestly saving my exams by explaining it so clearly I finally understand :')
You are 3x better at explaining this than my college professor at ASU. You should be making the absurd tuition money she does
@SimpleSnippets
3 жыл бұрын
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@brianayon1461
3 жыл бұрын
@@SimpleSnippets Most likely Arizona State University, I feel the same way
@frederickrichter1426
3 жыл бұрын
I am also a student of discrete mathematics at ASU who is finally getting a clear explanation. Thank You!
@SimpleSnippets
3 жыл бұрын
👍
@SimpleSnippets
3 жыл бұрын
That's great to know Fredrick 😊
I'm glad I watched this after several videos. Thank you so much
Thank you for the video, I finally understand the concept because of you, thank you again !
This covers theory quite well unlike other videos
Hey Bro you saved me my máster course your explanation is awesome, God bless you regards from México
@SimpleSnippets
3 жыл бұрын
Great to hear!
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As always amazing video and very nice explanation. Thank you so much!
@SimpleSnippets
3 жыл бұрын
Glad you liked it!
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@SimpleSnippets
3 жыл бұрын
Glad you like them!
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Thank you some much for this video!! Thanks to you in 30 min I understood perfectly what my professor didnt explain properly in 10 hours :))
@SimpleSnippets
9 ай бұрын
Glad it helped!
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Excellent explanation.
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superb explanation
carry on broo..... ur explaination was awesome
@gloryleonard224
3 жыл бұрын
Am even using the tutorial to prepare for an exam this morning and is so helpful
Whenever you choose a constant value c = ___ and a n0 value as n0 = ____, is it random that you choose the constant you chose? Is there a systematic way to do this, or would you just keep going with different n-values?
Your explanation is excelent!
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watching from Africa kenya. im already a teacher now because of this tutorial
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@SimpleSnippets
4 жыл бұрын
Glad it was helpful!
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Well explained
Nice explanation Sir
THANK YOU VERY MUCH SIR
Hi simple , great explanation , would you kindly provide an example out of say ML algos where it is better to use say Big theta relative say to big O and big Omega ? Thanks
best video ever found ❤
Nice explanation, but cases(best, worst and average) and asymptotic notations are two independent terms, like best case of linear search also can be mentioned as O(1).
Thank you so much
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Thanks for this video bro...
@SimpleSnippets
3 жыл бұрын
Most welcome Shreyas, please do share the videos & our channel with your friends too. Thats the biggest help and support you can give back to this channel! 😇
keep up the great work!!
Thanks so much man
thanks bro really you are a legend
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@SimpleSnippets
4 ай бұрын
Thank you Vaishnavi 😊
really good explanation! sir
@SimpleSnippets
3 жыл бұрын
Glad you liked it! Please support me by sharing the videos and our channel with your friends too. Thats the biggest help and support you can provide 😇
Thank you! Note: small error on Big theta slide, description says "Big Omega"
Very good lecture
great video!!!
literally youtube king
6:10 in this example what if we consider c=2 ad n=2? We need to desconsider the number without an n quocient for it to work?
Within the first 100 seconds this video explained Big-O better than my $200 textbook and my professor… combined.
@SimpleSnippets
2 жыл бұрын
Haha thank you for this feedback. Would be great if you can transfer that 200 dollars to me 🤣 Just kidding. Don't need donations. I'm happy that this video helped you 😊
You are great!
Superb sir nice explanation
@SimpleSnippets
3 жыл бұрын
Glad you liked it! Please support me by sharing the videos and our channel with your friends too. Thats the biggest help and support you can provide 😇
thnx for the help brother
Thanks bro
Bhaiya from where can i solve DSA questions...? Coz in geekforgeek , interviewbit they have only solution but not explaination (video explaination)
Excellent video
@SimpleSnippets
3 ай бұрын
Thank you very much!
Thank yooou!
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Amazing
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@SimpleSnippets
3 жыл бұрын
Thank you very much!
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Thank you
@SimpleSnippets
4 жыл бұрын
Glad to hear this from you. Please do share the videos with your friends too. Thats the biggest help & support you can provide for the channel 😇
Could anyone help me with this one? I understand Big O and the others, but my problem is finding c1,c2, and n0 for complex functions. Example: n^3/1000 - 100n^2 - 100n + 3. I need to express that one in order of theta notation.
Thank you ily
very good
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@SimpleSnippets
3 жыл бұрын
Thank you 😊 please do Subscribe 👍
Thanks a lot 🙏Sir. Can you show some questions on this topic.
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@SimpleSnippets
3 жыл бұрын
Glad you liked it! Please support me by sharing the videos and our channel with your friends too. Thats the biggest help and support you can provide 😇
@amrutachavan7686
3 жыл бұрын
@@SimpleSnippets you upload your videos on edyoda learning
@SimpleSnippets
3 жыл бұрын
@@amrutachavan7686 yes I have uploaded some video on edyoda platform 😊
Why do we take the closest to f(n) fn as the best case and the worst case scenario ,it has to be the farthest one right?So that for the best case if you take Omega(1) that will be the fastest taking less time compared to Omega(n).
hi, just a little suggestion: it's better to say f(n) is O(g(n)) or f(n) belongs to O(g(n)) instead of saying f(n) = O(g(n))
@jay-rathod-01
4 жыл бұрын
Have you ever heard of a dialect of English that comes from India. Indian English bro.😁 I am serious
Is there a reason why you chose 2n+3 for f(n)
Hey when are the rest of the videos (including hash tables, collision) in this series going to be released? Noticed you already started uploading videos on another series so I was hoping this would be completed soon!
@SimpleSnippets
4 жыл бұрын
Working on it simultaneously 😅 sorry for the delay, it gets a bit hectic to manage multiple things. ✌️ Hope you understand 😁
@M4v3RicK99
4 жыл бұрын
Thanks for the quick reply dude, your series are cohesive, easy to understand and very well put together so please take your time. Cheers.
@SimpleSnippets
4 жыл бұрын
@@M4v3RicK99 thank you so much for such wonderful feedback and for understanding my scenario 🤘 will cover note topics soon. In the meantime I'll be a huge help if you share the videos with your friends and contacts 😊 that's the biggest support ✌️
I have a doubt, It's that can we get various pairs of c and n which satisfy the f(n)=o(g(n)). i. e for f(n)
at 6:10 why did consider that c =5 but when n was powered by 2 we consider c =1 at 11:20 ?
when f(n) = 2n + 3 Big Omega is Ω(n) Big Theta is θ(n) But for linear seach algorithm f(n) would also be like f(n) = a*n + b; where a and b are some constants Then why Big Omega is Ω(1) in this case?
Bro how can Omega be the best case if we can still use constant to be more efficient ? plz help ..video was great and thanks Tanmay bhaiya for ur AMAZING CONTENT 😊😊..
Excellent video... I am waiting for this type of lectures.. 🤩🤩🤩🤩
nice video sir
You're a god
Great