Recursion Simply Explained with Code Examples - Python for Beginners 

Hey, can you please explain the calculation at 5.20min Fibonacci(idx-1)+Fibonacci(idx-2), as I understand if our index is 8, then ((8-1)+(8-2)), which equals 13, how did you get 21. I know that the Fibonacci number at index 8 is 21, but I don't understand this from calculation point.... Thank you!

If you don't already you should consider doing Udemy courses. Your ability to explain things clearly while also preemptively understanding potential questions and answering them in your trainings is extremely good. Kudos to you!

you really have created one of the most high value concise channels on compSCI and python, thank you !

omg that was such a concise and each to understand explanation about recursion! I didn't totally get the fibonacci part but your examples have given me confidence about the basics of writing a recursive function!

Wow your subs have doubled since the last time I checked in. Finally people are seeing the effort and excellent teaching of yours, well done!

I've been watching few of your vids.... very well presented, great content, timings good you will do well as time goes on. I've spotted many youtubers early on sub 10K with now over 500K+. You will be one of those, hitting 100K early 2022 and +300K 2023 if you keep vids coming.

Fantastic! You made this topic crystal clear and very easy to grasp..thank you

Thanks! Super awesome tutorials. Helping me to connect dots and feel like I can do this.

Thanks 🙏 , I have been confused for a long time. What a way of explanation with your examples.

I Have Been Waiting For This one, sweetie; Love You and This Fantastic Channel ~

You know she's a badass when the computer warned her about battery levels less than 3% and she was like .... *meh*

Awesomeeeeeeee Mariya!!! Thankyou so much, I am non CS final year student I tried many videos few days back and I thought to give up learning programming but today I am thorough with this concept through your video, you had really broke it down in a way that I can understand it very easily and clearly, all your videos' are giving me more confidence to learn every topics . Thankyou soo much you are doing a great Job.... Thankyou so much once again. I'm editing to write this 😉😉 by the way you are beautiful 🤣🤣🤣🤣🤣🤣

Nice video. I was working on solving a Fibonacci algorithm problem recently so it was good to see this video. Nice t-shirt too!

Great idea! If all programming tutors were like this, almost all men would be able to program.

If you want to improve the performance of the fibonacci function or something similar (factorials for example) you may want to use momoization to store previously computed numbers and use them rater than recomputing them.

it's worth to add that the iterative method is less cpu consumming but is more memmory consuming as you calculate each number until you get the desired one, when in recursion you directly calculate the number you are looking for. recursion is pretty good to use along with threads, that way you can take a complex operation (something that would require quite a buch of proccesing power or computations and time) and rather than running it all straight forward you divide it in parts and make several threads (that will run concurrently) to compute each part making it way faster.

I will have to watch this a least one more time to fully comprehend this recursion thing. Great video as always!!!!!!!!!!!!

It's a fact I didn't know. I'm so thankful. I hope there will be a day when it can be applied.

I was head faked, I totally thought recursion was going to win 😂 thanks for the explanation

Many thanks, You have simplified my life.

Love your videos and charisma. God bless you 🙏🙌

Amazing vídeo, it was well explained! Bravo 👏

Finally I understand recursion, Thank you

I've been seeing your videos pop up on my feed quite a bit lately, and this is my first time watching one, and I have a mix of compliments and criticisms. First, the compliments. Your presentation skills are quite good; you speak clearly, confidently, and concisely, as opposed to a number of other creators who tend to ramble a bit and then fail to edit those ramblings out. Your editing is also quite visually engaging, and it supports the points you're making quite well. However, I can't overstate what a massive L take it is to come to the blanket conclusion, based on a single test comparing two functions that are written very differently from each other, that iteration is faster than recursion. Even ignoring the fact that the functions are written so differently, a single test using only a single input is not very illuminating; you would need to run each function with a variety of inputs, and do multiple tests, in order to come to any kind of conclusion. But let's come back to the fact that the functions are written so differently from each other, because a brief examination makes it obvious that the recursive example is extremely disadvantaged because it has to run far more computations because it's doubly recursive, meaning it calls itself twice at the end of each call, so that's at least twice as much computation right there. This is in stark contrast to the iterative example, which holds previously computed values in a list, which takes a massive load off the CPU at the expense of some RAM, and that RAM cost might get significant when called with a large index (though in practice, a list of integers is quite unlikely to cause memory issues; this would be a bigger concern when holding a list of more complex objects) but in the example shown here, the iterative example is at a huge advantage, which is definitely majorly skewing the results of your test. Also, my understanding is that time.perfcounter() is better to use for measuring performance than time.time(). I don't know why that is, but that's the advice I've always heard. On a much less serious note, I'm simply SHOCKED and APPALLED at your use of PascalCase for a function name.

Thumbs up for the t-shirt 😁 Great work as always 👍

Nice subject! My view is that it depends. If you need too much nested loops, or you cannot know in advance how many nested loops you will need, recursion is the best (file system searching, user interface controls, trees in general...). If you need one or two nested loops (maybe three or four), then loops is good enough (and runs faster!)

Ny most recent use of recursion was to print MLM trees. Basically feeding the deeply nested JSON data into the recursive function.

Awesome explanation. Thank you for making these videos! Very, Very Helpful!!!

Good simple explanation❤.....you just gained a subscriber

Awesome, thanks for another great lesson. Sorry I missed the live lesson today. This is useful for the next stage in making my programming language, the compiler has to break down statements into small parts to evaluate them. I have to keep things simple.

I love the visual aids, I really makes a world of difference

Can't believe just when i search for recursion you just happen to upload a video 5 hours ago Hahaha, great vid! thanks as always great content. :D

Great explanations! Thank you.

Hi l love your videos they are really amazing and they get straight to the point

Superb! Well illustrated.

Hey Mariya, good subject for Today, Keep going, Waiting to see a lot more from your side.💪👍

just by watching ur videos....i love you !!!

thank you! you are great at explaning!

This is fantastic, you are awesome!

Super helpful! Thank you!

thank you this helped so much! subbed :D

By definition, is a local variable local to one call, or available to all calls in the recursion? The last definition is what I’m gathering here, or was there globally defined variables, for example, in there recursive fibonacci code. Very good explanation of recursion in python, thanks.

Do you happen to have any other videos discussing recursion? This is what I’m learning for college next week and I’m trying to get a head start. Thank you regardless.

Fun fact: I got a matryoshka from my father that held former Russian leaders from most recent to oldest. I also called the folder I kept coding lessons in "Matryoshka", because that's what code in general seemed like

Grazie for the this beautiful class!!

Might be worth mentioning that you can include recursive functions within for loops and, to overcome timing issues in recursion you can use lru_cache from the functions library.

Thanks for the tutorial. I definitely enjoy your videos because it look like Python is pretty easy to learn and I know sometimes it’s not XD. You’re amazing!

well explained. I love your selenium series. can you do one complete Project from scrapping to machine learning algorithm to visualization in any tool like power bi etc.. (eg. predicting stock price or any other project you would like)..It might help us to add to our resume..thanks

I love your explanations !!

it might be a very basic concept but it doesn't mean it's easy to understand. i liked your video because it's not recursion explanation with factorial, thxs

8:15 iteration is not twice as fast as recursion, it is thousands, if not millions of times faster as you add higher numbers because recursive is O(2n), meaning that every item makes it quadratically slower. Another downside of the recursive approach is that there is a pretty low upper bound limit until you hit a maximum recursion depth limit, which will happen even when using memoization

Love it! you are a genius!

It's a great video. By the way what if I wrote fibonacci(1000). The above code wouldn't work. Its basically calculating the same number again and again. So can we use dp(dynamic programming)to further optimize the solution so that we don't have to call the same function again and again.

I need that voice, I want my navigation, Siri, audiobooks and therapists to have that voice

Running tasks in parallel 😎

Thank you for this great explanation❤️

Awesome lesson! Ty!

Great video. Thanks!

Hi, thanks for the detailed video! however i have a question. in the function nowhere we have defined that fibo (idx) = Fibo(idx-1) + fibo(idx-2). How come the function is working then?

Wonderful lesson; thanks.

thank you for your videos, you have a new sub.

the editing level increased, i like it 💞

You can see a major difference between the iterative and recursive example. The iterative examples works its way through the loop continuing the calculation each time, the recursive example in its return statement calls two other copies of the function, so the program calculates Fibonacci(idx - 1), then it also calculates Fibonacci(idx - 2), the big issue here is that when it calculated Fibonacci(idx - 1) it also had to calculate Fibonacci(idx - 2) and then it calculates it again, so it had to calculate Fibonacci(idx - 2) twice, this happens for every level of recursion, which is what makes it significantly slower than iteration since it is repeating the same calculations many times. If you manually expanded the recursion this would be easy to see. With the iterative example it calculates one value and then moves directly onto the next, it doesnt repeat any calculations and onto has to deal with jumps, not function calls or putting values on the stack, this is another reason it is significantly faster. The difference in speed was relatively small (only 3x) in your example here using small numbers but I ran the code myself, I ran it with an input of 40 and the iterative approach took 0.0 seconds, whilst the recursive approach took 30.17 seconds, so as the input increases so does the speed difference, I am not 100 % sure but I think the time increase of the recursive approach is exponential whereas for the iterative approach it is linear. Partly confirmed by the fact that running it with an input of 41 makes iterative still take 0.0 seconds whilst recursive takes 48.88, so it doesnt double every time but it is a large increase, around 1.5x per 1 that the input increases by. I know others in the comments have mentioned that the iterative approach uses more memory but it doesnt have to, for the current calculation all you really need are the last two numbers in the sequence, so all you need to store is the last two numbers in the sequence plus a temporary variable for the calculation, not the whole sequence like shown in this example, so you could get the memory usage down to 3 integers and the index plus whatever variable you use for iteration. Another benefit of the memory optimisation is that it decreases the time that it takes drastically, when it stores the whole sequence it has to append the list every time, this takes time since it needs to allocate memory, using the memory optimised version it doesnt need to do this so is faster, when run with an input of 100000, the example given here needs to store 100002 values, whereas the memory optimised one stores 2 values, this lead to the example given here taking 0.31 seconds and the memory optimised version taking 0.12 seconds, this difference increases as the input size increases. Increasing the input to 300000 the iterative example given here used multiple gigabytes of memory whereas the memory optimised example just used the same amount of memory it always uses, also the speed of the given example was 26.08 seconds compared to 1.57 seconds for the memory optimised example. Increasing the input to 1,000,000 created a memory error, on a system with 32 GB of ram. One way to decrease the speed whilst also storing the whole sequence would be to allocate an array the size of the index right at the start, then you dont need to worry about expanding the array or list later, this doesnt get rid of the fact that it uses lots of memory though. A big problem with recursion is that as the input gets bigger the number of functions that need to be called increases drastically, you are pretty much doubling it for every time you increase the input by 1, so this can quickly end up with thousands of function calls and ending up with a stack overflow, with the iterative approach when memory optimised and only storing the last two values, the memory usage of the function is the same regardless of the input. This may not be much of an issue with small examples and systems with large-ish stacks, like desktop PCs but once you get into systems with small stacks then recursion becomes a problem, this is especially relevant in embedded systems and microcontrollers which typically have very small stacks and very low RAM and flash storage, where having a MB of RAM is a lot. This is also where you will see big difference in speed too since the processors are slower and often dont have all the functions a desktop computer would, like floating point units. Hence recursion is for the most part to be avoided in embedded systems. It would be very interesting to see what kind of optimisations could be done to the recursive version of this algorithm to speed it up and potentially reduce the number of function calls. Maybe it could be done with calling a single function per recursion rather than branching into 2.

good pronunciation: матрёшка)). subscribed when the video about kivyMD came out. they have a new kivyMD builder. like!!!

I heard that mesuring is best with perf counter, but i also just use time and i don't see much difference

thanks very much for the explanation. I was having issues understanding recursion. Isn`t python convention snake case, though? thanks

beauty and brains at work. good job

Hey, isn’t time.perf_counter() used as a better alternative for time.time() ?

OMG this was amazing

5:25 "perfetto, bravo!" Ahahaha glad to hear you speaking italian!

Great video but there's some extra information about recursion limitation. The biggest problem of recursion is related to call stack recursion deep level. Each time a function is called, their parameters, return variables and the next instruction address (the next address after the called function), are stored on stack (maybe some extra information too), so a lot of memory is needed to be stored on stack to call a function (now try to imagine call a function recursively several times). Well, the stack is limited at compile time if you're using a code managed by a virtual machine, interpreters or even a native code, so if you are calling a function recursively you'll reach this limit faster depending on architecture your software was written or running (x64, ARM....). Some C or C++ compilers limits, by default, this deep level of stack to something between 360~400 recursion levels. In Python I think this level is something up to 997.....so try to run your example (recursive function) passing a 998 index number or even a higher value. I think that Python runtime will complain something like (stack overflow) or even a recursion error. Changing this stack size is possible but the new limit can be reached in future scenarios, so using recursion is something unsafe for cases where recursion limits are higher. Regards

i like very much this kind of tutorial!!

Hey Mariya. I'll like to suggest that you make us a lecture on Git. :)

You are so great and its a réal pleaisure to ear you and to se you Gond job 👍

I wish i had a gorgeous teacher like this lol

Cool! like at pure functional language

Nice job with this video young lady. Perfecto! Bravo! in spanish. Love it!

Thanks a lot.. .. It helps me than Mark Lutz's book. ....

‘To understand recursion, you must first understand recursion’ - Recursion Explained ;-P

Nice WORK.

very good explanation ... and 😱 wow i love when you speak italian 😍

Thank you!

I love your Harry Potter t-shirt!. Our teacher make us stay longer at school so I wasn't able to come to the premiere ://. However, amazing video.

Thank you for your video (I know this is a year old but still), I was getting 0.0 for both recursion and iteration, so I decided to dial up the function call number to 500...............that didn't go so well. Dropped to 40 and recursion took approx 12 seconds, while iteration took 0.0 seconds still. I'm assuming this is due to the increase in speed from using python 3.11? What do you think? I commented out the recursion and ran iteration with an index of 5000 but iteration still only took speed : 0.001001119613647461 while trying 50000 I get an error returned "ValueError: Exceeds the limit (4300) for integer string conversion; use sys.set_int_max_str_digits() to increase the limit". I was able to squeeze under the 4300 character limit with 20000 as the index value but it still only took speed : 0.013011455535888672. Recursion with an index value of 40 took 11.886 seconds, while iteration with an index value of 20000 took around a hundredth of a second.

You help me a lot with my studies, thank you so much, the way you explain is perfect. Women in stem yas

def tail_rec_fibonacci(idx, a=0, b=1): if idx == 0: return a return tail_rec_fibonacci(idx-1, b, a+b)

I am taking the Coursera course and you explain things way better than the instructor on there

very good bueaitufl video

Nice 🔥👍

in this example : def tri_recursion(k): if(k > 0): result = k + tri_recursion(k - 1) print(result) else: result = 0 return result print(" Recursion Example Results") tri_recursion(6) the output: 1 3 6 10 15 21 i look eon stack overflow and i know that it basically is 6+5+4+3+2+1 , then 5+4+3+2+1 and so on. I'm confused on how its grabbing the sum of the previous iteration and storing it without using the += operator. Can someone please help!

Great lesson... Mariya ..I am a big fan of your classes and accent ❤️❤️

Having fun while learning python and programming. The best teacher 🙂

Muchas Gracias!

why am I getting different results for print(EvenNums(8)) and EvenNums(8) ? @ 1:54

As usual..... ❤❤❤

When i use the time module (like your example) in spyder my time results are both 0, when I use timeit with timeit.default_timer() the time is correct, I don't get it?

thank YOU!

Why in the else clause EvenNums(num-2) , why -2 ?

I really love your shirt 😍😎

Masha, do you do algorithmic trading?