This explanation gets an A*

I like how he says pseudocode then proceeds to write Python.

I think what would have added more interest is selecting two locations separated by a path obstacle, e.g. Athens to Palermo where the straight line Cartesian distance is small but the road path has to detour around the Adriatic Sea. Then it would be interesting to see how the algorithm adjusts the path weights.

I love it when math and science communicators use good animations. Good job!

Excellent video! Wonderful explanation involving many intuitions with cool examples to boot. Had a lot of fun listening and learning!

I love the intuitive understanding you present here, brilliant stuff 👍

A great video and an amazing channel!! I can't wait to see what you have in store for us next.

A+, keep the algo videos coming, so helpful, great explanation ..

this video is like a 20 minute long beautiful symphony of ideas

Well explained. I have been using A* pathfinding in my game for over a year now. It's insanely fast in video games compared to Djikstra for example, because the areas to be calculated are often very very large. I roughly knew how A* works, but this video certainly clarified well!

wow, this might be one of my favorite explanations of an algorithm ever! Thank you!

Happy to find a great channel like yours!

Amazing animations! The idea of modifying Dijkstra's algorithm with a 3d visualization is mind-blowing.

Love your videos. You are very good at explaining algorithms. Thank you. :)

This is a fantastic explanation! Thank you very much!

I am happy that the UKposts algorithm persisted and recommended me this video over and over again. It is really good!

Great video! Thanks. So happy that this type of content is shared and celebrated on UKposts. I subscribed. :)

Potentials has so many potentials... love the explanation @polylog

What a beautiful explanation!

While the first part of the video was clarifying and reinforced what I already knew + gave better intuition, the last part with the 15 puzzle was really illuminating! It kinda illustrates a thought I've had lately that "everything can be a graph problem if you squint hard enough"!

At first I wasn't very interested, I just figured I should start learning algorithms to improve my code, but by the time in all came together in "Implementation" my tiny little mind was blown. Intuitive, creative, and just downright cool; not only do you make A* easier to grasp, you also made it more interesting than a simple description of the process

This is what I was looking for. Thank you so much.

Loved the video. Very easy to follow along!

I hit like only for that 3D map explanation. Great work friend !

Good explanation! Thank you!

Really nice video. Great job!

Thanks for the video!

One major way that maps can give you answers so quickly is that they actually cache the results. One person searches for Prague to Rome and that result is saved for later searches, making the second search exceedingly faster. Saved results have a max timeout where they will always be forgotten after a certain time as they will invariably become obsolete at some point. And each node along saved paths have a list of saved routes going through it, should anything change with a node then all saved results are immediately invalidated or re-evaluated. Frequent searches for routes (say London City to Heathrow) are given a higher priority than infrequent searches such as Yakutsk to Lisbon. The high value routes are ALWAYS re-evaluated on node changes rather than just forgotten. To ensure that when the next search happens, the result is as always pretty much immediate. There's most likely also an imbalance in node lengths. Despite road ABC being shorter than DEF, DEF is always FASTER than ABC in the long term. Another place where results are cached are on the internet as a whole. Your ISP (Internet Service Provider) keeps the last result of a certain web request stored locally so subsequent requests can be satisfied much faster than having to contact the endpoint in say California when the client is in Berlin. A local copy in Berlin can be served in milliseconds where having to fetch all resources from California could take several seconds. Heck, even your browser has a local cache of pages. Especially the heavy stuff like images, audio and video. (Which is funny by the way, you are not allowed to download copyrighted material but at the same time your browser does exactly this when it caches copyright protected images etc) On an even grander scale, UKposts caches A LOT. When a new video is released in Tokyo and saved to a data center in Japan. That is the only actual copy of the video until it is slowly trickled across all UKposts's datacenters. But when a person from Norway watches that video for the first time, that video is immediately stored in a data center in Norway and so anyone else watching the video from Norway will have no issues with buffering it unlike the first one. Eventually, all of UKpostss data centers will have a (basic) copy of a newly released (and popular) video such that new viewers can at least see the video in real time without having to buffer it (though they might be seeing it in 480p at first) And videos that aren't as popular will simply fade away from non-major data centers over time as fewer to no one is watching them. In short, everything on the internet is generally going fast because results are cached. That is why data centers need petabytes of storage. Not because there's petabytes of video being uploaded to each of them but the fact that ANYTHING that is uploaded ANYWHERE is cached locally in data centers even if that local data center only really serves a thousand clients.

I always thought of A* in a similar way, however I thought of potential as more of an abstract selection/queuing process than something physical. This is why manhattan distance and binary heaps are so effective at speeding up the process. There is a fractal nature to the algorithm because the set of explored paths can be expressed as a node, where the paths escaping it are dynamically recomputed based on the discovered cost of the path to the discovered nodes adjacent to undiscovered nodes. This of course isn't how the algorithm works but it is isometric with the method. There is inherent comparative nature to the algorithm, where the actual distance does not matter, but instead the relative measure between possible paths.

Wow this is probably the best explanation of A* I've seen. I finally understand why A* always gives the true shortest path, rather than an estimate.

That explains something I've noticed about route planning apps. I live near a river, downstream of the most likely crossing for most destinations on the other side of the river. The route my satnav, Google Maps, etc. plots *to* the crossing depends on where I'm going *after* the crossing. I'd worked out that it was looking at routes nearest a straight line between my start and end points. The video has confirmed it, and told me what the algorithm is.

Nice subject, clear explanation, good animation. I did learn something

Well made and easy to understand. Great work!

Excellent explanation!

Great video! The use of Also Spoke Zarathustra by Strauss for the reveal of the "physical" interpretation of node potentials really tickled my funny bone. I also really loved how you avoid introducing the vocabulary of heuristic until it basically falls out of massaging the initial algorithm - I've often seen A* introduced and explained directly reasoning with straight-line distances, and I never really grasped how that is more of a special case for applying A* than the general case [operating on the graph by redistributing potentials].

Subscribed lightning fast, I need more algorithms intuitively taught not the mindless pseudo code without intuition or reason why something is done. Keep coming the great series on algorithms, I would also love to see systems topics covered, compilers, HPC and microprocessors. Do consider

why didnt I find this channel earlier ? Great job with the animation ! Subscribed.

you use soooo good animations. appreciate that!

Damn man this was by far the best explanation of an algorithm I have ever seen

Very interesting application to the 15 puzzle!

Amazing explanation

Great explanation!

Using A* to solve search problems is always fun. I've had a bunch of random problems about finding the shortest way to solve something where I pretty quickly decide that the graph search is just the best way. No wonder why these graph search algorithms are the main thing I remember from AI course...

New math video! I knew it was worth subscribing to your channel!

Thanks for the vid! You explained it better than my professor for sure

Amazing video!!! Congrats

Using the third dimension to visualise the direct distance of each node to Rome is GENIUS. I don't know if that was your idea but regardless the animation is great and the explanation is clear, this is a great video.

Thanks for valuable information

beautifully done.

I had to implement the A* algorithm in a college class. Beautiful explanation! I wish I saw this 3 years ago lol.

I am a physics undergrad and as soon as you started talking about potentials and showed the road map in a 3D view with Prague being at a high point and Rome at a lower one, it immediately started screaming in to my ears "Gradient". The way I visualize the problem is that we are trying to find the direction at which we must move from each node in order to have the most steep descent because the steepest descent means that the next node is going to be closer to Rome than the rest. This is exactly what the gradient in vector calculus shows you. For anyone who isn't familiar a gradient is a vector that shows you the direction of steepest ascent so by simply taking the negative of that you find the direction of steepest descent. So all you have to do to solve the problem is at each node to take the negative gradient for each path and then simply choose the one at which the grad was smallest. Then you repeat for the next node until you reach Rome at which point the grad will be zero because you're at the lowest point.

Thanks for mentioning L'viv!

Awsome video!

Great video, I think I finally understand A*after all these years! For the 15-puzzle, I thought we had to divide the heuristic by 2, but we're not swapping numbers so that doesn't make sense lol

Very nice explanation and animation. I came to understanding A* in a different, maybe the classic way, but this one with node elevation is definitely a very interesting view on the same thing. I started with Dijkstra (which is in turn a BFS with priorities added to the edges) and instead of using distance as the priority, use something that is commonly called a "cost". This cost can (under the rules you described well in the video) consist of more factors added up - like the road distance and straight-line distance. One can then add other factors as fuel consumption, elevation and toll prices as other factors by summing them up. I think some real-world route-finding algorithms are based on a bi-directional version of A*, where the boundary gets expanded from both starting and ending points and the route is formed when the boundaries meet (perhaps oversimplified). It should be also possible to find more alternative routes this way when the algorithm doesn't terminate immediately after the first route is found but tries, say, three times where some cost is already added to existing routes.

Super video kluci!!

That is explained so well that I understand it too.

I've been searching for Rubik's solution. Thanks dude.

Skvělé video, posílám pozdrav z Prahy !

This is nifty!

Really interesting!

skvěle vysvětlené jako vždy.

That was very interesting, ty

Lol @ the space odyssey music. Also the idea you highlighted at the beginning is nice. The weights on the edges makes the problem a discrete analog of finding length minimizing geodesics in Finsler geometry, as opposed to in Riemannian geometry.

great video!

This is a really nice video. this reminds me of a similar idea with kirchhoff's law. A cicuit is like a directed acylic graphy of potential differences.

Really amazing explanation, now i get it, thanks

great video

4:34 I knew what was coming for the explanation, but the Space Odyssey just made me burst into laughter, caught me completely by surprise! A+ editing!

I am a very confused aerospace engineering student who stumbled upon map algorithm youtube by clicking a video that I thought referred to the aerodynamic variable A*, which we use to find the throat area for perfectly sonic flow through a wind tunnel. A few videos later and I feel very educated about something completely different. :)

I did not squint at the rubrics cube to see if I was able to predict whatever you were going to say. Nope...didn't at all... On a different note, thanks for this clear explanation. Definietly a good starting point to understanding what this A* algorithm is about.

Very good video you got my sub, one precision about Maps and other maps software , 1 to 1 shortest path A* is great however when you have an extensible graph then a matrix distance is needed which is using dijkstra, when you talk about maps the distance matrix is using a dijkstra algorithm and once the shortest road is define a 1 to 1 is defined, maps turn by turn api will use A*.

Thanks!

Really good video

Okay, writing down my understanding: A* is a way to speed up a Djikstra search through a graph by providing an opportunity to input information from what the graph represents. For example, if each node in the graph represents a point in 2D space, you can use those points to set a “potential” for each node, which warps the graph into a new one which Djikstra will solve more quickly. So it will still produce the same output as Djikstra - but it changes the order in which Djikstra searches so that it makes its way to the solution sooner. Because Djikstra searches shorter path lengths first, if you warp the graph such that the better paths are shorter, it’ll search them first. It’s just a matter of warping the graph into something that still works for Djikstra, using a method which is actually faster. Do I have this right?

Wow, I am absolutely blown away by the quality of your videos! The content, the script, and the overall production value is truly amazing. I am a CS student myself, and I have been considering starting my own channel. Your work has truly inspired me and I can't wait to try my hand at creating something similar. Would it be possible for you to share the tools and techniques you use to make your videos? It would be an honor to learn from someone as skilled as yourself. I would be eternally grateful if you could make a video about it, your guidance would be invaluable!

All paths lead to rome we don’t need an algorithm

Wonderful video, you got a new sub

Super video

Yay, some guy with an accent explaining programming concepts! Never seen this before!

Good video

Awesome video! Have an exam in a week on autonomous robots and this is part of the curric. This video really helped set my studied knowledge in stone and give an alternative visualisation!

Excellent

Animator deserves a cookie. 👍

Skvělá práce. Moc povedené. Zrovna letos jsem pro Advent of Code hledal IDA* (iterative deepening A star).

I hope this work get proper appreciation

Very nice

Came looking for copper, found gold, amazing work.

Very nice, well done.

This is a trick question, because we know, that all paths lead to Rome.

What a stellar explanation with references to Interstellar music :D

I love this video, just one suggestion on the color scheme: the color of the dots being almost the same as the color of the sea made it hard to distinguish between them and to read the numbers. I would have chosen to not color the sea at all, just imply it with the outline to europe. Or made the sea a slightly different beige color, so it was easy to see it as different from the continent, but still having a big contrast with the dots and the numbers. Other than that, I loved this video! I learned a lot

Great Video! I enjoyed it a lot. Giving those 3b1b vibes

I feel like a huge mapping database like Google Maps could use some other strategies to improve the A* heuristic as well, like using previous queries to see what routes are generally faster than others.

I coded an A* algorithm from scratch after reading how it worked, and not looking up any code snippets. As a junior coder, it was very fulfilling and enlightening. I highly recommend anyone dabbling in this stuff, such as unity, to give it a try.

I learnt something new. Thanks! Very well explained. Your pseudo code looks suspiciously similar to python🙂

This is such a good video. How does this have so little views . Amazing explanation and graphics. Love it

Who else is here after the OpenAI Q* news?

The algorithm gave me some gradient descent vibes, really interesting dijkstra modification right there.

>lets write down the pseudocode for our algorithm Proceeds to write it in python 😂