Depth First Search (DFS) Explained: Algorithm, Examples, and Code
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- Опубліковано 31 тра 2024
- In this video, I explain the fundamental ideas behind the Depth First Search (DFS) graph algorithm. We first introduce the concept of a graph traversal. We then go through several examples of DFS to provide intuition. Afterwards, we then go through both a recursive and iterative implementation with provided code. We discuss the differences between the implementation and also make a distinction between a preorder and post order DFS traversal. We then finish the video off with some practical and fun applications of depth first search in graph theory.
0:00 Intro and Preview
0:50 Graph Traversal
1:20 DFS Walkthrough and Examples
6:26 Recursive Implementation
11:08 Iterative Implementation
15:06 Preorder vs Postorder DFS
17:01 DFS Applications
Support: / reducible
This video wouldn't be possible without the open source manim library created by 3blue1brown: github.com/3b1b/manim
Here is link to the repository that contains the code used to generate the animations in this video: github.com/nipunramk/Reducible
This is how I explore caves in Minecraft.
I had the exact same idea. Lol ;)
This is a surprisingly intuitive comparison. Thanks a lot. +
except caves in minecraft often have no dead end
@@ElektrykFlaaj yeah and they often loop back too
+1 best system, would recommend
The thing I love most about great channels using manim, is that i never feel like im watching a 3B1B rip-off, just an intelligent explanation of a topic. Keep up the amazing videos
TIL that manim is a thing.
I feel there are some channels that definitely feel like a rip-off, like vcubingx. It kinda hurts to see a 3b1b-ish thing with lackluster explanations and general quality. This channels pretty good though, and it’s improving noticeably.
Eh I don't know, they do feel a bit samey. The way things are shown and animated is pretty consistent, I think the biggest thing differentiating them from being a ripoff is their specific style. For example, 3B1B uses the little Pi characters to add more personality, I think that just shows even if they use manim there are ways to differentiate yourself in other ways.
By the way, a very interesting point is that you can convert any recursive function into a stack + while len(stack) > 0 loop because basically that's exactly how computers do that on a low level anyway. In some languages it has some advantages, because while function call stack may be limited, a stack as a structure is practically unlimited, and that lets us achieve very deep levels of recursion without stumbling into stack overflow.
Wow thanks this made me dig deeper and understand even better.
great video! I'll also point out (as a few others have hinted) that the iterative approach is very important for large graphs. Default stack sizes on modern OS' are still typically quite small, and it's easy to construct pathological graphs which will cause a stack overflow with a recursive DFS implementation. Using an explicit (and heap-allocated) stack as in the iterative approach works around this (until the machine runs out of memory, of course!), and is a crucial reason why this approach is often chosen.
Hi can u please tell me more about this? For example how is it possibile to construct a "pathological" graph. i'm assuming that a pathological graph is a graph whose nodes are linked in such a way that when the DFS algorithm is called on the graph, it goes into an infinite recursive loop that overflows the stack.
This is the best video on this! I love this channel, it is going to become really popular! Thank you! Love the animations. And the design.
Thanks for the kind comment!
The video is great, as always. However, I have a suggestion: maybe at the end of the video, you can ask some graph questions and let us think how to slove, and finally, you can give the java or python code and the step of it. (just like your recursion video because your recursion video is absolutely amazing.)
Thank for the feedback, will try to incorporate more problems in future videos.
One thing that I love about this channel is that, because the quality is so huge, all the comments will start praising the video but also adding new information and providing constructive feedback. I think that people feel compelled to give some retribution after watching such a great video for free.
The presentation of how to use a stack and pop together was really interesting. I always had trouble with while loops, this pattern makes it so apparent when it is best used.
i can feel your effort man, the planning, research, animation, music..
I'm glad i came across this channel.... you gonna get huge success..
Your content is incredibly good. It's not only comprehensive and to the point, but also enjoyable. Thank you for all the effort you are putting in.
This was a great video, explaining not only DFS, but both recursive and iterative versions of it, and presenting applications for DFS, all accompanied by illustrations to make it even more clear. Cant thank you enough!
I really love your explanation, it's short, concise, easy to understand, straight to the point. I watched many another's videos, they were lengthy and hard to understand.
You deserve so many more subs. This content is so well explained. Fantastic channel!
Well structured, easy to follow, beautiful graphics, use of video chapters and real world use cases included. What can I expect more? Superb video.
The way we designed the animation and the calmness of your voice in the time of explanation and the depth of your discussion just blow my mind. May Almighty Bless You💝
The best CS channel to understand graphs hands down! THANK YOU Reducible!! You are just awesome!
absolutely the best explanation on DFS that I have encountered.
Please make more videos on graph theory and algorithms.
This is the best way to explain recursive functions to newbies like me. Thank you so much for such great contents.
Thank you for making DFS and BFS understandable. Simple and on point
2:22 is an example of the classic Cycle Detection algorithm where DFS is used to detect any cycle in a graph G. Child node 2 has a "back-edge" that connects it with the root node 0. This is basically a cycle in the graph.
I love 3B1B videos and now these are my favorite too. Thanks for all the effort and excellent explanations!
Great video, great teaching, and great animation used here to make things understandable by going into a deeper level of abstraction of all the steps and processes. Before this video, I watched 4-5 videos on DFS that appeared on top after searching and had more views (even in millions) but couldn't understand them clearly. After all, this is the ultimate video that quenched my thirst. Thank you sir for your great content. This channel should grow more and more fast.
Your videos make the difficult concepts so easy to grasp!
Great Content Man and that Recursion video is Awsome . Keep Making more videos.
These videos are gold. They go into much more depth than their peers, with expanded intuition, alternatives, and application. Well done sir! P.S. the animation is also top notch.
looking forward to BFS too! Thank you for posting!
Best video so far I found on DFS algorithm. Very clear explanation. Thank you very much!
I couldn't help myself but comment how beautifully the content has been delivered..... Kudos to u guys, love and appreciation from India🤘🤘
Amazing video I have already done my bachelors in CS and have seen various videos explaining various Algos but your approach is simple, intuitive and precise among all others please keep it up!
This is the first time I'm posting a comment for a video, simply because I don't really bother to. But this is something. This is that good!
Sooooo good! Concise and yet complete. Simply brilliant!
So happy I found this channel and this video! It was really, really helpful.
Thank you for the amazing video. This is the most understandable explanation I've ever seen. Visualization, narration and music is very good:)
Thanks for that soft music in background, really helped boosting focus while watching this video. Great explanation as well. Thank you.
probably the best explanation of DFS I have ever come across! thank you! :)
Brilliant video. Those animations really helped to understand the whole process. Thanks!
It's really amazing...
your contents and way of explanation everything is awesome...
keep it up...
Amazing!!! Please do this for all concepts of DSA. You are a rare gem!!!
Okay, I'm 5 minutes in but I had to comment. This is, hands down, the best explanation of DFS I've ever encountered. Thank you so much for this phenomenal video - I hope you keep it up!
Brilliantly explained, so simple and clear. You gained a new subscriber!
I really love your format, great work, subbed right away
The best explanation!!This guy is a gem
Simple and Clear:) Thanks for the amazing videos!
Best Explained !!!!!
Thanks from India 🇮🇳!!!!!
I'm proud for being among the first 1000 subs while I know this channel will explode subs count to millions very soon
Me too! This channel is going to be huge!
It's absolutely happening. Pleased to be part of the blow up.
Literally just learned about this in class today and it popped up in my recommendation. UA-cam algorithm is getting insane.
Finally I found the best channel
That's amazing
I wish to support you more ...
I rarely comment on UA-cam but I must say you are the exact version of UA-camr and tutor I am dreaming to be..Before reading the solution and algorithm, we must understand why it was created , what was the intuition behind it... and second thing I loved is bg music..
this is probably the best explaination ive came across
great animations, video, and i love the last part where u mentioned the applications
Loved your amazing explanation, thank you!
JUST WAITING FOR THIS WONDERFUL WONDERFUL GEM OF A CHANNEL TO EXPLODE.
THANKYOU THIS IS AMZING
Thank you so much!!! Much love from India.
Perfect explanation. It is may 5th video and just understood everything thanks to you. Great.
I liked and subscribed. awesome explanation. Good visualization and best animation. Keep the good work.
Beautifully animated video, though forgive me if I don't like this way of introducing DFS.
The main problem is that most of the applications could just as well be solved without DFS:
Cycle Detection: DFS does not give you all cycles in the way you described, and just determining whether a graph contains cycles can be done by BFS or similar also.
Finding Connected Components: Any Traversal technique will do nicely.
Topological Sort: Take Kahn's algorithm. The idea there is your reasoning at 18:37, but translated more directly into an algorithm.
Maze: There are several ways to create a maze, but granted this one is elegant :)
This sometimes leaves students wondering whether DFS is just a bad alternative to BFS for the path finding problem. It is not!
Of course some applications are harder to explain in a video, but here is a surprisingly useful application somewhat related to your examples:
Partitioning a directed graph into strongly connected components (SCCs, Sets of nodes where you can reach every node from every other node).
This is useful in e.g. model checking, where you want to proove the correctness of a program, which can be reduces to finding an SCC with a special marking and a loop.
Checking whether an SCC has a loop and is marked is usually trivial (loop at least two nodes in the SCC or a reflective edge).
Or you might want to replace SCCs with single nodes, yielding a DAG. This e.g. extends many planning algorithms to handle circular dependencies (exactly the SCCs with several nodes).
Basic idea without any proofs:
Every SCC is represented by the node within it first encountered during DFS.
Start by assuming every node is its own SCC and start the DFS.
If you keep a hashset of all the nodes currently on the stack (or mark nodes as on the stack), you can efficiently determine whether a node was encountered twice along a path.
If that happens, you found a loop and can merge all SCCs on the stack from the first encounter to the second.
An SCC is guaranteed to no longer grow once DFS leaves it (through the node representing it, which you can detect).
At that point, note the SCC down.
Side node: Like in your example, the SCCs outputted this way are topologically sorted.
Sadly, most students never get to learn these more useful applications of DFS, but hey, thats why I'm writing long comments :)
Thanks for reading!
wait, this is really useful info. thank you for taking the time to write this all !
This is Gold! Just one video and I think I'm done understanding graphs. Thanks a lot!
there is a lot more, but yes the video explained it very well
I really love how you explain and the music, I really love this yt channel thank you so much
Best video ever. Helped me understand the DFS better.
great explaining video for Graph Thnaks
Great Effort there! Appreciate the time you took to fork Manim and manage it so well for all of us. Regarding the algo in preview, at 8:20, where you mention to maintain boolean values of marked nodes, it should be of size/length - G.order() rather G.size(). For a graph, order = number of vertices = |V| while size = number of edges = |E|. This could cause problems if we have a straight line graph with n nodes connected by (n-1) edges!
you do great job. you deserve more appreciation, and you will have it.
Really good explaination!
You get a new suscriber! Amazing videos and explanations! Really really very good!
Amazing explanation. My teacher did the same but you explained it way more easier.
Learnt 2 neat things about Graph algo from this video:
- Reverse of DFS post-order is the same as topologically sorted graph
- DFS can be used to generate maze. I always thought some dude spent hours to design mazes in the print newspapers. You are telling me it was just a DFS 😂
I wish this videos came earlier.....great content man!
This is the best video ive ever seen in my life
Thank you for the clear explanation very easy to follow. You got a new subscriber keep up the good content👍
Thanks for great explanation.
I love ur channel 🥺 such a wonderful explanation
thank you so much for the amazing explanation and such great animations!
Really amazing video 🙌🙌
Brilliant. Nice explanation. Really helpful 👌👏👍
The king of the hill is here... can't wait to become a patreon this content is 🔥...
superb explanation!
This is simply an amazing explanation
Very good explanation, thank you!
You're the man! Perfect explanation!
wow, what a great explanation! thank you!
Great video! Thank you so much for it.
slick video and great explanation
This seems like a very useful algorithm to know, I feel like I can already see some applications of it
Incredible video!
good animation easy explanation covered a variety of algos in just 20 min. 👍👍👍
great explanation, thanks.
So well done! Great job
The mooooost perfect tutorial video eveeeer
Awesome as always!
Thank you, I managed to implement this very easily. I am not a programmer and my itterative approach could only handle branches and cycles.
I guess It takes a lot of efforts to make this video. Well done! The details are handled well. e.g. same nodes added to the stack multiple times but only processed once due to the visited check. It is better than the solution in CLRS
Perfectly done. Thanks
best video of DFS for sure
It should be noted that outside of interpreted VM-based languages like Python, the manual stack-based algorithm is actually a necessity, since stack space, especially on the main thread, is scarce in unmanaged languages. Using the heap (std::vector in C++, Vec in Rust) to store the recursion stack is the only way to infallibly avoid stack overflows with graphs of untrusted size and deep call stacks on many OSes, which will hardly ever allocate more than 8 MB, or sometimes merely 1 MB, of space for the stack of the main thread.
Fantastic video! Kudos!
Thanks a lot for the explanation!
Awesome video you are a amazing teacher
very nicely explained thx a lot
*Great Content!!!*
Understood a lot
please continue making these kind of videos . .....!!!!!!
Great explanation, it would be awesome if you can create similar videos around Trees (diff trees and usages).