Topological Sort | Kahn's Algorithm | Graph Theory

[@puneetkumarsingh1484]

This video is simply great. When I read it first, it took 3-4 hrs to fully understand the algorithm. The video has done the same in 14min.

[@Aldrin32f]

Repeated the same feat, KZbin recommendation to the rescue. PS Thanks @WilliamFiset

[@democreation3594]

@@Aldrin32f did the same and now I am here😁

[@shouryasingh2193]

I just now Solved Course Schedule II on leetcode using this algo

[@williamadams5034]

My favourite ordering is to Keep Sleeping.

[@AtharvaRao0104]

@11:54 : It should be "Afterwards loop through all the *nodes* (not edges) of the graph and add all the nodes with an incoming degree of 0" This is a brilliant series. You teach in concise and clear manner. I first studied graphs in 2003 at college but never understood it and had great fear in the mind for graph problems. I found a great teacher after 21 years and I understand it easily. Thank you very much.

[@njkevlani]

TIL Superman didn't know topological sort

[@1hpdell]

William, really appreciate your effort in making this Video! Effort behind this Animation is awesome, explanation is awesome too!

[@geniamartynova8844]

Clean and concise explanation. Easy to comprehend and remember. Thank you!

[@arthurcosta6185]

Appreciate from Brazil! In the next week I'll have the last graph exam in Pontifical Catholic University, and you helped me a lot

[@dheerajgopinath1892]

The way you explained is simply superb!! especially the "getting ready for school" example..

[@centr0]

Wow. I understood that. Great way of teaching. You’re amazing. Thank you, sir.

[@KevinDesai]

What an example to start with. Thanks for not starting with gibberish numbers. This makes more sense than all the other videos

[@krealle]

Thanks!

[@LUKFUNTV]

Really takes an effort to make it sooooooooooooo SIMPLE🙏🙏🙏🙏🙏🙌🙌🙌🙌🙌

[@emwistu22]

Your videos and your teaching style are amazing!!

[@robaczliwy]

Thank you for a very clear explanation. Implementation was easy once I grasped the concept you've laid out in this video.

[@cardel-qq6xp]

Underwear -> pants -> shirt -> hoodie -> socks -> shoes -> school

[@m.movsar]

Лучший канал по алгоритмам! Thank you William!

[@abhishektiwari7643]

Was following a course and couldn't understand this concept there but this video was so simple and better explained

[@njww13]

This video helped a lot since before I would constantly wake up in the morning and put on my school before my socks

[@markwillis2336]

I work from home. Why do I even need this getting dressed algorithm again? What an incredible breakdown, thank you so much for simplifying this complex topic so much for complete beginners like me.

[@mister_mad]

amazing explanation and visualization of the algorithm! a video unlike no other

[@AbrahamWilson]

Hey William, just wanted to say thank you. If it's possible could you make a series on DP like the one you're doing for graph theory.

[@vedantsharma5876]

That would surely be the best DP course on KZbin. I love how he explains

[@sandeepjnv13]

Not to undermine William but there’s KZbin channel “Inside Code”, he explains lot of concepts pretty well. He has dynamic programming content as well. Also a Udemy course on dynamic programming

[@pelvispresley22]

The freecodecamp video from Alvin Zablan on DP is as good as it gets

[@JeremyIglehart]

Great video. Small suggestion - right at the end where you check if index is not equals to n it would be really nice if you also showed an example of what would happen with your code if there was a cycle in the graph.

[@jamesbon68]

For anyone wondering about this, if you imagine a 3 node cycle, A -> B -> C -> A. Notice that you will never add these nodes to the queue because their indegree will never be 0. This implies that index will also never be larger than n.

[@Sunny-vl1ff]

Thanks! It is great to see how the algorithm works in practice.

[@abhinavboyed6624]

I'm about to binge watch all your videos. Thanks for the awesome content!

[@mercyomwoyo985]

Thanks William for the visualization and Animation! I clearly understand the concept now!

[@przemekbary]

Thanks a lot for the explanation. You've got a great gift of explaining complicated thing easy (which IMO is the sign of a genius mind)

[@David-fy1sn]

Wow great explanation in only 13 mins!

[@shnerdz]

great explanation as always. please make a video on segment trees next! such a powerful yet simple data structure

[@kartarsingh7776]

That was a great example(dressing up) at the start of video.

[@NoName-ip4tt]

Animation you conduct has heart beat sound as background. I like it :)

[@Sauce-ke]

I hope all of my professors are teaching the same as you. I really need a data structure 1 on 1 teacher to teach me everything

[@yamatolowa2256]

this is 1 on 1 teaching i believe

[@zy3749]

Thank you so much, it is the most clear explanation I've found.

[@hix0071]

Keep it up William. May you reach million subs next year !

[@randm-6uy]

just looking at the playlists you made motivates me

[@jabir5768]

HI ! Really nice explanation but I was wondering about the complexity why is it O(E+V) ? Shouldn't be O(V) since we iteratre of the nodes twice to set the degrees, then the while loop iterates exactly V times ?

[@AryanPatel-wb5tp]

What is run time , O(V+E) ? can someone explain line by line using the pseudocode if possible

[@northridgefield]

Great clarity - quality content.

[@Junposs]

Thank you Wiliam, I finally understand what Topological Sort is!

[@fantasy9960]

thank you so much William! this is extremely helpful for beginners!

[@tarunstv796]

Will this approach also work for cyclic graphs? *When I say it will work, I mean it will let us determine whether the graph is cyclic or not, or if a DAG will provide valid ordering.

[@nehascorpion]

Awesome content! Thank you for putting in so much effort. Appreciate it!

[@AnonymousMaykr]

This is an excellent explanation, thanks!

[@shantanubapat6937]

We have to loop through all vertices to find those who have in degree of zero. Can we optimize this using heap or priority queue?

[@WhyAnkurGautam]

We have to loop through once to find the vertices which have indegree of zero and put it in queue. After that we just have to pop the element and decrement in-degree of its dependent nodes. When you are decrementing you can check if it is zero or not. If it is zero than you can put that node into queue. This way you dont need priority queue. Only using queue will work in O(N+E) I guess.

[@spicy_wizard]

FANTASTIC. The problem with DFS on topological sort is that the recursion is too expensive, BFS is faster in all other aspects

[@puneetkumarsingh1484]

Alternatively, we can implement the DFS topological sort algo, using stack.

[@vm7240]

What is the time complexity of calculating indegree? O(V^2) or O(V + E)? V = no of vertices E = no of edges Since there are two for loops, ig it should be v^2

[@Learner010]

Very nice explanation. please make a video on articulation point and bridges

[@agnelamodia]

Easy and simple. Marvelous.

[@soanonso]

Nicely explained - thanks for this.

[@leducphuclong]

Thank you so much, I really appreciate your video. Please continue...

[@FaustoCarvalho]

What tool have you used to draw and animate these graphs? Thanks

[@neerajkulkarni6506]

10/10 beautifully explained!

[@mickeynig1]

Thanks Mr. Fiset really awesome explanation

[@atharvas4399]

this is 100 times better than my algo professor

[@sstp105]

amazing explanation!

[@il5083]

Nice video. Is there a reason not to use Kahn's algorithm instead of the DFS topological sort in an interview since this is easier to memorize and code?

[@tanmaykharshikar9419]

This video is a gem, thanks! You have a new fan :)

[@VijayKiran225]

beautiful explanation .. keep up the good work.. subscribed as well

[@bxfootballphenom]

I've been running into a problem with this algorithm when there is no node 0. In this case, the inDegrees array will always have the 0th index be 0, and since there is no "0" node to add any incoming dependencies it will incorrectly add it to the queue. This also ends up breaking the rest of the algorithm since the true size of the inDegrees array is 1 less than what we were expecting. For example if our vertices are [1,2,3,4] the inDegree array at initialization will be [0,0,0,0] and will only match up to vertex 3, since at iteration it will be expecting i to start at 0. Has anyone else come across this and how have you solved this?

[@WilliamFiset-videos]

Hey Cesar, when labelling the nodes of the graph you should always label the first node as node 0, the second node as node 1, the third node as node 2 and etc... This should ensure that you always have a node 0, does this resolve your problem?

[@bxfootballphenom]

@@WilliamFiset-videos Thanks!

[@ManishaSingh-yk5en]

Can we get the ppt which is being used in the video?

[@twistedlog24]

thanks for explaning this so clearly!!

[@76lunagogogo]

Regarding the DAG, isn't the (3) also not he DAG as the same reason that (4) one has?

[@avipatel1534]

Thanks this video helped me optimize my sort code for leetcode course scheduling

[@droy7528]

Thanks a lot, William for all these golden videos. I recently came across Aho- corasick and finding it really difficult to umderstand it properly. So I am commenting on the latest vdo here...hoping u would see my comment. We would be really grateful if u could pull up a vdo on Aho-Corasick. Thanks in advance.

[@RushOrbit]

Where did you find the intro music for your videos?

[@andreyvalverde4780]

hi there, quick question, based on the code, how do we make sure that we are not adding vertices that we've already visited?

[@babumon5351]

Very nice explanation. Thanks

[@algorithmscasts902]

Nice animation and great explanation, thank you

[@kevintran6102]

Good as always. So easy to understand.

[@ameynaik2743]

Nice video, how is this different from another video you have on top sort using dfs?

[@lazysky1234]

Thank you for your video, great explanation!

[@m-meier]

This was awesome! Subscribed!

[@30天冥想练习]

Kahn : Implements Topological Sort. Superman : Am i a joke to you ? Wears underwear after pants.

[@akashshirale1927]

can u post videos on identifying kadane's algorithm for dynamic programming

[@amanbhatia7442]

just realized you have a similar algorithm for the dfs approach as well? , But I really like this, feels intuitive

[@LUKFUNTV]

I recommend this.........to all the before_watching_read_comments_section people 🙌🙌🙌

[@djchrisi]

Came here from advent of code day 5 ☺

[@ankclub1444]

Same

[@ligma5168]

Bit late but same

[@jeehar1]

It was clear, thanks again man

[@无名-c1f]

What drawing software to use？ The picture is very nice

[@yujianzhao6461]

Thanks a lot man! I really appreciate your work!

[@mostafaarafa1461]

Thanks, You explained it really perfectly

[@ricardo7240]

Awesome, keep it up!

[@prabhat2342]

wonderful explanation, thanks man:)

[@pankajpanwar9385]

Even tho you say that the in-degree array has to be number of nodes the current index is connected to indegree[0] = 0 Actually in code it seems like you're populating the in-degree by adding the number of nodes connected to the current index indegree[0] = 3

[@adityatripathi9045]

great work !!

[@geomichelon]

great video! Thanks man!

[@ksenthu]

Best explanation ever, thank you!

[@jisanson]

Thank you for this awesome video!

[@bullymaguire2335]

Dude just increase ur volume .no other complains .👍

[@akidanis6984]

holy shit this was such a great explanation, tysm!!

[@WebSurfingIsMyPastime]

Great Video!

[@caseyyeow1649]

Sound?

[@djklsdf-32sdf]

최고의 영상

[@AZ-id1oo]

4:20 6 is incorrect. It carries a cycle between the three bottom-most vertices.

[@WhyAnkurGautam]

No there is no directed cycle in 6

[@pamp3657]

very good video

[@mnchester]

great vid

[@gainingcrouch]

My son often puts his pants on before his underwear; sweater before shirt, just to go back to do it all over again. I think I forgot to install the TopSort algorithm for him.

[@akshatmehra3951]

You're the best man

[@rajanlagah4529]

u r 3brown4blue guy Am i correct?

[@amalbiju7805]

python3 implementation: graph = [[1, 2, 3], [5], [], [], [2, 3], [2]] queue, in_degree, ordering, index = list(), [0] * len(graph), [-1] * len(graph), 0 for Neighbour in graph: for To in Neighbour: in_degree[To] += 1 for i in range(len(graph)): if in_degree[i] == 0: ordering[index] = i queue.append(i) index += 1 for node in queue: for neighbour in graph[node]: in_degree[neighbour] -= 1 if in_degree[neighbour] == 0: queue.append(neighbour) ordering[index] = neighbour index += 1 print(ordering if index == len(graph) else 'cycle detected')