5 Simple Steps for Solving Any Recursive Problem 

I don't know about the others, but tower of Hanoi is one the the easiest recursive problem I've ever solved. Maybe that day was my day... It's simple logic. Like if you want put n+1 disks to leftmost, first put n disks to middle, then put largest plate on leftmost, then put n from middle to leftmost. As simple as that....

Your first statement that it is the hardest topic in computer classes to learn is categorically wrong. And I am proof.

@@kpw84u2 Because clearly the hardest topic of all time is reversing linked lists or binary trees LOL

Ah yes, the 3Blue1Brown of comuter science. Keep up the excellent work!

how can I understand and dont undrestand in the same time?

My mathematical intuition tells me that this is not a recursion

@@overloader7900 recursion is defined as something that is defined in terms of itself. Like if i define the following function f(t) = f(t - 1) × f(t - 2). I could define another function in the following way, g(t) = g(t). This isn't helpful at all, but it's a function defined in terms of itself.

but func a(){a();} does literally nothing... Does it mean that it is impossible to solve recursion?

@@overloader7900 it's not that it does nothing, is just that we don't have enough information to know what it does. And just because this specific case of recursion isn't solvable, doesn't mean that every recursion problem isn't as well. It's like saying that the equation x = x + 1 doesn't have a solution and then concluding that no equation has solutions.

Thanks, but how do I solve the recursion problem?

Yeah that's a great perspective! Thanks for sharing!

"we tell the computer what to do but not how to do it." Sounds like a bad idea.

@@Green24152 really! Why?

@@DesertRose124 Wasn't saying you were bad, just that telling a computer/A.I. what to do, but not how, usually results in the entire universe becoming paperclips.

@@Green24152 Given that most of the people who write compilers know more about programming than the average application-level dev, I don't see any problem with it. Logic languages like Prolog go even further: All you have to do is specify the logical structure of the problem; the compiler will write all of the imperative-level code for you. Not to mention SQL, which does that for databases. They're called 4GLs (fourth-generation languages).

Thank you, I appreciate the kind comment! New videos coming in the near future :)

@@Reducible sir please explain tower of hanoi(TOH) problem in same way i can not relate you idea to solve for TOH problem.

@@chandraprabhat3496 Next video is going to be on Towers of Hanoi! Your comment gave me the idea, so thank you! Stay tuned for that video!

Bhai mereko kuch samaj nahi aara...😭

mad lad

Sometimes a well rested mind leads to epiphany

There's actually an explanation for that. Your mind has a thread running on the background. When you stop thinking about a problem that thread takes it and processes it. If you want to know more, Coursera's Learning How to Learn explains that (it doesn't call it thread though).

As someone has mentioned, when we really think deeply about something yet still don't get it and take a rest, a part of our brain is still fixated on that topic. So when we return back, we may have the answer to it.

I guess your brain working is a miracle?

I thought I was the only one who struggled with recursion

Thanks, I appreciate the kind comment!

Basically induction

@@recepcanakdemir1558Yes!

That is some high praise! Thank you! And yeah, like with anything difficult but worthwhile, it takes some time. Enjoy the process!

probably would stick with deque and for loop in the future though, recursion still costs too much brain juice for me and this time I was just lucky that the code's bug-free first try

Thanks for the comment, I have a couple more recursion related ideas on future videos so stay tuned! :)

That's the goal! I'm happy to hear that this video was helpful and thank you for subscribing! More videos are coming in the near future!

I face the same problem

What can you say about it now?

@@eyeteeee9507 You mean how I solve recursion problems now? I memorized multiple templates to solve them. There are not many different types of recursion problems out there and many recursion problems share the same core techniques. This works enough for me, but still, I don't think I fully understand it.

what name would you use

@@michil.1192 something that isnt a function already

@@Ganerrr what is in a particular namespace already is a specific language/environment thing, using a generic name like sum in pseudo-code like as done here, isn't an issue, don't be such a pedant.

@@MrGryph78 Can't agree more.

Commenting to bookmark it :)

@@AdityaKushwaha-r5l great 😂

watch kunal kushwaha recursion videos

Honestly the best thing you can do is practise. Start simple then gradually increase difficulty. You are not stupid, anyone can understand it. Never compare yourself to others and learn at your own pace.

You are not stupid. We just need to think differently. Which will come with practice and solving more problems using recursion

Comments like this one are really awesome! I'm glad that this video was able to give you that "aha" moment, that's what it's all about at the end of the day.

Reducible I think it’ll also be cool if you do another video where you show how this type of thinking about recursion translates to other applications such as binary search and trees! I’m watching your other videos in the DS series and they’re pretty cool as well 👍

​@@user-gp8fr1nd3w Yeah, I agree that it's a good idea and it's definitely something I want to try to tackle in the future. To give you some inside info on my thought process on trees, the challenging aspect with presenting tree problems is it's tough to find (at least in my experience) some really engaging set of problems that aren't just a variation of traversing the tree in some manner with some constraints. In many ways tree traversal is just another way to do graph traversal, which I am making videos on. Also tree representations as a data structure could be an entire video on its own. And lastly and probably the biggest factor, when I've played around with animations of these ideas with trees, I just wasn't too happy with how they turned out, but if I find something that I'm excited about going through, I'll try to make a good video about it.

Reducible I see that makes sense! Trees are definitely a subset of graphs and I agree that the applications are essentially a variation of the traversal, but I think there are other applications, such as checking whether a tree is a BST requires knowing beyond the traversal. The brute force way would be to use nested recursion, essentially traversing more than once. And the efficient method brings it down to just a traversal, but the problem is how to think about the efficient method, and how also be able to do the brute force way for a better understanding. So I think while the final answer is really a variant of traversal, the thought process can be challenging. It’s really about learning how to think and approach the problem. Sorry I’m in no way telling you what you should do, but I hope this offers some perspective.

​@@user-gp8fr1nd3w Ha funny enough, the check if a tree is a BST was the one example that I was taking a look at since it is different from standard tree problems so I totally agree with you there. I've seen a lot of videos about this particular problem on RU-vid since it's kind of the "classic" BST problem so I wasn't sure if people would be engaged by my approach to the problem. But maybe it is a good example if other folks like you are interested in it. I'll keep that problem in mind for the future. And no problem, I appreciate comments and suggestions such as this one since it helps me get a sense of what my audience is interested in so feel free to let me know if there's anything else you would like to see!

Isn't that epiphany the best feeling as a student? Whether casually or devotedly, something suddenly *clicking* like that is a great feeling!

Thank you! Glad you found it helpful!