Algorithms Course - Graph Theory Tutorial from a Google Engineer

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This full course provides a complete introduction to Graph Theory algorithms in computer science. Knowledge of how to create and design excellent algorithms is an essential skill required in becoming a great programmer.
You will learn how many important algorithms work. The algorithms are accompanied by working source code in Java to solidify your understanding.
💻 Code: github.com/williamfiset/algor...
🔗 Slides: github.com/williamfiset/Algor...
🎥 Course created by William Fiset. Check out his RU-vid channel: / @williamfiset-videos
⭐️ Course Contents ⭐️
⌨️ (0:00:00) Graph Theory Introduction
⌨️ (0:13:53) Problems in Graph Theory
⌨️ (0:23:15) Depth First Search Algorithm
⌨️ (0:33:18) Breadth First Search Algorithm
⌨️ (0:40:27) Breadth First Search grid shortest path
⌨️ (0:56:23) Topological Sort Algorithm
⌨️ (1:09:52) Shortest/Longest path on a Directed Acyclic Graph (DAG)
⌨️ (1:19:34) Dijkstra's Shortest Path Algorithm
⌨️ (1:43:17) Dijkstra's Shortest Path Algorithm | Source Code
⌨️ (1:50:47) Bellman Ford Algorithm
⌨️ (2:05:34) Floyd Warshall All Pairs Shortest Path Algorithm
⌨️ (2:20:54) Floyd Warshall All Pairs Shortest Path Algorithm | Source Code
⌨️ (2:29:19) Bridges and Articulation points Algorithm
⌨️ (2:49:01) Bridges and Articulation points source code
⌨️ (2:57:32) Tarjans Strongly Connected Components algorithm
⌨️ (3:13:56) Tarjans Strongly Connected Components algorithm source code
⌨️ (3:20:12) Travelling Salesman Problem | Dynamic Programming
⌨️ (3:39:59) Travelling Salesman Problem source code | Dynamic Programming
⌨️ (3:52:27) Existence of Eulerian Paths and Circuits
⌨️ (4:01:19) Eulerian Path Algorithm
⌨️ (4:15:47) Eulerian Path Algorithm | Source Code
⌨️ (4:23:00) Prim's Minimum Spanning Tree Algorithm
⌨️ (4:37:05) Eager Prim's Minimum Spanning Tree Algorithm
⌨️ (4:50:38) Eager Prim's Minimum Spanning Tree Algorithm | Source Code
⌨️ (4:58:30) Max Flow Ford Fulkerson | Network Flow
⌨️ (5:11:01) Max Flow Ford Fulkerson | Source Code
⌨️ (5:27:25) Unweighted Bipartite Matching | Network Flow
⌨️ (5:38:11) Mice and Owls problem | Network Flow
⌨️ (5:46:11) Elementary Math problem | Network Flow
⌨️ (5:56:19) Edmonds Karp Algorithm | Network Flow
⌨️ (6:05:18) Edmonds Karp Algorithm | Source Code
⌨️ (6:10:08) Capacity Scaling | Network Flow
⌨️ (6:19:34) Capacity Scaling | Network Flow | Source Code
⌨️ (6:25:04) Dinic's Algorithm | Network Flow
⌨️ (6:36:09) Dinic's Algorithm | Network Flow | Source Code
--
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Опубликовано:

31 июл 2024

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Комментарии : 747

@TheAIGuy 4 года назад

I feel smarter just by clicking on this video

@W1nDfd 4 года назад

you will feel even smarter if you click "like."

@sajateacher 4 года назад

How Pavlovian.

@arifarslanturk2951 4 года назад

@intvar8372 4 года назад

from InternetLib import smartnessModule

@meditating010 4 года назад

@@W1nDfd lol

@CuongHut 4 года назад

OMG, thank to RU-vid for recommending this video to me while I'm studying it for 3 days. You guys really save my life.

@iliyaniliev6798 4 года назад

This is crazy good and somewhat demanding video to comprehend for the viewers. Thank you so much!

@ProgrammingwithPeter 4 года назад

I got interested on this when I saw a presentation which explained briefly why graphs are fast to find data. Now this is here, great, going to watch it all.

@foobars3816 3 года назад

What presentation do you mean?

@kinghadu9611 3 года назад

The way the graphics are done with black backgrounds and colorful diagrams and colored texts makes this video incredibly engaging, fun and addicting to learn.

@maksymshvernenko799 Год назад

I keep coming back to this for refreshers while preparing for my interviews. Such a wonderful resource.

@weiyao806 4 года назад

I like the the parts you provides real word applications on each algorithm/graph. It helps a lot when solve problem described as a real problem.

@KotaAvengers 4 года назад

OMG! Glad to see your here William, I owe my career as a developer to you from your python lectures.

@ashishbisht1805 3 года назад

OK Bye how did u get 203k subs with very few views

@jwadaow 3 года назад

@@ashishbisht1805 Algorithms!

@aurobindsahu7513 3 года назад

@@jwadaow 😂😂😂😂

@neilmande5148 3 года назад

@@jwadaow nice one

@siddiquijaan4169 3 года назад

@@ashishbisht1805 a

@sdsa007 3 года назад

Thank you so much William, for your kind attention to details. I did not receive any teaching on Graph Theory in the 90s when I thought I had graduated. Your patience has made it possible for me to understand a topic that has tremendous value, I believe both for other advanced topics and implementing real-world solutions right away! Thank you, again William!

@prakashg1944 3 года назад

this guy is awesome..He covered almost all the concepts in Graph... really worth it...

@kunaljoshi8038 4 года назад

Got my DS Exam in few days which extensively covers Graphs. I needed this. Thanks.

@akshaykumar-io5nu 2 года назад

This is really phenomenal work. You guys are doing wonderful work. Thanks a lot♥️

@batmanarkhamcity3684 3 года назад

Finest selfless work in history of computer science ever! thank you sir, you will be remembered for ages to come!

@gsb22 3 года назад

Open Source community : Hold my Open Source Code.

@anurandutta2217 4 года назад

My search history be like: 3 min memes - 5 min funny videos - 6 HOURS+ GRAPH THEORY

@IrizarryBrandon 4 года назад

😂😂😂 so true

@Vladislav888 3 года назад

Also six hours The Last Jedi analysis.

@timothy6955 3 года назад

mine's the other way around

@anurandutta2217 3 года назад

@@timothy6955 that's the right way!

@Rayyankhantheboss 3 года назад

gunny how u spend more time watching innumerable meme and funny videos but only 3 or 5 min watching a freecodecamp video lol

@pedrolopes7813 2 года назад

Love this man, really. Very good presentation of such a complex topic. Thanks for doing this William!

@chetanraikwar3546 3 года назад

Amazing !!! That's what I wanted. All graph algorithms in one place.

@redhood7105 4 года назад

Really appreciate this type of content. Very useful. Thanks

@pial2461 4 года назад

Please Make a Dynamic Programming Series

@hubertjk200 3 года назад

If you are still interested, he made one on his channel.

@AsskickerCesar 3 года назад

@@hubertjk200 where is it ?

@shailypatel585 3 года назад

@@hubertjk200 what do u mean by still interested??

@srimanproductions8396 3 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-oBt53YbR9Kk.html

@srimanproductions8396 3 года назад

dynamic programming

@sgdfdsgs 2 года назад

William thank you so much, you are a fantastic teacher and I am happy I found your channel through this video.

@MiffyDad 4 года назад

O!M!G! almost 7 hours algrithms course, I can sleep until next week!

@bhavanachaganti6952 4 года назад

🤣

@devangsrivastava6736 4 года назад

Ikr

@computersciencecafe 3 года назад

Great video, and well explained. Particular like the explanation of Dijkstra's Algorithm. 7 hours of algorithms video, good going !

@akshbansal7715 3 года назад

These pseudo-codes are amazing and easy to understand. Thanks a lot!

@arnavdeshpande3764 4 года назад

The best and the most practical explanation ever

@shubhamshinde5643 4 года назад

I can't tell you how happy I am just finding this video becoz lately I was learning a course but the only this missing was graph on mycodeschool RU-vid thnx man for making these

@praveen3123 4 года назад

one of the most selfless work !!

@KaWiz 2 года назад

great video, very easy to follow! just wanted to say, at 49:08 where having separate x,y,z queues is suggested in order to avoid using a coordinate wrapper like struct coord { int x,y,z } that has to be packed/unpacked - keeping everything in one queue will preserve memory locality (sequential accesses in the same area of memory, likely in the same cache read), while having to access 3 different queues every iteration will likely be a performance hit as they cause cache misses (which, even if they're contiguous, would be inevitable above a certain number of vertices), and quite possibly be worse than packing/unpacking a structure depending on how the compiler optimizes that as an alternative, if you want your queues to just be primitives without any packing, just push x,y,z sequentially onto the same queue, and dequeue them 3 at a time as well. it's not any more complex than managing 3 queues at once, avoids packing, and most importantly doesn't require both allocating and accessing multiple data structures. the choice of having 3 queues just to avoid using a wrapper is pretty baffling!

@aman4434 Год назад

pretty cool explanation. i like the dequeue 3 at a time idea.

@AstheaTV 3 года назад

Graph Theory, my favorite! Awesome, now I can refresh my knowledge, thank you for sharing this! :D

@nihadalmahrooq4335 3 года назад

Great effort putting this together. Thanks, graph data structure and its enumerations has excellent properties, while combines knowledge and computation for difficult solutions

@mervemall151 4 года назад

I was going to make a timestamp map for the topics but realised you already did it. Great video and it has no ads??? You are great. Thank you

@pyarepiyush 4 года назад

Wait where is this timestamps map?

@mervemall151 4 года назад

@@pyarepiyush video description SHOW MORE

@that_funny_guy496 4 года назад

Thank you so much for such a detailed and easy explanation.

@douglashurd4356 4 года назад

Wow! There is smoke coming out of my ears! VERY well explained. Thank you!

@himanshuraj1874 3 года назад

Are you alright?

@douglashurd4356 3 года назад

@@himanshuraj1874 Yes, my brain was overheating but I feel much better now.

@techkyguy 4 года назад

thanks for making this video. You made algorithms very easy to learn. I wish you could add Kruskal's minimum spanning tree to the list. Thanks

@tanho7614 3 года назад

I love William so much. Thank you so much, Sir!!!!

@nipunikalnu8645 4 месяца назад

Everytime I need to revise graphs I watch this video. Thanks William!

@Bargains20xx 4 года назад

That covers all the algorithms I was taught in my undergrad and much more

@RonnieLutaro 4 года назад

Really?

@jivan476 4 года назад

No A* though

@Garentei 3 года назад

@@jivan476 I'd say that algorithm doesn't belong here.

@chatrughanprasad7778 4 года назад

Stat of art explanation! Thanks for the knowledge sharing.

@deepaksinghverma8751 4 года назад

Really really thank u,you guys are providing free education for us.Thank u

@i_dont_likevodka3062 4 года назад

the preview looked really cool so I decided to learn the skill

@ritikchail7330 2 года назад

Everything covered from scratch. Loved learning from this lecture.

@NareshKumar-dw9xp 4 года назад

Thank RU-vid for a recommendation . I was wandering to learn graph in java or algorithms. Now I have found a treasure. Thanks!

@HelloWorld-tn1tl 3 года назад

This is gold !!! Very very good !!! Easy to understand !!! Should get more up vote !!!

@user-xg6ez8mj7i 4 года назад

That's amazing ! thank you.

@davidepasini3807 4 года назад

This video is gold! Thanks

@r_u_p_d9776 4 года назад

⭐️ Course Contents ⭐️ ⌨️ (0:00:00) Graph Theory Introduction ⌨️ (0:13:53) Problems in Graph Theory ⌨️ (0:23:15) Depth First Search Algorithm ⌨️ (0:33:18) Breadth First Search Algorithm ⌨️ (0:40:27) Breadth First Search grid shortest path ⌨️ (0:56:23) Topological Sort Algorithm ⌨️ (1:09:52) Shortest/Longest path on a Directed Acyclic Graph (DAG) ⌨️ (1:19:34) Dijkstra's Shortest Path Algorithm ⌨️ (1:43:17) Dijkstra's Shortest Path Algorithm | Source Code ⌨️ (1:50:47) Bellman Ford Algorithm ⌨️ (2:05:34) Floyd Warshall All Pairs Shortest Path Algorithm ⌨️ (2:20:54) Floyd Warshall All Pairs Shortest Path Algorithm | Source Code ⌨️ (2:29:19) Bridges and Articulation points Algorithm ⌨️ (2:49:01) Bridges and Articulation points source code ⌨️ (2:57:32) Tarjans Strongly Connected Components algorithm ⌨️ (3:13:56) Tarjans Strongly Connected Components algorithm source code ⌨️ (3:20:12) Travelling Salesman Problem | Dynamic Programming ⌨️ (3:39:59) Travelling Salesman Problem source code | Dynamic Programming ⌨️ (3:52:27) Existence of Eulerian Paths and Circuits ⌨️ (4:01:19) Eulerian Path Algorithm ⌨️ (4:15:47) Eulerian Path Algorithm | Source Code ⌨️ (4:23:00) Prim's Minimum Spanning Tree Algorithm ⌨️ (4:37:05) Eager Prim's Minimum Spanning Tree Algorithm ⌨️ (4:50:38) Eager Prim's Minimum Spanning Tree Algorithm | Source Code ⌨️ (4:58:30) Max Flow Ford Fulkerson | Network Flow ⌨️ (5:11:01) Max Flow Ford Fulkerson | Source Code ⌨️ (5:27:25) Unweighted Bipartite Matching | Network Flow ⌨️ (5:38:11) Mice and Owls problem | Network Flow ⌨️ (5:46:11) Elementary Math problem | Network Flow ⌨️ (5:56:19) Edmonds Karp Algorithm | Network Flow ⌨️ (6:05:18) Edmonds Karp Algorithm | Source Code ⌨️ (6:10:08) Capacity Scaling | Network Flow ⌨️ (6:19:34) Capacity Scaling | Network Flow | Source Code ⌨️ (6:25:04) Dinic's Algorithm | Network Flow ⌨️ (6:36:09) Dinic's Algorithm | Network Flow | Source Code

@root8088 4 года назад

Woahh! Thanks

@astrohan 4 года назад

hum....god bleess you!

@madalinspoiala1249 4 года назад

You are the real mvp. Thank you!

@emenikeanigbogu9368 4 года назад

wow everyone can copy and paste

@infoeducardo6915 4 года назад

@@emenikeanigbogu9368 this copy paste is beneficial for those watching on mobile app which doesn't show intervals as links in description

@rahulmistry9173 4 года назад

Awesome!! Please make a series on Dynamic Programming & Greedy Algorithms!!!

@adipratapsinghaps 3 года назад

I solved the Dungeon problem link in your video. I jumped to Kattis and solved the problem. 0.27 seconds with Java. With the 3D matrix. Now I wish I was a compatitive programmer. But I hardly care now. I wrote a simple to read solution. And got it running in the first attempt. Writing clear code in Competitive programming slowed me down initially. But then writing clean code is all about clear thinking. And in the long run, it has helped me make less mistakes, and actually be able to solve problems. I couldn't even solve a simple problem earlier. Thanks to my decision of learning and practicing writing clean OOP code I am able to solve problems today.

@SebinMatthew 2 года назад

you are awesome. thanks for the service. when i reach my goal, i will definitely contribute. thanks so much.

@mohammedjawahri5726 4 года назад

I love how the "pseudocode" is just straight up python lmao

@Otomega1 4 года назад

He use "function" kw instead of "def" kw

@Otomega1 4 года назад

This make all the difference

@morgengabe1 4 года назад

@@Otomega1 so you claim

@arrakisarrakis4696 4 года назад

it's the main aim of python

@mishasawangwan6652 4 года назад

Mohammed jawahri not exactly (ie function definition , looping with a scoped index variable , the reverse function and prbly a bunch of other little things) but i do see why one would think it ..anyway it’s not difficult to transcribed into python (or any language really heh.. hence ‘pseudo code’)

@ritwek98 4 года назад

Thanks, really helpful work !!!

@shizx2z 4 года назад

Almost done going through this video. I've been doing javascript implementations of everything taught in this video and it's really leveling up my coding skills & understanding of graph theory. Love this content!

@vinaynair1911 4 года назад

can you share the code on github?

@shizx2z 4 года назад

@@vinaynair1911 Sure, I'll put together a repo and comment back here with a link.

@vinaynair1911 4 года назад

@@shizx2z you're the best!! Thank you so much.

@Pclub4ever 3 года назад

@@vinaynair1911 lol

@user-de8uu9vr3l 2 года назад

@@shizx2z where's the repo???

@mitchiarikov2614 3 года назад

Fantastic video! Thank you!

@shubhamvardaan3576 3 года назад

very crisp and clear video

@games4us132 4 года назад

huge like for "no ads" !

@7th_CAV_Trooper 2 года назад

wow, this is pretty much everything you need to know about graphs

@souravkedia9102 4 года назад

Good work and good explanation, really made simple

@rahulkumarsinha4239 3 года назад

Just one word for this tutorial..Very very thankyou..

@BinDerUser 3 года назад

good to see my university taught me all the algorithms shown here

@ekejma 3 года назад

I really enjoyed this thanks.

@AjayKumar-bb4yk 4 года назад

Thanks a lot for the Course.

@yuhanzhang2882 4 года назад

Great. I skipped the easy parts, all the coding explanation, and the played the video at 1.5 speed to go through. Graph Theory is the math class that I regretted having missed during college. Thanks for making this tutorial.

@danielk8452 4 года назад

This is awesome, if you could please make a video about dynamic programming please🙏

@juancamiloq1 4 года назад

Awesome videos as always

@silviuciobanu8730 2 года назад

Great stuff, thank you!

@BeastMaster-dq8vt 4 года назад

This channel is simply amazing

@entropy7571 2 года назад

I had a smile on my face as soon as I heard the familiar voice. Pleasantly surprised to find William here

@debbahisaad109 4 года назад

An absolute must watch would be this very same course using C++ OOP implementation.

@Garentei 3 года назад

You can do it yourself.

@varunpatkar501 3 года назад

I came here as i was doing the Free Ticket problem on Codechef and one of the first type of data structure to store was an Adjacency List. And i did not know anything about it. The thing that its so intuitive is really good to know. Great Course by the way. Really interested in Graph Theory because i was trying to solve a question. Great way to learn i guess.

@cristianiorga6393 3 года назад

Every time i come back to your video I want to give you one more like!

@jamest7700 2 года назад

Great explanations!

@Rock28099 4 года назад

You guys are the best....

@nandagopalnaskar2452 4 года назад

Dynamic programming please.Thank you for your efforts....

@azizbekibnhamid642 Год назад

amazing course!

@peternguyen9995 3 года назад

20:01 I think it should be "whose removal increases the number of disconnected components." Found the "disconnected" part on GeeksForGeeks and it makes sense.

@toggotoggo 3 года назад

I agree, I was stuck on it trying to justify it for a minute, then I thought about visiting the comment section

@ub-relax6800 24 дня назад

Thank you so much! My battle with insomnia is finally over!

@sasankv9919 4 года назад

This video is a gold mine

@darthvader_ 3 года назад

He is such a person

@georgedrooj8800 4 года назад

Very helpful DP next time please 🥰

@sahilanower9189 2 года назад

This is Gold!

@prakhar4585 4 года назад

He is a gem and also an ICPC world Finalist.

@manicsurfing 3 года назад

Insane clown posse champion?

@tristanhurley9071 4 года назад

this is good. thank you.

@shawnmofid7131 4 года назад

Wow, I am so glad I found this content. Thank you so much. Re: Eulerian paths and circuits, I guess the rule that all nodes have to be connected does not apply to the directed graphs? The last example you shared had a node just by itself, but you said that it has a path b/c the other component had in - out = 1 and out - in = i and the rest had the same number of in and out edges.

@riantix 4 года назад

Nodes that have no edges do not have to be connected. However, all nodes with at least one edge must be connected to each other.

@prashantbhrgv 4 года назад

Truly Invaluable!

@yashpandey350 4 года назад

can you explain why?

@Stl71 4 года назад

Happy for the video content, happy for Java being used!

@gitlit5489 4 года назад

⌨️ (0:00:00) Graph Theory Introduction ⌨️ (0:13:53) Problems in Graph Theory ⌨️ (0:23:15) Depth First Search Algorithm ⌨️ (0:33:18) Breadth First Search Algorithm ⌨️ (0:40:27) Breadth First Search grid shortest path ⌨️ (0:56:23) Topological Sort Algorithm ⌨️ (1:09:52) Shortest/Longest path on a Directed Acyclic Graph (DAG) ⌨️ (1:19:34) Dijkstra's Shortest Path Algorithm ⌨️ (1:43:17) Dijkstra's Shortest Path Algorithm | Source Code ⌨️ (1:50:47) Bellman Ford Algorithm ⌨️ (2:05:34) Floyd Warshall All Pairs Shortest Path Algorithm ⌨️ (2:20:54) Floyd Warshall All Pairs Shortest Path Algorithm | Source Code ⌨️ (2:29:19) Bridges and Articulation points Algorithm ⌨️ (2:49:01) Bridges and Articulation points source code ⌨️ (2:57:32) Tarjans Strongly Connected Components algorithm ⌨️ (3:13:56) Tarjans Strongly Connected Components algorithm source code ⌨️ (3:20:12) Travelling Salesman Problem | Dynamic Programming ⌨️ (3:39:59) Travelling Salesman Problem source code | Dynamic Programming ⌨️ (3:52:27) Existence of Eulerian Paths and Circuits ⌨️ (4:01:19) Eulerian Path Algorithm ⌨️ (4:15:47) Eulerian Path Algorithm | Source Code ⌨️ (4:23:00) Prim's Minimum Spanning Tree Algorithm ⌨️ (4:37:05) Eager Prim's Minimum Spanning Tree Algorithm ⌨️ (4:50:38) Eager Prim's Minimum Spanning Tree Algorithm | Source Code ⌨️ (4:58:30) Max Flow Ford Fulkerson | Network Flow ⌨️ (5:11:01) Max Flow Ford Fulkerson | Source Code ⌨️ (5:27:25) Unweighted Bipartite Matching | Network Flow ⌨️ (5:38:11) Mice and Owls problem | Network Flow ⌨️ (5:46:11) Elementary Math problem | Network Flow ⌨️ (5:56:19) Edmonds Karp Algorithm | Network Flow ⌨️ (6:05:18) Edmonds Karp Algorithm | Source Code ⌨️ (6:10:08) Capacity Scaling | Network Flow ⌨️ (6:19:34) Capacity Scaling | Network Flow | Source Code ⌨️ (6:25:04) Dinic's Algorithm | Network Flow ⌨️ (6:36:09) Dinic's Algorithm | Network Flow | Source Code

@bxsed 3 года назад

Finally a tutorial in plain English

@chandra3370 4 года назад

thanks for the video

@wolesae4784 3 года назад

Thanks you very much, great explanations..

@NonTwinBrothers 3 года назад

6 hours of subtitles, that's pretty badass

@rammyabandara7666 3 года назад

GREAT TEACHING, THANKS SIR,

@dabbopabblo 2 года назад

you gotta love it when extremely well-informed programmers take their time to teach you a bunch of super fascinating mathematics for hours for NO COST. Thastd how you know a passionate programmer from a money chaser

@papusa9878 2 года назад

Wha

@joeunderwood8973 2 года назад

advertisements are not free...

@dabbopabblo 2 года назад

@@papusa9878 wanna hit my juul

@papusa9878 2 года назад

@@dabbopabblo 🚬

@quadroninja2708 3 года назад

Wow, very intelligibly, thank you very much! I will code these algorithms in C

@invisibleinvisible83 11 месяцев назад

Thank you so much ❤️🙏🏻

@Epistemer 4 года назад

13:30 actually I would argue that edge list the most ubiquitous representation of a graph, since it's how anyone would normally model a many-to-many relation in a relational database

@bikerboy3k 3 года назад

Reading your comment made me understand that i'm too stupid to be here

@Epistemer 3 года назад

@@bikerboy3k my comment is just stating an observation I had while using a relational database management system, which is not relevant at all to the content of the video, so you can just ignore my comment and keep watching the video

@bikerboy3k 3 года назад

@@Epistemer in that case, ok.

@Yt1mg 3 года назад

@@bikerboy3k you shouldn't, since it's a pedantic comment that adds nothing to the conversation

@bikerboy3k 3 года назад

@@Yt1mg I fear what kind of reply is he gonna come up with. And yes I agree with you, but it's just a bit of fun.

@so_raajas 4 года назад

Another Con for Adjecency Matrix is that adding nodes becomes very cumbersome, as you have to create a resized matrix and fill all elements.

@hetfadia6219 4 года назад

i love your pusedo code really awesome

@youssefel-shabasy833 4 года назад

amazing course

@greenya84 3 года назад

Thank you for good content! The only thing I want to note is that at 26:50 you have only "visited[at] = true" but you never set it to false, so it will never actually "back track". I believe there is missing "visited[at] = false" right at the end of the function, so we unmark the node when leaving the function.