Maximum flow Minimum Cut Algorithm

[@amandabrown1696]

The "water through the driver side" explanation really helped me understand which paths should and shouldn't be counted. Thanks!

[@jdcasanasr]

I love how creative you are with examples. Congrats mate!

[@vivianoranges]

When they taught networks at school, I missed the topic and I have my HSC (NSW) standard/general maths exam in a week so this really saved me. It's a bit tedious, but going through each cut one by one visually to find the minimum definitely helped clarify my understanding! Massive thanks😭

[@prefix7774]

for me its in 12 hours and im not ready

[@DD-uh5to]

i need you to know that youre saving my life right now thank you so much

[@ry3833]

YOU EXPLAIN SO WELLLL thank youu

[@gokulvellingiri4445]

Great one. I am so impressed with your driver and passenger concept.

[@liv3580]

best explanation i've seen for this topic so far

[@RetiringMotivation]

Wow, You're so great at explaining and teaching, I have my external math exam tomorrow, and this was the one I got stuck on, but you made it so easy to understand and figure out. Tysm 🙏, you're great man!

[@pradeexsu]

Thanks joel 😊 i really love the way you explain the concept. Thank you so much ❤️🙏 for amazing explanation.

[@JoelSperanzaMath]

Thanks Pradeep, I'm glad you enjoyed it.

[@sumitar6478]

Very well explained

[@iremmatasoy]

best video ever on this topic. BEST

[@rubenmatton6258]

I'm wondering how do they make these kind of videos where there is an invisible board

[@Dule-my1yc]

I'm mindblown every time haha

[@yashkumarkandoi8143]

Amazing explanation. Understood in one go!

[@theCRGlife]

Awesome Video, Really Informative. Commenting for KZbin Algorithm

[@jordiespinafont2984]

Thank you so much for good videos, it is so helpful to get clear and step by step explanations on concepts. Really appreciate your teaching! I was wandering if there is a last cut that can be made: Starting from E(A,C) -> E(C,D) -> E(D,E) -> E(D,B) -> E(A,B)

[@Dule-my1yc]

I don't think that would work, because when you are making that last cut through (A,B), your cut is going downward rather than upward. Although you have managed to cut through each line only once, you won't be able to work out the minimum cut maximum flow. The car (as Mr Speranza mentioned it) will not be moving at the top of the page as every single other cut had done, rather it would be moving downwards

[@ihaveskillissue69]

Got confused when you were talking about driver's side and passenger side, then I realized you are Australian! Regardless amazing video! Cheers from the States.

[@JoelSperanzaMath]

Sorry mate, I hope it wasn't too confusing.

[@imtiredgoodnight]

Great video and channel, very well explained.

[@BenHizak]

Beautiful presentation. Are you actually drawing on a transparent board? Thank you for the video

[@HausOfStream]

THANK YOU SIR

[@259mit]

Best NF video

[@DuckInRow]

Great job!

[@ashberry2852]

Thank you mate

[@allgood2176]

Good job helped me get good mark, very good explanation 👍

[@Jmart786]

Great video, but isn't there an 8th cut hat goes through AC, CD, DE, DB, AB?

[@JoelSperanzaMath]

Good question and it highlights the most common source of error in this kind of question. The cut you describe is fine through AC, but if you then "drive your car" through CD the "water" will be flowing into the "driver's side". Remember when making cuts the "water" can only ever flow in the "passenger side".

[@jonathanwhite1733]

@@JoelSperanzaMath But isn't C3 going through CD?

[@zippykat6517]

I was wondering if there is any way to know if you have gotten all the cuts? For spanning trees you can see that the number of edges is equal to the number of vertices, minus 1. Is there some rule for cuts too?

[@basedstvr3132]

really well explained

[@stanley9653]

If the start pipe is on the right and the sink is on the left is it better to re-draw the pipe network from left to right and then do the algorithm? Or would it be better to just do the algorithm and switch the drivers side. Thanks for the video by the way! 👍

[@JoelSperanzaMath]

How about just turning your page upside down?

[@stanley9653]

@@JoelSperanzaMath Yes that works :) thanks for all your math help I've finished my Networks topic successfully 👍

[@michaelklaczynski3650]

Okay, but how do you do this on a 1000-node, fully connected graph?

[@max-_-6352]

Wow this saved me for my test tmr thanks heaps!

[@JoelSperanzaMath]

Glad it helped!

[@heelsadhna]

One cut is missed 11-3-5-5-8. Although it doesn't matter.

[@lauminator]

Well, according to Joiel it does matter, otherwise the algorithm doesn't work!

[@aybuke9495]

Hello thanks for video. But I didn't understand why you ignored "5". I think c5 should be 1+3+5+3 ?Am I wrong?

[@JoelSperanzaMath]

I'm ignoring 5 because that water is flowing away from the sink, not towards it. In the video, I explain water needs to follow in the "passenger side" of the car, not the "driver side".

[@aybuke9495]

@@JoelSperanzaMath Aaa got it. I missed the that part of video, sorry. Thanks for explanation😊❤

[@antongarcia7044]

Where is the algorithm???

[@JustAqua]

This saved my exam thank you so much

[@JoelSperanzaMath]

Good to hear!

[@conxx1333]

but the driver is on the left side side ,in real car right

[@JoelSperanzaMath]

I'm Australian

[@humza_shah]

Awesome video! I found another cut that you missed. The cut that represents the partition of the nodes {A, D}. So drive up through A-C. Then turn right through C-D. Then up through D-E. Then left through B-D. Finally, up through A-B. This still cuts A off from E completely since the car goes from the bottom all the way to the top. The way I think about cuts for network flow problems is partitioning nodes into every possible subset of nodes (always including A and excluding E). So we have {A}, {A, B}, {A, C}, {A, D}, {A, B, C}, {A, B, D}, {A, C, D} and {A, B, C, D} thus 8 cuts in total. To connect with your cuts. c1 = {A}, c2 = {A, B}, c3 = {A, B, D}, c4= {A, C}, c5 = {A, B, C}, c6 = {A, B, C, D} and c7 = {A, C, D}. The only one we are missing is {A, D}. Thankfully, since {A, D} = 11+5+5+8 the min-cut/max-flow solution is still correct but I thought it might be worth pointing out to help with not missing any cuts! Hope this helps anyone to have a systematic way in finding and not missing any cuts.

[@Shoeb-D]

Thank you ❤

[@kingbreaux]

Hi Mrs, I'm studying are you proud?

[@lilbigger5387]

my teachers say cut from top to bottom

[@justin_w7160]

Video so we’ll done ✅

[@johnmifsud6814]

An average student would spend half an hour doing this method - stuffing the exam. What if you miss a cut - disaster....

[@adventurer2395]

1:48 hehehe

[@adventurer2395]

The passenger/drive analogy does not translate well to a global audience and confused me more. I also did not understand the why behind this.

[@zxoowoo6094]

thanks, super clear, like ur examples