Binary Exponentiation

Binary exponentiation (or exponentiation by squaring) is an algorithm that quickly computes a big power a^b in O(log(b)). This tutorial for beginners includes the intuition, examples, and two C++ implementations: recursive and iterative. Check out cp-algorithms.com/ for articles on more advanced algorithms.
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- Frequently Asked Questions: github.com/Errichto/youtube/w...

[@danieldawson8018]

It's cool to see you get better and better at explaining as time goes on, and you were already good to begin with. Thank you, and keep it up!

[@devendrasingh4776]

Quite obvious as he is a fighter and he knows it.

[@marvinlessknown3702]

He really is very good. Is he russian?? They're the best teachers / mathematicians I've ever. kantorovich being maybe the greatest??

[@justsvk1500]

​@@marvinlessknown3702 polish

[@shubhamghule4606]

Your videos are the reason I started competitive programming 🙌 thanks a lot!

[@Errichto]

that's great to hear!

[@digitalgandu1511]

Why ?

[@fahadhos]

@@Errichto so your code will support this 5^(10^5)?

[@hil449]

@@fahadhosyes, its lob(b)

[@rakshithdogra793]

Hey Errichto i saw your video and got motivated towards CP and today only i solved my first problem on codeforces thank you bro

[@Errichto]

Cool, good luck!

[@jdhp3696]

Errichto, when you first released it, I didn't understand the concept of it, but decided to save it in my playlist to watch it later. Today, I was solving the daily challenge on Leetcode and suddenly remembered your video. Watching it now, things start clicking for me. Thank you so much. Please make more videos like these.

[@nickheyer]

I truly appreciate the "over-explanation" of even the more simple concepts. If anything it is a reinforcement that helps drive the concept home, instead of just skimming over it without any actual absorption.

[@tomtan298]

Your videos are the reason I started competitive programming ! Thanks so much for the contribution to this community,keep up the great effort and keep on pumping out more videos for the beginner series :D

[@yeetholmes619]

I like how you smile when you explain the concept, shows your deep love for the art! A pleasure to learn from you !

[@ANKITVERMA-fl1zn]

The Overall Quality of videos are getting better great work indeed! waiting eagerly for Gaussian Elimination.

[@manishsharma2211]

Errichto , The picasso of CP👌🔥

[@TyButNowYouDie]

I had already solved this problem recursively before but I didn't understand the iterative solution until watching this video. Your explanation and visualization was really helpful. Thanks!

[@hardikupadhyay9837]

Waiting for some more advanced stuff to come :) This videos are really great

[@ritikbaid4318]

Great content Erricto!.would be great to see some videos in the future on segment trees as well!

[@tonystarc9567]

Errichto you are a savior.... Please keep up doing this good work ... This matters a lot specially in the countries with small per capita income...

[@CarlosMartinez-ed7ey]

Thank you very much, you have a natural talent to explain clearly and make it easy.

[@SebastianTysler]

Thanks Errichto! This is good and easy explanation for fast-power (Binary Exponentiation)

[@ductran7258]

Thank you! Your explanation for this algorithm is awesome!

[@LearnWithAnmolll]

your article is just awesome

[@ashwinmadke486]

Wonderful explanation ❤️! Understood every little thing. Thankyou 🙏

[@Garentei]

Best channel ever. This was actually my Facebook interview question.

[@vikku_19]

Really? Or They asked about of digits? Generally, we're asked about digits of big powers.

[@Garentei]

@@vikku_19 No, it was binary exponentiation. But he didn't explicitly ask me to do so, he asked me to optimize a^b.

[@johnstephen8041]

Thanks much... keep doing these kind of videos.. really helps!

[@MojahooProducer]

wow another video, i thought your stream was planning a lot. thanks for your dedication, remember not to push so hard that you burn out! youre perhaps even the best educational channel i've seen, the way you explain things helps you understand how to get there too.

[@Errichto]

:3

[@dipankarkumarsingh]

thank you for your wonderful explanation... you are an amazing teacher .

[@craigmiller9380]

Best videos on youtube, thank you!

[@vinitsharma6630]

i wasted my time in another video watching it again & again trying to figure this out this made it crystal clear covering every doubt the previous video created like the shift and mod ones

[@jonathanparlett1172]

This was super helpful for my cryptography class thank you!

[@shameekagarwal4872]

thats very good!! please do cover diophantine equations, fft etc as well...and in such topics maybe include popular question and variations thanks!!

[@vedshrutisarkar4319]

Thank you for a perfect and easy explanation😄

[@Aman_Panchal27]

This video helped a lot. Thanks Man.

[@sujan_kumar_mitra]

Best explanation of binary exponentiation

[@yatharthfrommeerut9006]

I always thought why we studied this multiplication in principle of programming language. Now I know. Thanks

[@siddharthpanigrahi3855]

Thank You, explained really well.

[@Aditya-fx2tv]

Love your video errichto ❤

[@rakeshghosh8234]

Great way. Its very nice than previous.

[@sajinamin328]

awesome video bro. take ❤️ from 🇧🇩

[@hackytech7494]

Thanks for the explanation

[@souravsaha933]

Fine answer. Thanks ❤️

[@AbhishekSingh-ws5rz]

Another great video. 😊

[@yashrastogi3726]

Thanks man. Keep it up

[@kgCode658]

wow u also have great teaching skills ..Thanks for helping

[@arushsaxena1213]

great video. It would be awesome if you could make a video on Merge sort tree.

[@SmartCoder89]

I like the new background 👍

[@em_nikhil_007]

Are you kidding me ERRICHTO!! How can you read my mind for what topics i need????

[@parnabghosh7877]

great explanation !

[@adityatewary7174]

Hey, Errichto thanks for the video. Can you also put some questions link in your description box?

[@CodeDecipher]

Great video you upload 👌 I myself make computer science videos . Can you tell me which mic do you use ?

[@RamisaAnjum]

12:10 Thanks, man :D I thought I was the only one.

[@asifanwarsajid8332]

Kamil, we need more videos from you. :D

[@AbhishekKumar-ky3uc]

Hi Errichto, I am a subscriber of your KZbin channel and admire your work alot.Wanted to ask for an advice , how to learn solution of a problem when it's solution is not present anywhere on internet. Even if I get a hint it's easier. But there are some problems like asked on an interview whose solution afterwards I get nowhere in internet. How to learns solutions of such problems?

[@w4rd3nclyffe74]

can you make some videos about fractals in action? also, you're videos are *CRAZYYY* you're so good at explaining stuff

[@vijendrasaini3050]

Just Watching A.B%N and this one pop out. Seems like whole series on NUMBER Theory coming out.😎

[@Errichto]

As some people might know from my recent stream, next is matrix exponentiation and gaussian elimination ;) then more advanced topics

[@loneshaan8531]

@@Errichto looking forward

[@shahbazalam3722]

@@Errichto Excited to learn Matrix Exponentiation.

[@Gauravverma-ed7fw]

@Errichto please continue the series for mathematics in CP

[@Gauravverma-ed7fw]

@@Errichto please continue series for mathematics in CP

[@omaraljarrah5089]

When the Matrix expo is coming? We have been waiting for a long time now, looking forward to the new video

[@CarrotCakeMake]

It amazing how there exists and algorithm to create an output of size B*log(A) in time log(B).

[@Errichto]

The complexity O(log(B)) assumes that multiplication is done in O(1). This makes sense because we mainly compute a huge power modulo P.

[@097kushagrarawat9]

really helpful content :)

[@carbyte2673]

Thanks a lot man!

[@riadhasan9725]

Very helpful 👍

[@Ghayth.Moustpha]

Thank you a lot ❤ Can you please recommend some problems to implemented as a training... Thanks again ❤❤💙💙💙

[@omaraljarrah5089]

Thank U, U are awesome 🤘🌨❄

[@amanrazz2091]

GOD level explantation .... 🖤

[@preetamvarun9219]

Thank you

[@dadisuperman3472]

Did you added the tag "Easy" on the thumbnail of the video? It was not there before.

[@ChandraShekhar-by3cd]

Errichto Your are the "Einstine of CP".

[@ChandraShekhar-by3cd]

@@audiogear4412 Yes I do.

[@rajshubhankar1725]

Hey what if I remove the 0 condition instead of 1. why just if(b==1) return a is not correct ?

[@enside8822]

Thank you!!!

[@ahsanulameensabit]

Waiting for the next one...

[@user-ui2qk6jg5n]

can u please make a video abot how to setup your cp setup - how to download and use yor ide? would also like to see some c++ toturials tank you very nuch!

[@falseee4445]

Thanks !

[@diwyanshukanthwal8669]

can you tell about left to right binary exponential

[@venkatkumar5220]

Can you do a video on Matrix Exponentiation?

[@rohanprak]

@errichto *please* make a video on Segment tree *iterative* with *lazy propagation* , everyone teaches recursive one, with memory 4*n and 5 arguments !! non recursive if okay till point updates, but range updates ( lazy propagation ) seems way too complicated. please make a video on *lazy update* on *non recursive segment* tree, we belief you will make it simpler, and also no video on you-tube exists on it.

[@ankitchoudhury9678]

Damnnn.. love you

[@ujjawal_]

which whiteboard website you are using

[@rujixie9025]

So neat

[@hil449]

didnt understand a single thing from the inverse part but ok, great video

[@kakashisenpai99]

Bro post your Hackerrank problem , 'Lisa's Workbook' approach and solution!

[@II_xD_II]

respecckt

[@HelloWorld-sy4yc]

Do u have a blog or channel in telegram for instance?

[@shoryasinghal5241]

good eric

[@harshamusunuri1924]

I don't understand the iterative part, is there any other simpler way to understand this?

[@i.anandsingh]

can you please explain how to find PRIMITIVE ROOTS,? and EULER'S TOTIENT FUNCTION.

[@tarsala1995]

You can calculate 9^9 I remember that it's 387420489 But it doesn't really matter

[@shubhamghule4606]

Missing the teddy 🧸!

[@climbnexplore1187]

But instead we have alcohol left of errichtos shoulder... wait why does Oxygen have three connections ?

[@shubhamghule4606]

@@climbnexplore1187 Its carbon bro !

[@VachaspatiMishra99]

Dimitri finds out.

[@himanshudixit490]

Problem: You are given a sequence of length n. Apply to it a given permutation k times. Solution: Simply raise the permutation to k-th power using binary exponentiation, and then apply it to the sequence. This will give you a time complexity of O(nlogk) Can anybody explain what its talking about ?

[@i_am_wiz]

I didn’t understand how 0th bit contributes to a....1st bit to a^2.....2nd bit to a^4.....and so on.....can anyone please help?

[@iliavasilenko4961]

Is it normal when somebody uses ints instead of long long?

[@abhudyasingh9109]

How to calculate pow(a,pow(b,c)) under modulo

[@amalsakkoumi1392]

If a^-b how we can slove it please

[@mdfahad2726]

I love your background 😍. Any specific reason why it contains High school physics, chemistry, maths equations?

[@Errichto]

All science is beautiful, isn't it?

[@5590priyank]

geeky background :)

[@baxi9227]

don't forget to flex how you came up with matrix expo yourself

[@Errichto]

Is it that important though? :D

[@mksybr]

@@Errichto What video was that?

[@anmol_tomer]

I am a simple man, if(Errichto uploads) { make notes && like the video} # :D

[@tombrady7390]

wow 200k kamil take a bow

[@debadityasutradhar7962]

why cant we just use pow(a,b) by taking a & b as input

[@joyo2122]

🙏

[@node3079]

4:57 Can someone please explain ..thanks🙏

[@MrPatrickbuit]

I understand it completely but it’s another one of those things I would not have come up with

[@hamzakhiar3636]

you said recurssive programs are slower than iterative programs why

[@sawvikdipto3087]

Only for My help. Please ignore. def p(a,b): res=1 while b>0: if b%2==1: res=res*a a=a*a b=b//2 return res

[@aquibansari3941]

can anyone please tell which tool is he using to draw and sketch

[@sakshamjain6900]

software is ONE NOTE available on windows 10 and he is using graphic tablet to draw on screen (a board and a pen)!

[@PankajKumarGladiator]

10:54 😂That awkward moment 😂 !!

[@vetiarvind]

6:45 - no need to check for odd in the while loop. just do int result = b&1 ? a : 1; //in the init. This is because b can only be odd once in the loop.