Genetic Algorithms Explained By Example

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  • Опубліковано 25 чер 2024
  • Did you know that you can simulate evolution inside the computer? And that you can solve really really hard problems this way? In this tutorial, we will look into the question: What are genetic algorithms? I will try to explain genetic algorithms using an example. And we will look at different applications of this evolutionary algorithm. We will also try to solve one historic problem in computer science by example: The Knapsack problem.
    Genetic algorithms are a subgroup of evolutionary algorithms or evolutionary computing and they are used in self-learning machine learning algorithms and AI. They use the concept of natural selection to simulate the survival of the fittest and natural selection inside your computer.
    This video is number one of a course of video tutorials to teach you the very basics of genetic algorithms in Python.
    🙏 Support me: / kiecodes
    🛰 Join our Discord, to interact with other Coders and me: / discord
    🧠 Pick my brain: calendly.com/kiecodes/ai-cons...
    Check out my newest video: • How to use the OpenAI ...
    Follow me here:
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    Questions of the day
    ■ What would you use genetic algorithms for?
    P-VERSUS-NP-PROBLEM:
    ■ I love the simple explanation and the relations to the Simpsons and Futurama: • P vs NP on TV - Comput...
    RESEARCH:
    ■ Eiben, A. E. et al (1994) "Genetic algorithms with multi-parent recombination"
    ■ Geijtenbeek, van de Panne, van der Stappen (2013) "Flexible Muscle-Based Locomotion for Bipedal Creatures" - www.goatstream.com/research/p...
    ■ Hornby, Globus (2006) "Automated Antenna Design with Evolutionary
    Algorithms" - ti.arc.nasa.gov/m/pub-archive...
    Timestamps:
    00:00 Intro
    00:23 The Problem
    02:48 The Knapsack Problem
    03:20 What are Genetic Algorithms
    04:17 How does it work?
    06:49 Summary
    07:52 Is it worth it?
    08:40 Results
    10:23 Applications
    ---
    This video contains advertising content.
    ---
    Attribution:
    ■ Photo by Anush Gorak from Pexels - www.pexels.com/photo/man-hold...
    #python #machinelearning #geneticalgorithms
  • Наука та технологія

КОМЕНТАРІ • 453

  • @KieCodes
    @KieCodes  4 роки тому +32

    Thanks for stopping by! Today we will encounter a problem we can't easily solve with our normal algorithmic tools so we deep dive into a class of algorithms called: GENETIC ALGORITHMS!
    I hope you find it as interesting as I do. *What would you use them for?*

    • @DevOpsDirective
      @DevOpsDirective 4 роки тому +1

      I first learned about evolutionary algorithms from this TED talk www.ted.com/talks/bill_gross_a_solar_energy_system_that_tracks_the_sun/
      Since then I have wanted to use them to write a program that attempts to learn how to write brainf***. BF seems like a good language choice since there are only a handful of symbols and writing/instrumenting an interpreter to also evaluate an objective function to feed back into the evolutionary algorithm would be simple!
      I haven't gotten around to it yet, but perhaps soon!

    • @Stopinvadingmyhardware
      @Stopinvadingmyhardware 11 місяців тому

      Thanks, you just helped me solved a vector problem I was having.
      Oddly, I didn’t even use an algorithm.

  • @kx9473
    @kx9473 2 роки тому +156

    This guy explained everything from 2 weeks long boring lecture in under 12 minutes with extremely clear explanation. I love you because you just saved my degree.

    • @KieCodes
      @KieCodes  2 роки тому +3

      You are more than welcome my friend. 🙏 Rock on! 🚀

    • @davidi686
      @davidi686 8 місяців тому +1

      2 hour’s lecture in 12mins how about that .

    • @Terra_Cognita
      @Terra_Cognita 7 місяців тому +2

      Do you know how he calculated the total number of combinations in a naive brute force approach? I did permutations and combinations and the values were not equal.

    • @Terra_Cognita
      @Terra_Cognita 7 місяців тому +1

      Never mind I figured it out, It is the sum of all possible (N chooses k) combinations k = 0, 1,..N which simplifies to 2^N

    • @mr.boomguy
      @mr.boomguy 2 місяці тому +2

      This is why I love watching UA-cam. Sure, 95% of the time is trivia and entertainment, but then you stumble upon things you either where looking for or not, and you learn them in minutes instead of the years it takes from professional lecturing.
      (Granted, processing that information is a whole other ordeal, but at least you have it on hand)

  • @sergioseco9835
    @sergioseco9835 3 роки тому +92

    this deserves a million views

  • @adityagarg2185
    @adityagarg2185 Рік тому +21

    This video was AMAZING. I can't believe the amount of time and effort you took to explain this topic so clearly. It sucks that you stopped making videos. What can I do to motivate you to make an algorithm series?

  • @xandrovich5976
    @xandrovich5976 2 роки тому +13

    I must say - the quality of this video is top-notch. The crisp editing, sound, and illustrations do a great job of demonstrating the point.

    • @KieCodes
      @KieCodes  2 роки тому

      Thank you so much! 🙏

  • @colinmignot6309
    @colinmignot6309 2 роки тому +15

    you're great teacher. taking time to edit engaging videos with visuals like you do is very effective to help ppl grasp concepts

  • @abdullahsheriff_
    @abdullahsheriff_ Рік тому +4

    According to me, his video is THE BEST explanation on UA-cam on Genetic Algorithms. My mates and I understood Genetic Algorithms like never before, loved it, and implemented it in our University Course Project.
    Thank you, Kie.

    • @KieCodes
      @KieCodes  Рік тому

      You are more than welcome! Enjoy your studies!

  • @TarunRavi
    @TarunRavi 4 роки тому +20

    Wow your video is awesome! You explained a pretty complex algorithm in a simple way. I've always wanted to use genetic algorithms for one of my videos, this is a fantastic intro to the field! btw I love your video quality, it looks soo good.

    • @KieCodes
      @KieCodes  4 роки тому

      Thanks so much for your kind words. 🙏

  • @georgeruellan
    @georgeruellan 3 роки тому +6

    Dude this video is amazing. Great explanation, I liked the real world example too. Your editing style is sick too! Can't wait to see more from you

    • @KieCodes
      @KieCodes  3 роки тому

      Thanks George. This means a lot and is really motivating! Great to have you here. Rock on!

  • @willboler830
    @willboler830 2 роки тому +21

    Excellent video! One of the better selection algorithms and more typical is a tournament selection. Rather than choosing the best fitness genes for the next generation, each gene is given a probability of selection based on their fitness. Better genes have a higher probability of selection, and worse genes have a lower probability of selection, but the odds of selection are not 100% and 0% respectively. This takes a bit longer when it comes to finding a solution, but it gives a better search of the solution space.

  • @CristalMediumBlue
    @CristalMediumBlue Рік тому +2

    Toll. Das ist das beste Video, das ich bisher zu diesem Thema gesehen habe

  • @subpixelsalt7648
    @subpixelsalt7648 4 роки тому +7

    Great video! I've been facinated by genetic algorithms after seeing people use it to beat levels in Super Mario Bros. There's just something so fascinating about watching a computer "learn" how to get better at doing something.

    • @KieCodes
      @KieCodes  4 роки тому +1

      Thank you! I totally feel the same. It is modern magic. 🙃

  • @aliticx
    @aliticx 3 роки тому +3

    Man I wish everyone explained concepts this good! Awesome video!

    • @KieCodes
      @KieCodes  3 роки тому

      Thank you Aliticx. This comment really means a lot to me. 🙏 Having people to really understand what I try to explain is way more worth to me than subscribers and views. Thank you.

  • @mesticasamelapapna708
    @mesticasamelapapna708 Рік тому +1

    Thank you for this Kie! I'm amazed that you use Genetic Algorithm to solve the Knapsack problem :)

  • @zacrobyte
    @zacrobyte 3 роки тому +6

    Yo dude, this is some next level way of teaching your channel should've had atleast 1 mil already

    • @KieCodes
      @KieCodes  3 роки тому

      Thank you. 🙏 Maybe some day. Thanks again for the motivating words.

  • @lohithkandukuri5579
    @lohithkandukuri5579 Рік тому +1

    SOOOOOOOO gooood.... Nobody could have been more concise and informative at the same time.

    • @KieCodes
      @KieCodes  Рік тому

      Thank you very much! 🙏🙏🙏

  • @evrmk
    @evrmk Рік тому +1

    Three 1.5-hour-long lectures in my university explained in 11 minutes. Thanks!

  • @BehniaFB
    @BehniaFB 3 роки тому +4

    Every second I that goes, I realize more how complete this video is ! This vid should definitely have more than a million views .

    • @KieCodes
      @KieCodes  3 роки тому

      Thank you so much!

  • @r.ramirez1521
    @r.ramirez1521 2 роки тому +1

    Please don't ever go away. This was amazing

  • @alvaroarcelus8949
    @alvaroarcelus8949 11 місяців тому +1

    Amazingly explained!! Thank you so much. 🙌

  • @kr0tyara
    @kr0tyara 3 роки тому +4

    You are such an underrated gem. GOOD JOB!!!

  • @adinvella4665
    @adinvella4665 Рік тому +1

    Very informative video; full of information yet very easy to follow. Thank you!

  • @thop7964
    @thop7964 2 роки тому +2

    Fantastic example. Really helps show how the conceptual steps actually work!

  • @TheTehnigga
    @TheTehnigga 2 роки тому +3

    Really well explained and cured, these are the kind of explanations that I prefer, there's love and dedication behind it. Thank you!

  • @fasaipuengudom5412
    @fasaipuengudom5412 Рік тому +1

    Best video regarding this topic. Very visual and easy to understand

  • @MeANDmyPETgoat
    @MeANDmyPETgoat 3 роки тому +5

    Great video bro, helped me understand what my teacher's mumbling couldn't for our test, keep it up!

    • @KieCodes
      @KieCodes  3 роки тому +1

      Thanks for your kind words. 🙏

  • @shouryaraj5913
    @shouryaraj5913 3 роки тому +1

    Astonishing video! Thanks for sharing the incredible research papers. Looking forward to learn and explore more. Thanks

    • @KieCodes
      @KieCodes  3 роки тому

      Thanks for you kind words! :)

  • @annashchukina3768
    @annashchukina3768 3 роки тому +3

    This was an amazing introduction to the topic and great intuition. Thanks for the video! It was also fun to watch😄

  • @mahdilatreche4501
    @mahdilatreche4501 3 роки тому +1

    This video is astonishing, you deserve a lot more views, keep up the good work :)

  • @BehniaFB
    @BehniaFB 3 роки тому +14

    I've never imagined that one day Seth Rogen will be teaching me Algorithms😂 (Jokes aside this video was amazing and well-made; GOOD JOB!❤)

  • @hansergonzalez6646
    @hansergonzalez6646 2 роки тому +2

    What an amazing content, explained with simple words. Thanks and keep up the hard work.

    • @KieCodes
      @KieCodes  2 роки тому

      Glad you liked it! Thank you!

  • @BraidyMerkle
    @BraidyMerkle 4 роки тому +2

    I have not yet had to use genetic algorithms, but want to try them out after watching this video! Thanks for the introduction!

    • @KieCodes
      @KieCodes  4 роки тому +1

      Thanks Braidy! Let me know what you used them for. :)

  • @daphnelenders4207
    @daphnelenders4207 3 роки тому +2

    Thanks a lot for your explanation, looking forward to use genetic algorithms in the future!

    • @KieCodes
      @KieCodes  3 роки тому

      Thank you. Have fun, its a great tool!

  • @GlynisDance
    @GlynisDance Рік тому

    That was an excellent video. Clear, engaging, inspiring and fun! I will be watching more of your videos.

  • @ForTheOmnissiah
    @ForTheOmnissiah 11 місяців тому +1

    Wish you uploaded more. This is quality content.

  • @diegocruz8187
    @diegocruz8187 3 роки тому +1

    This channel should have more subscribers! Really amazing video and explanation

    • @KieCodes
      @KieCodes  3 роки тому

      Thanks Diego! 💪🙏

  • @hamidnodehi
    @hamidnodehi Рік тому +1

    Helped a lot. Thanks so much.

  • @Joselo09111
    @Joselo09111 2 роки тому +4

    Fantastic explanation! I learned more in this video, than my professor

    • @KieCodes
      @KieCodes  2 роки тому

      Great to hear! Thank you so much!

  • @michellesainos3443
    @michellesainos3443 3 роки тому +1

    Thank you!!! your explanation was very clear and awesome!! Definitely checking out the implementation

    • @KieCodes
      @KieCodes  3 роки тому

      Thank you Michelle!🙏

  • @roct07
    @roct07 Рік тому +1

    This is so well explained

  • @ragabnadim
    @ragabnadim Рік тому +1

    Thank you for the video, will recommand to my students

  • @srinivaskollipara1293
    @srinivaskollipara1293 3 роки тому +2

    this is awesome!!!!!!! I am a mechanical engineer with 0 knowledge in these type of algorithms but for the sake of a project on scheduling using the genetic algorithm I was surfing youtube, this is the best explanation I ever had and it is very clear if possible, please suggest algorithms similar to this which are good for job shop scheduling.

  • @TWFDeadzoneII
    @TWFDeadzoneII 3 роки тому +2

    Mind blowing. I can't wait to implement this.

    • @KieCodes
      @KieCodes  3 роки тому

      It surely is. Have fun!

  • @TheCzarsoham
    @TheCzarsoham 3 роки тому +1

    Great video! Exactly what I was looking for!

    • @KieCodes
      @KieCodes  3 роки тому

      I am sooo glad it helped you! 🙏

  • @MohamedHassan-xf5wb
    @MohamedHassan-xf5wb Рік тому +1

    Really well explained

  • @mohammadabdurroufhrithik5152
    @mohammadabdurroufhrithik5152 Рік тому +1

    very helpful video!!! excellently explained!

  • @samidahdouh7863
    @samidahdouh7863 4 місяці тому +1

    This is actually one of the best videos I've ever seen on UA-cam. Thank you!

    • @KieCodes
      @KieCodes  4 місяці тому

      Wow. Thank you. 🙏🎉

  • @arianalini8636
    @arianalini8636 8 місяців тому +1

    how is it not booming yet?! thank u for the clear explanation + the awesome edits!

  • @jayha5924
    @jayha5924 11 місяців тому +1

    good man, keep it up!! really appreciated

  • @nishitpatel5686
    @nishitpatel5686 2 роки тому +1

    one of the best videos on genetic algorithm

  • @vasachisenjubean5944
    @vasachisenjubean5944 3 роки тому +6

    man the effort you put in this video is - "Salute"

  • @MaTrOoOoD
    @MaTrOoOoD 3 роки тому +5

    After watching the video I opened the channel expecting to see millions of subscribers. You deserve much more!! What an awesome video. Simple and right to the main points! Keep up the good work!

    • @KieCodes
      @KieCodes  3 роки тому +1

      Wow. Thanks for your kind and motivating words Mo. I will try my best. To be honest I wouldn’t be ready for millions of subs. Glad to hopefully hit a 1000 till 2021.
      Have a great day! 🙏

    • @KieCodes
      @KieCodes  3 роки тому

      And thanks for subscribing! One sub closer. ☺️

    • @MaTrOoOoD
      @MaTrOoOoD 3 роки тому +1

      @@KieCodes dude your videos are extraordinary! I couldn’t resist 🤷🏻‍♂️
      Wish you best of luck man! Can’t tell you how happy and excited I am to see what you have next!

  • @shahed.hijjawi
    @shahed.hijjawi Рік тому +1

    GREAT EFFORT BRO!

  • @seriouscoder1727
    @seriouscoder1727 2 роки тому +1

    I,ve watched many clips in this regard but your explanation was one of a kind, absoulotlly deserve thousends of million of billion views

    • @KieCodes
      @KieCodes  2 роки тому +1

      Wow. Thank you for your kind words! 🙏

  • @eddazzo
    @eddazzo 3 роки тому +5

    Im a computer science degree student and this helps me to understand better on my final year project's topic! Thank you very much sir!

    • @KieCodes
      @KieCodes  3 роки тому

      You are more than welcome my friend. 🙏 Rock on! 🚀

  • @sardororipov1302
    @sardororipov1302 3 роки тому +2

    I’m here before this channel get 1million subs. Keep up the great work man!

  • @o.rudyemonvuon64
    @o.rudyemonvuon64 3 роки тому +1

    Absolutely amazing !!!! You perfectly outlined the points and I'm defenetly more intrigued in doing additional research and watching your other videos !!!

    • @KieCodes
      @KieCodes  3 роки тому +1

      Thank you for your kind words.

  • @paragvadhiya8019
    @paragvadhiya8019 2 роки тому +2

    Video is on point, accurate and does not waste your time. Thanks so much man.

    • @KieCodes
      @KieCodes  2 роки тому

      I really appreciate your kind words! 🙏

  • @shwetakale246
    @shwetakale246 2 роки тому

    Best video with good example
    thank you!!

  • @1stpatrickha
    @1stpatrickha 3 роки тому +1

    To be honest, this is the best video explained about this Genetic Algor concept. Quality contents. Keep going dude!

  • @yasminejas5007
    @yasminejas5007 2 місяці тому +1

    Thank you so much this video is very helpful for my thesis!

    • @KieCodes
      @KieCodes  2 місяці тому

      Glad it was helpful! 🙏

  • @robert__
    @robert__ 3 роки тому +1

    Really good video, thank you so much, subbed

  • @ouahidalalga9437
    @ouahidalalga9437 2 місяці тому +1

    Just Wow! Hats off to you, that's a great explanation.

  • @sevdalink6676
    @sevdalink6676 6 місяців тому +1

    Whoah men! You fascinated me. What a level of explanation.

    • @KieCodes
      @KieCodes  6 місяців тому +1

      Thank you. I hope it helped. 🙏🫡

  • @jiahaochang8628
    @jiahaochang8628 2 роки тому

    This is an awesome video to match. Thank you for your explanation, that is a great visual approach!

  • @pranshujayswal1458
    @pranshujayswal1458 3 роки тому +1

    THANK YOU so much!! AMAZING VIDEO.WORTH THE TIME!!

    • @KieCodes
      @KieCodes  3 роки тому

      Thanks for your kind words!

  • @aaradhyanegi639
    @aaradhyanegi639 4 місяці тому +1

    I've never learned anything in this way
    I love it!

    • @KieCodes
      @KieCodes  4 місяці тому

      I am glad to hear that!

  • @rafaelpmimoso
    @rafaelpmimoso 2 роки тому +1

    Much love for your work!!!

  • @marcellorossetticonti3002
    @marcellorossetticonti3002 Рік тому +2

    Hi Kie, congratulations on the clarity of your explanation. It gave me some suggestions on how to improve the way I explain these algorithms.
    I work in Italy as a physics researcher and in my group we routinely employ these kinds of algorithms to optimize the performance of particle accelerators redesgning them (with a similar approach to the antenna problem you mentioned). I can confirm that they work wonders at solving systems whose dynamics are extremely complex (especially when due to highly correlated variables)!
    I wanted to tell you that in our code we apply elitism as the last thing (even following mutation) to be sure that the best fitness value never goes down in subsequent generations. If you apply mutation later, you risk losing the best solution from the previous cycle.
    Nothing catastrophic though, the genetic information to reconstruct the best solution is mixed in the rest of the population anyway and will probably re-emerge soon anyway.

    • @mgwyndolin4262
      @mgwyndolin4262 Рік тому

      Hi thanks for sharing your insight! It is very instructive and helps me clarify the confusion about the top performers of the previous generation being mutated instead of kept intact in the video. But this video really offers a great explanation.

  • @Mohamed_Shabaik
    @Mohamed_Shabaik Рік тому +1

    I don't usually make comments. but that was a really well-explained and interesting video, Thanks!

  • @harishsingh5225
    @harishsingh5225 3 роки тому +1

    Explained brilliantly.

    • @KieCodes
      @KieCodes  3 роки тому

      Thank you so much. 🙏

  • @danmiller4091
    @danmiller4091 3 роки тому +1

    Thank you very much great explanation!!!!!

    • @KieCodes
      @KieCodes  3 роки тому

      You are more than welcome my friend. 🙏 Rock on! 🚀

  • @taylan8973
    @taylan8973 3 роки тому +1

    I rarely leave a comment but your explanation is just amazing. Good job

    • @KieCodes
      @KieCodes  3 роки тому

      Thanks Taylan! 🙏

  • @brendanmcnamara8648
    @brendanmcnamara8648 3 роки тому +1

    Beautifully explained, thank you

    • @KieCodes
      @KieCodes  3 роки тому

      Thank you for your kind words, Brendan. 🙏

  • @zecool7041
    @zecool7041 3 роки тому +1

    really good explanation , better than most of videos that i have seen and better than my teacher's lecture , keep up the good work , greetings from algeria

    • @KieCodes
      @KieCodes  3 роки тому +1

      Thank you for your kind words! Have a great day. 🙏

  • @rajathalexander406
    @rajathalexander406 3 роки тому +2

    best possible explanation, became ur FAN

    • @KieCodes
      @KieCodes  3 роки тому

      Thank you and welcome! 🙏

  • @Copybook
    @Copybook Рік тому +1

    I was really hard to digest it and I don't mean mathematically
    BTW, tomorrow I have an exam and you save my life, a blessing from an AI student

  • @user-kk6tl7dm5c
    @user-kk6tl7dm5c Рік тому +1

    Really well explained.
    I will appreciate it if you can make a project to solve time table scheduling problem with genetic algorithm.

  • @ammarazlan2919
    @ammarazlan2919 Рік тому +1

    Thank you so much! Please do Clonal Selection Algorithm next please...!

  • @hzmuhabbet
    @hzmuhabbet 3 роки тому +2

    Great explanation dude, thanks so much.

    • @KieCodes
      @KieCodes  3 роки тому

      You are more than welcome my friend. 🙏 Rock on! 🚀

  • @kritagyagupta8619
    @kritagyagupta8619 3 роки тому +5

    Dude, Your videos are higher quality then Pewdiepie and Dream combined
    Not exaggerated
    I have literally understood a concept u have tried to learn from past 10 months

    • @KieCodes
      @KieCodes  3 роки тому

      Thank you. 🙏 I am glad I could help. And thanks for your nice words. ☺️

  • @shauryan23
    @shauryan23 2 роки тому +1

    Great Explanation!!!👏

  • @AMaoR14
    @AMaoR14 2 роки тому +1

    This was awesome. Great explanation. thanks !

    • @KieCodes
      @KieCodes  2 роки тому

      You are more than welcome my friend. 🙏 Rock on! 🚀

  • @pokpikchan
    @pokpikchan 2 роки тому +1

    Very nicely explained

  • @Felicia-126
    @Felicia-126 Рік тому +1

    Amazing video, thank you.

  • @bernatmoleroagudo851
    @bernatmoleroagudo851 2 роки тому +1

    Hahaha thanks a lot for your video and also for how you explain it! It was really funny the video of the locomotion for bipedal creatures. I understood the basics so thanks!

    • @KieCodes
      @KieCodes  2 роки тому +1

      Thank you. 🙏 I am glad you liked it!

  • @mcbot1344
    @mcbot1344 3 роки тому

    Wow this is incredibly helpful for my exam. Keep up the good work!
    Greetings from Germany

    • @KieCodes
      @KieCodes  3 роки тому

      Thank you for your kind words, Mc Bot. 🙏

  • @roylevy178
    @roylevy178 3 роки тому +1

    Great explanation man! thank you :)

    • @KieCodes
      @KieCodes  3 роки тому

      Thank you! You are welcome. 🙏

  • @charlesplate6728
    @charlesplate6728 2 роки тому +1

    Great explanation, thank you!!😀

  • @hoaralatoan845
    @hoaralatoan845 Рік тому +1

    What a fantastic explanation! Clearly explain GA. Can you tell me what classical problem inspired you about the "backbag problem" in 0:23?

    • @KieCodes
      @KieCodes  Рік тому

      Hey. Thank you. The knabsack problem.

  • @shahlaanasab2898
    @shahlaanasab2898 3 роки тому +1

    You are amazing! Thank vey much for this excellent explanation.

    • @KieCodes
      @KieCodes  3 роки тому +1

      You are more than welcome my friend. 🙏 Rock on! 🚀

  • @marco.nascimento
    @marco.nascimento 3 роки тому +1

    Excellent explanation, such an interesting topic!

    • @KieCodes
      @KieCodes  3 роки тому

      It is right? Thanks again! 🙏

  • @imanelamnaoir590
    @imanelamnaoir590 Рік тому +1

    Dude, you 're just amazin

  • @jiujuntang
    @jiujuntang 11 місяців тому +1

    Amazing!

  • @HarunFarah
    @HarunFarah Рік тому +1

    Great vid done a better job at explaining than a university lecturer

  • @kattagarian
    @kattagarian 10 місяців тому +1

    thank you for the video

  • @shadowshaman4437
    @shadowshaman4437 2 роки тому +1

    awesome video, thanks brother

  • @yelamankarassay
    @yelamankarassay 3 роки тому +1

    Great You helped me in my HW assignment.

  • @danielfortesque3536
    @danielfortesque3536 3 роки тому +1

    Fantastic work bro!

  • @user-ll7el5xp7d
    @user-ll7el5xp7d 3 роки тому +1

    You're awesome!
    I don't speak English as well, but your explanation is really good, and I understand the main idea!