Network Flows: Max-Flow Min-Cut Theorem (& Ford-Fulkerson Algorithm)

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  • Опубликовано: 10 янв 2025

Комментарии • 347

  • @FirstTimeDad23
    @FirstTimeDad23 5 лет назад +275

    Ben your stuff is also helpful for senior devs(like myself). I’ve just landed a job at Amazon SA CPT. Thank you young man. Continue doing what you do.

  • @alexanderson753
    @alexanderson753 3 года назад +85

    > Textbooks could do 10 times of a better job than I could ever do.
    Textbooks could stretch out what you described in this video to be 300 pages. This is beautiful and is more than I learned from a week of Algorithms. Thank you!

  • @BackToBackSWE
    @BackToBackSWE  5 лет назад +99

    Check out the free DSA Mini-Course 👉backtobackswe.com/five-day
    Table of Contents:
    Defining The Flow Network 0:00 - 3:35
    Greedily Pushing Flow 3:35 - 5:16
    Recovering From The Greedy Choice 5:16 - 8:01
    The Residual Graph 8:01 - 15:36
    Ford-Fulkerson Algorithm (Overview) 15:36 - 17:42
    Max-Flow Min-Cut 17:42 - 21:55

    • @noahcoomer9170
      @noahcoomer9170 5 лет назад +2

      Thanks so much for this channel dude. Your videos on backtracking and sorting were absolutely key to my technical interviews at Amazon this past week. Ended up getting an offer, cheers mate.

    • @BackToBackSWE
      @BackToBackSWE  4 года назад

      Nice!

    • @rookiecookie8258
      @rookiecookie8258 4 года назад

      @@BackToBackSWE So as far as i understand the min cut (S,T) is an indication/bottleneck for the maximum flow we can push if all outgoing edges of the S part become saturated,right?

    • @ryanmacanzie1846
      @ryanmacanzie1846 3 года назад

      @@BackToBackSWE What purpose does a cut serve ?

  • @tvishathakur8947
    @tvishathakur8947 Год назад +20

    This 20 min video was more clear than a whole chapter of a book or any other lecture! Thanks for this beautiful explanation :D

    • @BackToBackSWE
      @BackToBackSWE  Год назад +1

      Happy Holidays 🎉 Thank you for this beautiful comment, tvishathakur! We'd love to offer you a 40% Off our exclusive lifetime membership just use the code CHEER40 - backtobackswe.com/checkout?plan=lifetime-legacy&discount_code=CHEER40

    • @anhkhoiaoduy6072
      @anhkhoiaoduy6072 2 месяца назад

      super super succinct, straightaway, something that professors lack is the ability to articulate and give ways to teach students more obviously.

  • @qR7pK9sJ2t
    @qR7pK9sJ2t 5 лет назад +143

    You already have achieved the minumum cut..Cause you(source) are clearly trying to maximize the amount of flow of knowledge that can reach us(sink)..
    Well done bro..

  • @anastasiagavrilita6567
    @anastasiagavrilita6567 4 года назад +13

    There aren't enough good words in the world to describe my gratitude towards you and the videos you make!

    • @BackToBackSWE
      @BackToBackSWE  4 года назад +3

      May the internet grow big and strong

  • @qqww1345
    @qqww1345 2 года назад +3

    This is literally the best video I've seen for explaining the min-cut problem.

  • @enricomilettogranozio8817
    @enricomilettogranozio8817 3 года назад +7

    First year Computational Science student here. Thanks a lot for your videos, man. They're really helping me for my Data Structures & Algorithms class

  • @mengengao7657
    @mengengao7657 4 года назад +6

    This is so helpful! I memorized Ford-Fulkerson algorithm but never got an intuitive understanding until I saw this video. Thanks!

  • @alitcher4425
    @alitcher4425 2 года назад +3

    Big Thanks from a novice com-sci student here! I couldn't follow this in class but you explained everything clearly!

  • @abdi6141
    @abdi6141 5 лет назад +7

    DUDE. I am still really early on in your videos but just wanted to come to your latest video and say.Your videos are incredible they are such an enormous help. The amount of research and thought you put into each video Is very clear in how well you explain all of the concepts you cover. Thank you very much for all your hard work. I appreciate it and godspeed brother wishing you all the best in your career and studies.

  • @ollieeilon4061
    @ollieeilon4061 Год назад +2

    This is actually the best source out there which simplifies and explains properly!

  • @dianaayt
    @dianaayt 4 года назад +10

    This was really helpful! I'm studying to be a data engineering and we talk a lot about graphs so your videos really help. You are very clear and explain things in a very visual way which helps a lot. Thank you so much!

  • @CrzyAsianGuy
    @CrzyAsianGuy 5 лет назад +4

    Watched like several videos on this topic, and this video by far the most clear and concise.

  • @nayararossi7513
    @nayararossi7513 5 лет назад +20

    I'd like to thank you cause I didn't understand anything my professor told us in class, and his slide were also a mistery until I saw your video.

  • @addemfrench
    @addemfrench 4 года назад +1

    The choice of example was perfect. Simple but complex enough to illustrate the need for backflow. Great video for the intuition.

  • @SR-ti6jj
    @SR-ti6jj 4 года назад +5

    Thank you for explaining why we can traverse backwards edges when finding an augmented path. Most other resources seem to gloss over this when it's the trickiest part of the algo!

  • @kureshimiru
    @kureshimiru 4 года назад

    Many thanks from graduate students at the Faculty of Electrical Engineering and Computing, Zagreb, Croatia!
    Amazing video!

  • @pedro_soares_bhz
    @pedro_soares_bhz Год назад

    Great. It really helps seeing a fellow human being gesticulating and talking and drawing. I never thought about it, but it really helps binding my attention. Thanks, my dude.

  • @Arush-eu2xz
    @Arush-eu2xz 5 лет назад +2

    Hey man, thank you for your interview preparation videos. I have got a very good job offer from a startup in India, and your videos played a substantial role in building up my understanding of concepts during interview preparation. Thank you for explaining things so elegantly!

  • @IAmNigHtMaReTR
    @IAmNigHtMaReTR 5 лет назад +2

    5 mins in and I’m subbed. These videos are true gems. Thank you very much

  • @riddlediddleriddle
    @riddlediddleriddle Год назад

    Your ability to transmit information in a clear and complete way is golden.

    • @BackToBackSWE
      @BackToBackSWE  Год назад

      Thank you 🎉 Please enjoy a special coupon from us - backtobackswe.com/checkout?plan=lifetime-legacy&discount_code=SUB 🚀

  • @sumitlahiri209
    @sumitlahiri209 5 лет назад +3

    Great Tutorial man. It saved me the pain of reading a whole paper. Thanks. This is a really good explanation. One can go back and code without much of a problem.

  • @danielescotece7144
    @danielescotece7144 5 лет назад +4

    Mathematical engineering student here! Thanks man, this is helping me with my OR exam!

  • @dariusbuhai9074
    @dariusbuhai9074 4 года назад

    Dude, best explanation ever. I tried looking at 4 different videos, yours is the best.

  • @sam-lr4lz
    @sam-lr4lz 5 лет назад +3

    Found your video literally a day before my exams. Thanks heaps

  • @vicd32
    @vicd32 4 года назад +13

    Amazing Explanation! You have some great communication skills for a topic that is definitely not the easiest

  • @MrKingoverall
    @MrKingoverall 4 года назад +5

    Operations Research student here , thanks Ben !

  • @dorsamotiallah3998
    @dorsamotiallah3998 6 дней назад

    Thank you man you explained better than houndreds and hundreds of text books. Let me say it once more, Thanks a lot for this video again 🙏🏻

  • @bryanthandamparambil1581
    @bryanthandamparambil1581 3 года назад +1

    Thank you for your help, I'm currently studying in year 12 in Australia and this is really helpful, Thank You!!!

  • @saneewhy
    @saneewhy Год назад

    perfect. thanks so much.. spent hours watching lectures and this one vid helped me more than all of them combined!!!!

  • @shawn77160
    @shawn77160 Год назад +1

    god bless you, i was trying to understand an exercices and just by saying it's like water pipe everything was so clear ! i wasn't thinking i can understand so fast with just a trivial comparaison xD
    But anyway thanks ! you're the best :)

  • @SDKThe8God
    @SDKThe8God 5 лет назад +3

    Glad I couldn’t find any German videos on this topic, this is great!

  • @tljstewart
    @tljstewart 2 года назад

    "S-T cut, S must be in A and T must be in B" exactly what I was searching for, most memorable. Thanks

  • @coffee-syrup
    @coffee-syrup Год назад

    Thank you so much, I finally understood what was happening there. I read the book, not only consumes a lot of time but it can be tricky to understand. You helped me finally clearing up any question I had.

    • @BackToBackSWE
      @BackToBackSWE  Год назад

      Happy Holidays 🎉 Thank you for your kind words, Anto-y! We'd love to offer you a 40% Off our exclusive lifetime membership just use the code CHEER40 - backtobackswe.com/checkout?plan=lifetime-legacy&discount_code=CHEER40

  • @fb_a
    @fb_a 5 лет назад +3

    Awesome explanation bro!!! Just Watched till 5:47 but felt amazing man!.

  • @MohammadAlshariar
    @MohammadAlshariar Месяц назад

    Bro you are genius. You saved my time.

  • @ckc2498
    @ckc2498 2 года назад

    Really love the word "undo". It help me understand what the hell there's an reverse arrows in this algo

  • @irukandjiShred
    @irukandjiShred 8 месяцев назад

    God, thank you so much for this video. I was pulling my hair out reviewing some modules before my upcoming final. This clarified things so much!!

  • @brettjenkins1645
    @brettjenkins1645 2 года назад

    So clear! Thank you! I find the textbook stuff is so bogged down with notation that I have a hard time seeing the intuitions. You made it crystal clear!

  • @sourishkrjana3126
    @sourishkrjana3126 4 года назад +2

    Best explanation.....
    Love from India🇮🇳

  • @gtmashok
    @gtmashok 4 года назад

    THANKS a ton! You're explanation of max-flow min cut was so valuable, better than my course lectures.

  • @shmulimargulies5462
    @shmulimargulies5462 4 года назад

    someone get this man a medal

  • @iustincondrea2105
    @iustincondrea2105 4 месяца назад

    This made it easier to understand the Ford-Fulkerson Algorithm iterations on a graph.Thanks😁

  • @mariasandru7
    @mariasandru7 5 лет назад +14

    Amazing! My university professor recommended your videos last week in class🤗 Could you also explain when you have time the Bellman Ford algorithm?

  • @henrynguyen911
    @henrynguyen911 4 года назад +5

    my man Ben doing God's work! Thank you so much!

  • @priyanshugupta4875
    @priyanshugupta4875 Год назад

    literally one of the best explainations

  • @boris5214
    @boris5214 3 года назад +1

    This is amazing, thank you so much for explaining what the residual graph actually means. I've studied the proof but never understood it fully until now.

  • @xflory26x
    @xflory26x 4 года назад +2

    So glad I found your channel!! Your explanations are so clear :)

  • @caothanhlong7577
    @caothanhlong7577 2 года назад

    wow, it's so clear and intuitive. Thanks a lot. It helps me to understand more after diving complicated concepts in textbook.

    • @BackToBackSWE
      @BackToBackSWE  2 года назад

      Thank you, glad you liked it 😀
      Do check out backtobackswe.com/platform/content
      and please recommend us to your family and friends 😀

  • @jackkrueckeberg2352
    @jackkrueckeberg2352 Год назад

    Thank you so much, you made this so much more understandable than my instructor

  • @DUSHYANTPANCHAL
    @DUSHYANTPANCHAL 4 года назад +5

    Really well explained the intuition. Exactly what I was looking for!

  • @Daniel-iy1ed
    @Daniel-iy1ed Год назад

    This video was fantastic, I needed a visualization badly. Thank you so much

  • @zcjsword
    @zcjsword 3 года назад

    Your "undo" gives me the epiphany! Thank you!

  • @daniellewis6228
    @daniellewis6228 10 дней назад

    i passed my algorithms class bc of u

  • @mahditalebi1770
    @mahditalebi1770 4 года назад +1

    great explanation. no stutter.no bullshit. just good solid well explained!
    thank you

  • @summerxia7474
    @summerxia7474 Год назад

    Please continue to do this series of lectures!!! You are way better than my teacher in college.

  • @ShashidharG_addString_
    @ShashidharG_addString_ 4 года назад +1

    Great job in explaining the reason why the undo operations work!!

  • @Young_Mocka
    @Young_Mocka 5 лет назад +1

    i don't know what to say but this vid saved me ... thx a lot

  • @mathewa7450
    @mathewa7450 Месяц назад

    This has helped me so much for me exam. Thank you so much.

  • @umairfaisal5861
    @umairfaisal5861 5 лет назад +3

    Hey man, that was really really helpful. Thank you so much for the awesome explanation.

  • @magickb7255
    @magickb7255 4 года назад

    best lecture i ve found so far, thanks!

  • @amaefulemercy8974
    @amaefulemercy8974 8 месяцев назад

    Thank you so much for this video, I've been struggling to understand this for awhile.. Buh now I get it..

  • @niritcohen7199
    @niritcohen7199 10 месяцев назад

    Thank you!! You make it so simple. Keep on, it's great!!

  • @nimidi2568
    @nimidi2568 2 года назад

    Thanks 🙏🏻
    Your way of explaining is perfect

  • @Nika-i6p
    @Nika-i6p 8 месяцев назад

    Best video on this subject! Thank you!

  • @isaacbuitrago2370
    @isaacbuitrago2370 4 года назад +1

    Thanks for explaining this. You have good teaching skills.

  • @markusmichaeldavidsnelder3395
    @markusmichaeldavidsnelder3395 4 года назад +1

    You're videos are amazing! Keep it up

  • @ZPSu-gs5hc
    @ZPSu-gs5hc 5 лет назад +1

    thanks for your video it help me to understand maxflow -mincut more directly

  • @AlwaysFiesta
    @AlwaysFiesta 4 года назад +2

    Thank you! Brilliant explanation, so easy and clear!

  • @constantinemacris9047
    @constantinemacris9047 8 месяцев назад

    Fantastic video. Beautiful work.

  • @MarkedMuichiro828
    @MarkedMuichiro828 2 года назад

    Thank you for making this great video! :) It's helping me with my graph algorithms course.

  • @sergten
    @sergten 4 года назад

    Finally an explanation that makes sense to me.

  • @rio-ty9vr
    @rio-ty9vr Год назад

    thanks, was so much easier to understand after i watched the video

    • @BackToBackSWE
      @BackToBackSWE  Год назад

      Thank you, appreciate it 😄 Also check out our Free 5 Day DSA Interview Prep Mini-Course - backtobackswe.com/ 🎉

  • @rutujashah3919
    @rutujashah3919 3 года назад

    Excellent teaching skills! I finally understood the concept now! Thanks a lot :)

  • @ADorssers
    @ADorssers 4 года назад

    Well done! Thank you very much for your work putting together this helpful video

  • @Lee-hd1eu
    @Lee-hd1eu 7 месяцев назад

    Better than my algorithm prof

  • @ankityadav-zz9gf
    @ankityadav-zz9gf 5 лет назад +3

    Thanks a lot for all your videos. Could you please upload some more videos on greedy problems and about the approach to solve them. for ex the gas station problem in Leetcode.

  • @bencameron8840
    @bencameron8840 3 года назад

    Great stuff! Really helped me understand these concepts!

  • @boratsagdiev6486
    @boratsagdiev6486 4 года назад +1

    Wow really clear and good video! Thanks!

  • @imotvoksim
    @imotvoksim 2 года назад +2

    Isn't the idea of the min-cut just that it is the bottle neck between s and t? Hence, pushing flow from s to t will be capped by the min-cut edges, therefore their value tells you the max-flow through the network. At least that is my intuitive takeaway from this :)

  • @sakshammahajan3568
    @sakshammahajan3568 3 года назад

    Best video i have ever seen thanks a lot.

  • @CarlosHenrique-pb5lz
    @CarlosHenrique-pb5lz 3 года назад +1

    Thank you a lot for this!
    This has helped me a lot with my presentation

  • @jakob1379
    @jakob1379 4 года назад +1

    Great explanation. Just a note Ford Fulkerson, it is not an algorithm but rather a method as it has multiple possible implementations with different run times

    • @BackToBackSWE
      @BackToBackSWE  4 года назад

      en.wikipedia.org/wiki/Ford%E2%80%93Fulkerson_algorithm 😳😳

    • @jakob1379
      @jakob1379 4 года назад

      ​@@BackToBackSWE okokok so it's just a matter of how strict you are before it is not categorized as an algorithm :D

  • @sippy_cups
    @sippy_cups 4 года назад +1

    Awesome video! really well presented

  • @崔裕铭
    @崔裕铭 2 года назад

    Thanks! Your video lets me understand the theorem.

    • @BackToBackSWE
      @BackToBackSWE  2 года назад

      Thank you, glad you liked it 😀
      Do check out backtobackswe.com/platform/content
      and please recommend us to your family and friends 😀

  • @ManishKumar-rz9ub
    @ManishKumar-rz9ub 10 месяцев назад

    I never understood that back edges concept until i saw this one.

  • @divyaranga6058
    @divyaranga6058 5 лет назад +3

    Hi Ben, Great work! These videos are so helpful for interview preparation. Can you make a video to go over Union-Find data structure ?

    • @BackToBackSWE
      @BackToBackSWE  5 лет назад

      Yes I can, just time limits my ability to contribute here.

  • @sr3277
    @sr3277 4 года назад +1

    thank you so much you made it very clear to understand.
    Saved me from failing ahaha

  • @patchiang13
    @patchiang13 4 года назад +1

    Thank you. The tutorial is quite helpful.

  • @nikhiljain3549
    @nikhiljain3549 3 года назад +1

    20:45 Can't we cut from in front of U for the minimum cut that will be 2+1 = 3?

    • @yuktikumari6042
      @yuktikumari6042 3 года назад +1

      graph is changed by then.....it is not the initial one ....now it is 4+3 = 7

  • @satthu7593
    @satthu7593 4 года назад +1

    Really good work! Thanks

  • @bodobaumstamm8386
    @bodobaumstamm8386 4 года назад

    Great video, clearified a lot! Thank you

  • @shamanstation6821
    @shamanstation6821 Год назад

    Thanks for nice explanation. Much appreciated.

    • @BackToBackSWE
      @BackToBackSWE  Год назад

      Happy Holidays 🎉 Thank you for your kind words, Shamanstation! We'd love to offer you a 40% Off our exclusive lifetime membership just use the code CHEER40 - backtobackswe.com/checkout?plan=lifetime-legacy&discount_code=CHEER40

  • @agnesakne4409
    @agnesakne4409 3 года назад +1

    20:35 why the heck do you not count the edge weighted 2?

  • @md.muidulalamtuhin1863
    @md.muidulalamtuhin1863 5 лет назад +1

    Thanks, Man for the awsome explanation

  • @tudor6210
    @tudor6210 4 года назад +1

    Great explanation!

  • @XORBob
    @XORBob 3 года назад

    Well done, that was a big help. Thanks!

  • @yashrajpriyadarshanpatra566
    @yashrajpriyadarshanpatra566 Год назад

    Thanks that was worth the watch!

  • @happyandinformedlife1212
    @happyandinformedlife1212 5 лет назад +1

    Great video , thanks. Love all your videos. Can you please make a video on 647 Approach #2: Manacher's Algorithm