Master Theorem Visually Explained

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  • เผยแพร่เมื่อ 17 ก.ย. 2022
  • Here we go over the intuition behind the master theorem / master method, which often times gets lost behind all the math required for the proof.
    Visualized with Manim Community.
    Sources and further links:
    - [Al Gore Clip, Simpsons episode 113](simpsons.fandom.com/wiki/Gram...)
    - [Animating Fluid Sediment Mixture in Particle-Laden Flows]( • [SIGGRAPH 2018] Animat... )
    - [Control Strategies for Physically Simulated Characters Performing Two-player Competitive Sports]( • Control Strategies for... )
    ---
    - [Bubble-sort with Hungarian ("Csángó") folk dance]( • Bubble-sort with Hunga... )
    - [Insert-sort with Romanian folk dance.flv]( • Insert-sort with Roman... )
    - [Merge-sort with Transylvanian-saxon (German) folk dance.flv]( • Merge-sort with Transy... )
    - [Quick-sort with Hungarian (Küküllomenti legényes) folk dance.flv]( • Quick-sort with Hungar... )
    - [Select-sort with Gypsy folk dance.flv]( • Select-sort with Gypsy... )
    - [Shell-sort with Hungarian (Székely) folk dance.flv]( • Shell-sort with Hungar... )
    ---
    - [Model Checking](en.wikipedia.org/wiki/Model_c...)
    - [Hoare Calculus](www.researchgate.net/figure/H...)
    - [Z3: An Efficient SMT Solver](doi.org/10.1007/978-3-540-788...)
    ---
    - [What Is Big O Notation?]( • What Is Big O Notation? )
    - [Khan Academy: Asymptotic notation](www.khanacademy.org/computing...)
    ---
    - [The Hammer Party - Divide And Conquer]( • Video )
    - [PINK GUY - HELP]( • PINK GUY - HELP )
    - [Look at this graph]( • Video )
    - [JO1 - Algorithm ]( • JO1|'Algorithm' PERFOR... )
    ---
    - [How Karatsuba's algorithm gave us new ways to multiply]( • How Karatsuba's algori... )
    - [2. Divide & Conquer: Convex Hull, Median Finding]( • 2. Divide & Conquer: C... )
    - [Geometry of football (Voronoi)]( • Geometry of football (... )
    - [3. Divide & Conquer: FFT]( • 3. Divide & Conquer: FFT )
    - [The Fast Fourier Transform (FFT): Most Ingenious Algorithm Ever?]( • The Fast Fourier Trans... )
    - [FFT Example: Unraveling the Recursion]( • FFT Example: Unravelin... )
    - [4. Divide & Conquer: van Emde Boas Trees]( • 4. Divide & Conquer: v... )
    - [Closest Pair of Points (Divide and Conquer) Explained]( • Closest Pair of Points... )
    - [Strassen algorithm](en.wikipedia.org/wiki/Strasse...)
  • วิทยาศาสตร์และเทคโนโลยี

ความคิดเห็น • 68

  • @stefano3618
    @stefano3618 หลายเดือนก่อน +1

    In 5:26 I haven't understood why the index of the sum is from j=0 to log b (n-1) rather than j=0 ti log b (n) - 1

    • @larsquentin8249
      @larsquentin8249  หลายเดือนก่อน

      Sorry for the late reply. Because the last/n-th term are the leaves, which are the term afterwards, i.e. Theta(n^(log_b(a)))

    • @stefano3618
      @stefano3618 25 วันที่ผ่านมา

      It' s fine. I mean if we don't consider the last level in the summation we should do height minus 1, with height = log_b(n), so the minus 1 is outside the bracket. Correct me if I am wrong

    • @larsquentin8249
      @larsquentin8249  12 วันที่ผ่านมา

      @@stefano3618 Didn't see it again haha. Yes, you are completely correct, it should be
      sum_{j=0}^{log_b(n)-1}
      I've pinned your comment for everyone else. Thank you so much!

  • @chinglemba9136
    @chinglemba9136 9 หลายเดือนก่อน +29

    it's a crime that your channel does not have millions of subscribers. THANK YOU for this

    • @Kaorii1905
      @Kaorii1905 หลายเดือนก่อน

      I agree

    • @West_Waktole
      @West_Waktole หลายเดือนก่อน

      with only 2 videos?

  • @abhirup619
    @abhirup619 10 หลายเดือนก่อน +14

    Everywhere I searched they just used the formula or showed how to use the formula! This is EXACTLY what I was looking for. Brilliant work

  • @LarryBordo
    @LarryBordo ปีที่แล้ว +16

    I had a really hard time understanding the Master Theorem when I was studying Algorithms so long ago. You've made understanding this complex formula so much easier. Thank you.

  • @xLany
    @xLany 8 หลายเดือนก่อน +6

    Lars why are you so cool. This is one of the best algorithm teaching videos I've ever seen in my life. I’m relearning Master’s Theorem at 2am right now. Every couple mins I audibly say “what the f!!!” and pause the video to take agitated paces around the room because something you said just blew my mind again. Thank you for the clear explanation, the visualization, the scattered meme-ry, and the montage of cool applications at the end (I dropped so many "what the f"s going through that). Above all THANK YOU for all the time and care you put into this video, it is a cut above everything else I've seen!!!

  • @tauheedakbar3781
    @tauheedakbar3781 ปีที่แล้ว +6

    absolutely beautiful work, really appreciate all the hard work you clearly put into this

  • @stefano3618
    @stefano3618 25 วันที่ผ่านมา

    thank you so much for the video. I really appreciate it: the topic is well and CLEARLY explained with fantastic animation.

  • @stark.aritra
    @stark.aritra 6 หลายเดือนก่อน +3

    I have never seen such an eloquent explanation of the master theorem in books or any videos, hats off.

  • @maxschikofski251
    @maxschikofski251 ปีที่แล้ว +1

    Very well visualised. Good Job, Lars!

  • @lukam.7575
    @lukam.7575 ปีที่แล้ว

    great video, well explained and well made, making it very easy to visualize the concepts being apllied to the problems.

  • @AyanKhan-dc3eu
    @AyanKhan-dc3eu ปีที่แล้ว +2

    Best video on master's theorem ! Thank You so much for this.

  • @kingshukcs
    @kingshukcs 6 หลายเดือนก่อน

    Very good presentation and I loved your style of teaching!!

  • @redj_dev
    @redj_dev 8 หลายเดือนก่อน +1

    confirmed best vid on YT about this. Saved my homework grade ty bb

  • @samarthtandale9121
    @samarthtandale9121 7 หลายเดือนก่อน

    Really awesome explanation brother ... kudoes!!! You diserve so many subs!

  • @brunomoreira6416
    @brunomoreira6416 3 หลายเดือนก่อน

    please make more videos, engaging, easy to understand and funny, great job!

  • @yunoletmehaveaname
    @yunoletmehaveaname ปีที่แล้ว

    Omg please post more videos. I love this!

  • @user-kz1en1qj3g
    @user-kz1en1qj3g 10 หลายเดือนก่อน

    nice video man! Good explaination on the master theorem!

  • @emanabdelhaleem7561
    @emanabdelhaleem7561 6 หลายเดือนก่อน

    This is just amazing work!
    Thank you so much.

  • @phillipsmith4220
    @phillipsmith4220 9 หลายเดือนก่อน

    What an incredible video. I would have saved so much time if I had found this video first! Thank you so much.

  • @ejsafara456
    @ejsafara456 ปีที่แล้ว

    this is such a good explanation! :D thank you, i finally understand ^^

  • @tatox2167
    @tatox2167 6 หลายเดือนก่อน +1

    brrrruuuuh you need to create more videos this was awesome

  • @arniedeb2305
    @arniedeb2305 ปีที่แล้ว

    Holy fuck this is high quality, I'm surprised you don't have more subs

  • @johnwang41
    @johnwang41 ปีที่แล้ว

    U are amazing, I hope u can continue to do this, it is wonderful viode.

  • @powermax6391
    @powermax6391 3 หลายเดือนก่อน

    first time finally understanding it, thanks a lot

  • @Tiniku
    @Tiniku 11 หลายเดือนก่อน

    where have you been all my life. thank youu!

  • @Trohnald
    @Trohnald 5 หลายเดือนก่อน

    I LOVE YOU LARS THIS HAS BEEN SO HELPFUL

  • @speedwagon1524
    @speedwagon1524 7 หลายเดือนก่อน

    You saved my Master's Degree! Thanks Lars, I love you!!!

  • @williamyang8408
    @williamyang8408 หลายเดือนก่อน

    This is so op wtf how do you only have 300 subs

  • @sonikaagarwal931
    @sonikaagarwal931 หลายเดือนก่อน

    why do you only have one video??? i was so hoping to look at more :( but thanks anyway! great video

  • @wyatt3112
    @wyatt3112 4 หลายเดือนก่อน

    This is amazing. Thank you so much, Lars. Do you post videos anywhere else? I am studying "Introduction to Algorithms" by Cormen right now in school but I am much more a visual learner. Does anyone have any good playlists or outside resources to help with this material? I know a lot of folks really take to Abdul Bari's videos but I don't understand his explanations as easily as others seem to.

  • @Ned_.
    @Ned_. 3 หลายเดือนก่อน

    great video, thanks bro

  • @JS-dn9cr
    @JS-dn9cr 3 หลายเดือนก่อน

    make more vids pleaseeeeee this is god tier

  • @lethalbacon3299
    @lethalbacon3299 ปีที่แล้ว

    Please! PLEASE MAKE NEW VIDEOS ABOUT OTHER COMPUTER SCIENCE TOPICS! This video war really great and I understood the Theorem!

  • @maxbill1921
    @maxbill1921 ปีที่แล้ว

    This is Wonderfull.... Best explanation

  •  4 หลายเดือนก่อน

    What a great video!

  • @notchicken
    @notchicken ปีที่แล้ว

    This makes things so clear. Wow.

  • @user-em1bq6sk7f
    @user-em1bq6sk7f 5 หลายเดือนก่อน

    brilliantly explained

  • @kevalgandhi9162
    @kevalgandhi9162 10 หลายเดือนก่อน

    Best Video so far on MT

  • @silentco2254
    @silentco2254 ปีที่แล้ว +1

    can you provide your code for the animation in manim I am new to manim and I would really learn a lot from you

  • @haiphan8360
    @haiphan8360 5 หลายเดือนก่อน

    Time-efficient at its best!

  • @sillaceestekay2069
    @sillaceestekay2069 ปีที่แล้ว

    You sir are a legend!

  • @mostafayounes9490
    @mostafayounes9490 3 หลายเดือนก่อน

    Thank You❤

  • @gabriel-oc4pt
    @gabriel-oc4pt ปีที่แล้ว

    bro I owe you one THANK YOU

  • @xash3000
    @xash3000 5 หลายเดือนก่อน

    Thank you

  • @user-em1bq6sk7f
    @user-em1bq6sk7f 4 หลายเดือนก่อน +1

    I think you are a kind person

  • @a.m.4154
    @a.m.4154 4 หลายเดือนก่อน

    3:55 - "what is the depth of our tree?" - No such thing exists. You have the depth of a node, the height of a node, and the height of a tree.

    • @ilayohana3150
      @ilayohana3150 3 หลายเดือนก่อน

      🤓even professors would say the depth of the tree to refer to the deepest point of the tree

  • @wannabehuman.production
    @wannabehuman.production 25 วันที่ผ่านมา

    May you live a long happy life

  • @anik._.
    @anik._. 6 หลายเดือนก่อน

    brilliant

  • @adityagujaria2598
    @adityagujaria2598 ปีที่แล้ว

    Hey nice video.!!!

  • @wolfgangamadeusmozart3200
    @wolfgangamadeusmozart3200 8 หลายเดือนก่อน

    Why you have ONLY ONE video ???

  • @bryanshaong2333
    @bryanshaong2333 5 หลายเดือนก่อน

    Where more video, hw due tmr , need help

  • @theali8oras274
    @theali8oras274 ปีที่แล้ว

    thank you for this , my prof is garbage and im having a hard time with math

  • @rea5782
    @rea5782 ปีที่แล้ว

    Notification gang ☑ we lit 🔥

  • @gabut1839
    @gabut1839 3 หลายเดือนก่อน

    YOUR VIDEO IS AMAZING, BE CONSISTENT AND ULL BLOW UP SIR!

  • @JenniRocket
    @JenniRocket ปีที่แล้ว +1

    Damn man I finally really get it 😂

  • @justavine487
    @justavine487 11 หลายเดือนก่อน

    Very strong video. You could have a bigger audience if you also uploaded your videos in german ;)

  • @visionz831
    @visionz831 ปีที่แล้ว +1

    3:16 What does he say here ? Subtitles please

    • @theali8oras274
      @theali8oras274 ปีที่แล้ว

      automatic subs help.
      they get it right at 3:16

  • @spooki9813
    @spooki9813 5 หลายเดือนก่อน

    dude thank you for this video i explained this to some autistic girl at a party and she went home w me :)

  • @ellenkoning3491
    @ellenkoning3491 ปีที่แล้ว

    to few people have seen this!

  • @jurycould4275
    @jurycould4275 9 หลายเดือนก่อน +1

    Bitte ende nicht als 0815-Entwickler. Das ist meine Domäne.

  • @mikhailwebb8377
    @mikhailwebb8377 9 หลายเดือนก่อน

    I see that you are trying to explain as best as you can, but I still don't understand. The other videos on TH-cam for Master Theorem are also garbage.