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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Пікірлер: 201

  • @SimpleSnippets
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    @aryaman5603

    4 жыл бұрын

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    @chandanakoram9836

    4 ай бұрын

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    @JacobACoulson3 жыл бұрын

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    @SimpleSnippets

    3 жыл бұрын

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    3 жыл бұрын

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    3 жыл бұрын

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    7 ай бұрын

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    @exodia_right_leg2 жыл бұрын

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    @peanutsee3 жыл бұрын

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    @SimpleSnippets

    3 жыл бұрын

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    @plumSlayer

    Жыл бұрын

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    @Sunny-qe5el3 жыл бұрын

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    @atlanta2203 Жыл бұрын

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    @nicklloyd30903 жыл бұрын

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    @SimpleSnippets

    3 жыл бұрын

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    3 жыл бұрын

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  • @frederickrichter1426

    @frederickrichter1426

    3 жыл бұрын

    I am also a student of discrete mathematics at ASU who is finally getting a clear explanation. Thank You!

  • @SimpleSnippets

    @SimpleSnippets

    3 жыл бұрын

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    @SimpleSnippets

    3 жыл бұрын

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    @funkemoney3 ай бұрын

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    @nerodant852 жыл бұрын

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    @availkrishmytube3 жыл бұрын

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  • @SimpleSnippets

    @SimpleSnippets

    3 жыл бұрын

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    @Insan123_ Жыл бұрын

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    @deepakmaidasani15123 жыл бұрын

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    @SimpleSnippets

    3 жыл бұрын

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    @User1-6t5 ай бұрын

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    @MD-zw5nl3 жыл бұрын

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    @yomnahamed71473 жыл бұрын

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  • @SimpleSnippets

    @SimpleSnippets

    3 жыл бұрын

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    @fang86602 жыл бұрын

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    @konodioda1268 Жыл бұрын

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    @aleksandraaa20109 ай бұрын

    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

    @SimpleSnippets

    9 ай бұрын

    Glad it helped!

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    @ketchup7867Ай бұрын

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    @som_girl6702 Жыл бұрын

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    @geschichte4u25110 ай бұрын

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  • @MegaDoc360
    @MegaDoc3602 ай бұрын

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    @tangent9052 ай бұрын

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    @abhinavl999 Жыл бұрын

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    @saladisatyanarayana71663 жыл бұрын

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    @gloryleonard224

    3 жыл бұрын

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  • @nikolajnguyen4273
    @nikolajnguyen4273 Жыл бұрын

    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?

  • @DavidParathyras
    @DavidParathyras Жыл бұрын

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    @sudakishorekumar3 жыл бұрын

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    @funnyshiittt2 жыл бұрын

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    @samuelmaina66598 ай бұрын

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    @freezinfire2 жыл бұрын

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    @codingwithanonymous8904 жыл бұрын

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    @The_Programming-Teacher Жыл бұрын

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  • @cf0e6d7b83
    @cf0e6d7b832 жыл бұрын

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    @izharkhankhattak2 жыл бұрын

    Excellent job, man!

  • @sunraiii
    @sunraiii4 жыл бұрын

    Decent tutorial! Thank you

  • @SimpleSnippets

    @SimpleSnippets

    4 жыл бұрын

    Glad it was helpful!

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    @samarthyapatel21572 жыл бұрын

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    @moshibudimathabatha26112 жыл бұрын

    Well explained

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    @santoshpalli21092 жыл бұрын

    Nice explanation Sir

  • @georgey4151
    @georgey41514 ай бұрын

    THANK YOU VERY MUCH SIR

  • @samidelhi6150
    @samidelhi61504 жыл бұрын

    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

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    @twinkleshaw693 Жыл бұрын

    best video ever found ❤

  • @pankajmhaske09
    @pankajmhaske093 жыл бұрын

    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).

  • @samuelolayinka6948
    @samuelolayinka6948 Жыл бұрын

    Thank you so much

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    @cheems3202Ай бұрын

    You are a life saver bro

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    @bhargavnagacharan18992 жыл бұрын

    Best explanation ever ❤️❤️❤️

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    @cinders-and-smoke3 жыл бұрын

    Best video on notations 💪

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    @ferhadmehdizade47723 жыл бұрын

    Thanks, it helped a lot👍

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    @giggleglyphs3 жыл бұрын

    thanks for this video, even thanks for this playlist dude....:)

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    @user-dl7ui4ii6r Жыл бұрын

    thanks a lot, you are the best 😍

  • @shreyaskulkarni526
    @shreyaskulkarni5263 жыл бұрын

    Thanks for this video bro...

  • @SimpleSnippets

    @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! 😇

  • @mustafag6334
    @mustafag63342 жыл бұрын

    keep up the great work!!

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    @oliviazhai18312 жыл бұрын

    Thanks so much man

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    @youssefmohamed-jt8qp2 жыл бұрын

    thanks bro really you are a legend

  • @vaishnavinandane4050
    @vaishnavinandane40504 ай бұрын

    best explain....u r amazing😃

  • @SimpleSnippets

    @SimpleSnippets

    4 ай бұрын

    Thank you Vaishnavi 😊

  • @AnujKumar-ev4fm
    @AnujKumar-ev4fm3 жыл бұрын

    really good explanation! sir

  • @SimpleSnippets

    @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 😇

  • @jamesstark4136
    @jamesstark41362 жыл бұрын

    Thank you! Note: small error on Big theta slide, description says "Big Omega"

  • @muktagavli1106
    @muktagavli11062 жыл бұрын

    Very good lecture

  • @joshuatorres3342
    @joshuatorres33422 жыл бұрын

    great video!!!

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    @talahareb5863 Жыл бұрын

    literally youtube king

  • @diegoferreirarapaci6856
    @diegoferreirarapaci68569 ай бұрын

    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?

  • @gustavrisager8939
    @gustavrisager89392 жыл бұрын

    Within the first 100 seconds this video explained Big-O better than my $200 textbook and my professor… combined.

  • @SimpleSnippets

    @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 😊

  • @albertd.bangura3794
    @albertd.bangura37942 жыл бұрын

    You are great!

  • @lakshmipathakamuri967
    @lakshmipathakamuri9673 жыл бұрын

    Superb sir nice explanation

  • @SimpleSnippets

    @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 😇

  • @akashdwivedi4716
    @akashdwivedi47163 жыл бұрын

    thnx for the help brother

  • @dalisalvador9167
    @dalisalvador91672 жыл бұрын

    Thanks bro

  • @_tanujpokhriyal
    @_tanujpokhriyal2 жыл бұрын

    Bhaiya from where can i solve DSA questions...? Coz in geekforgeek , interviewbit they have only solution but not explaination (video explaination)

  • @Abinash0323
    @Abinash03234 ай бұрын

    Excellent video

  • @SimpleSnippets

    @SimpleSnippets

    3 ай бұрын

    Thank you very much!

  • @keanaleong7745
    @keanaleong7745 Жыл бұрын

    Thank yooou!

  • @CodeHive1
    @CodeHive12 жыл бұрын

    Great content. Easy to follow and to the point. Wonderful!

  • @gul3831
    @gul3831 Жыл бұрын

    Amazing

  • @DangThinh261
    @DangThinh2613 жыл бұрын

    Awesome !!!

  • @omarrefaye3105
    @omarrefaye31053 жыл бұрын

    Very well done

  • @SimpleSnippets

    @SimpleSnippets

    3 жыл бұрын

    Thank you very much!

  • @kodandaraochellapilli6212
    @kodandaraochellapilli6212 Жыл бұрын

    Do you have implementation for these concepts. Thank you for your help. It is very clear and simple. It is way better than my university teachings.

  • @midhunskani
    @midhunskani4 жыл бұрын

    Thank you

  • @SimpleSnippets

    @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 😇

  • @Oscar-we5ke
    @Oscar-we5ke2 жыл бұрын

    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.

  • @nataliehodnett
    @nataliehodnett4 ай бұрын

    Thank you ily

  • @weilee8838
    @weilee88382 жыл бұрын

    very good

  • @luisdominguez-gx8zj
    @luisdominguez-gx8zj3 жыл бұрын

    awesome video!

  • @SimpleSnippets

    @SimpleSnippets

    3 жыл бұрын

    Thank you 😊 please do Subscribe 👍

  • @nitismita1035
    @nitismita10352 жыл бұрын

    Thanks a lot 🙏Sir. Can you show some questions on this topic.

  • @alienmo6653
    @alienmo6653 Жыл бұрын

    great vid

  • @amrutachavan7686
    @amrutachavan76863 жыл бұрын

    I like your ds lecture now I will complete your ds course thank you I am last year student

  • @SimpleSnippets

    @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

    @amrutachavan7686

    3 жыл бұрын

    @@SimpleSnippets you upload your videos on edyoda learning

  • @SimpleSnippets

    @SimpleSnippets

    3 жыл бұрын

    @@amrutachavan7686 yes I have uploaded some video on edyoda platform 😊

  • @ruskindrag9649
    @ruskindrag96493 жыл бұрын

    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).

  • @Albert-of4pg
    @Albert-of4pg4 жыл бұрын

    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

    @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

  • @availkrishmytube
    @availkrishmytube3 жыл бұрын

    Is there a reason why you chose 2n+3 for f(n)

  • @M4v3RicK99
    @M4v3RicK994 жыл бұрын

    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

    @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

    @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

    @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 ✌️

  • @nitismita1035
    @nitismita10352 жыл бұрын

    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)

  • @ahmadxgame8885
    @ahmadxgame88859 ай бұрын

    at 6:10 why did consider that c =5 but when n was powered by 2 we consider c =1 at 11:20 ?

  • @naweddiwan
    @naweddiwan2 жыл бұрын

    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?

  • @ommishra6032
    @ommishra6032 Жыл бұрын

    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 😊😊..

  • @satya5072
    @satya50723 жыл бұрын

    Excellent video... I am waiting for this type of lectures.. 🤩🤩🤩🤩

  • @shubhamwavhal9421
    @shubhamwavhal94213 жыл бұрын

    nice video sir

  • @sexyjesu
    @sexyjesu Жыл бұрын

    You're a god

  • @Mozamel89
    @Mozamel89 Жыл бұрын

    Great

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