Introduction to Big O Notation and Time Complexity (Data Structures & Algorithms #7)
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- Опубликовано: 12 май 2018
- Big O notation and time complexity, explained.
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Special thanks to Brilliant for sponsoring this video.
This was #7 of my data structures & algorithms series. You can find the entire series in a playlist here: goo.gl/wy3CWF
Also, keep in touch on Facebook: / entercsdojo
After I finish my course I want to send this vid to my professor and tell him to explain it this way to make the student's life easier.
Noice
Lol
savage
ikr... why are most eng profs shit...
Me too homie
Humble message to all the teachers I ever had:
This is how you teach.
Dara to mention them @sunil shetty😅😂
Yes exactly I hateeee my lecturer
ifkr
Teachers are obsolete.
I'm pretty sure that spending 36 minutes to explain something pretty simple isn't the right way to teach, unless your students are ...
"I'm gonna use pseudocode"
**uses Python**
Python: "Am I a joke to you?"
UAHAUHAUHAUH
@@MrKiraBR yareet there pal?
Top 10 anime plot twists.
My professor does the exact same thing. Assignment: Write the pseudo code for a sorting algorithm and run it. You can’t run pseudo code!!
@@melvinsoto Sure you can. Make a state table where the columns are variables/registers/array elements etc and the rows are the state after the line number is executed. Treat the pseudocode as interpreted code, with you standing in for the interpreter, and track the state on the table as you 'run' the code.
I sat in class for the whole semester struggling to figure this out. Then I see your video and understand it in 30 mins. College is a joke.
That is the problem
Teachers who teach us those things
Got their computer science degrees from a long ages .
They are old , so serous and boring
college is an expensive joke
@@muhammedmishal1237 facts
You are so right!
In college, you would rigorously define O notation, along with theta and omega. This video isn't rigorously defining it, which is why it's so much easier to understand.
In high school, and intro calc class, limits are easy and intuitive to understand, but it's the rigor of the epsilon delta definition that causes so much confusion.
I don't think it's fair to say that your professor is a worse teacher when the video isn't necessarily explaining the same content.
I'm in my late 50s and starting a DS & A university course, and of course the first term I hit was "big-Oh" and when I saw the academic definitions it nearly triggered a panic attack. I am SO grateful for this engaging lecture and also immensely grateful that the Internet makes such valuable content available.
why are you not fishing or living in a hut
Why don"t u study instead of being rude@@Imsupposedtostudy
We're on the same boat, and this lovely tutorial also saved me from panicking! Keep on going my friend!
0:20 sum function
1:30 how much time does it take to run this function ?
-> depends on the computer & programming language etc..
some tools to answer the question : Big O notation & Time Complexity
2:40 testing the function in python
4:54 Time Complexity
-> Linear time
-> constant time
-> quadratic time
5:42 Big O notation
-> Linear time, O(n)
-> constant time, O(1)
-> quadratic time , O(n^2)
7:30 how to find big O from an expression
-> find the fastest growing term
-> take out the coefficient
10:54 convenient features
-> gives you a rough idea about how your function scales as input increases
-> doesn't depend on your practical environment
12:38 practice_1
17:40 practice_2
-> O(1)+O(1)=O(1)
20:51 practice_3
25:06 practice_4
31:52 practice_5
edit : Free Palestine !!🍉🍉
based
Free Palestine
Free Palestine
4 years of University couldn't explain what you just did in 40 mins.
You truly have a gift!
bro, my lecturer just explained it so poorly for 4 hours. And you just made it so understandable in half an hour! good job man thank you
I went to UC Irvine in Southern Cal. I had a professor (obviously PhD) who graduated from a big Ivy league who explained this. I could not understand. I couldn't F understand from the course book also. Now I understand. You are such a great teacher.
The ability to teach is truly something only a few ppl who are actually good should be allowed to do. Otherwise, you end up thinking you're the dumb one when really delivery of the material was bad. So many dreams crushed this way
Lol pattis
@@saveUyghurs Completely agree. Teaching is not only a highly respected but also a high demanding profession.
I think the way teachers are recruited should be totally revolutionized and teachers themselves should prepare and plan the lecture before delivering it.
lmao shindler?
Knowledge of effective teaching is what they needed in order to teach effectively rather than just having an Ivy league and Ph.D. background.
Hey guys, sorry for the delay on this video.
I traveled for a week, and I sort of fell out of my routine after that. But I’m back!
Anyway, thanks a lot to everyone who messaged me or commented on my videos while I was away.
As usual, please let me know if you have any video requests in a comment below :)
CS Dojo you will start all new languages but you don't continue it
And you will start again new language we are suffering
Which languages?
Bro pls make videos on competitive programming
CS Dojo what is the complexity of the original sum function? In python i think you could do func = (lambda given_array: sum(given_array))
CS Dojo Please make separate videos on big oh, big theta and big Omega.
Thank you for the helpful video! Great examples for a beginner
0:21 Intro w/ example function find_sum
2:40 Testing actual runtime of example function in microseconds
12:37 Another Example: stupid_function O(1) compared with O(n)
17:03 Without Testing runtimes: BigO + TC for stupid_function and find_sum
25:05 Another Example : O(n^2)
34:04 Wrap up
🎉
YK, just wanted to say how much I appreciate you for dedicating your valuable time and knowledge to the youtube community of developers. I am starting out fresh as a software developer and CS major this fall. Your videos are excellent learning tools are are helping me to grasp the discipline so thanks man!
Did you graduate now?
I should be paying my tuition and fees to you lmao
Seriously, thanks!
Having to pay tuition for going to university/college must suck /🇸🇪
Cruzer ikr 🇳🇴
The flow of your explaining is excellent. After getting frustrated from reading this from text books, I came here and now it looks so simple to understand. Really excellent man..☺
I remember when I was taking CS Applications I was so confused when watching this video, but now that I am watching it I can’t believe I couldn’t understand it the first time. It’s explained so well!
I have learning it at university at 2013 and i couldn’t understand this s***t. After ten years, i can proudly say i get it. Thanks you guy. You are genius. That’s the best algo complexity’s explanation that ever seen
Hey Dojo. Keep up with the amazing videos. You're destined for greatness!!
And can you also add O(logn) and O(nlogn)
No, it has to be a mapping inside O(). O(n -> logn) O(n -> nlogn)
@Youssef Zahir Data Structures and Algorithms in Python [Goodrich, Tamassia & Goldwasser]. Chapter 3
I tried so many channels and learned something but nobody taught us like you. Your content is too much deep. hats off men
Sir, you are doing a really great job. I am able to understand each and everything in this tutorial. You put so much effort into your tutorials. I cannot thank you enough for this crystal-clear explanation. You even quit your job at google, just to teach and share your knowledge with us and that too for free, mad respect for that. Thanks again sir.
I learnt this concept from a course and I swear no lecturer explained it better than you did. Good work man😎
This is by far the best explanation of time complexity and how to calculate it for any function that I have seen on RUclips. Thank you.
Thank you for this video! You did what my professors couldn’t! You’re really good at explaining in a simple way but getting all the information across anyway! I’ve tried for a week to understand this and your video really helped!
I've been struggling with this concept in my data structures & algorithms course, the way you explained it helped 👍
Amazing! my university professors were not able to explain this as well and clearly as you. I'm so happy that I finally understand this concept. Thank you for sharing and taking the time out
I'm sorry but the 151 people who disliked this video need Big O explained to them in crayon. This video is perfect.Thanks a million!
>:( n IS A LETTER NOT A NUMBER HOW DO I MULTIPLY IT
Imagine not being able to understand basic algebra and trying to learn computer science.
i need it explained in crayon.. lolol
@@ericcapiz6516 same. Pls explain in crayon 🖍 with pictures and colors 🥺
A lot of arrogance on display here. No, this video is not "perfect."
The instructor could have given examples of a 2D array that was not square.
Ultimately, the final example is _either_ O(n²) or O(N) depending on if you're referencing your input size to being either n rows (in a square array) or N total elements. Both descriptions are valid, but you need to clarify. This is an important point that is not discussed.
It would have been better to use an example such as: a function that takes each element in a 1D array and multiplies it against each every element, returning the sum of all i×j. That would have resulted in a O(n²) complexity with a 1D input. Everyone would agree on this without ambiguity.
It also would have been nice if the video had shown examples of O(n×log[n]).
By far the most comprehensive explanation of time complexity and big O notation I've ever met, so simple and clear. Thank you!
when I watched this a week ago , I didn't quite understand this.Maybe because that was my very first time to learn Big O and time complexity.But this time,I really understand everything U taught.Thanks sir! and if there were someone out here who didn't understand this right away , don't be discourged.U will understand this when u watch next time.
Thank you so much for explaining this. I have a quiz on Big O analysis tomorrow and I was completely lost before watching this video.
Finally, in my current life. I understood this concept. Can't thank you enough dojo.
I was about to Google Big O Notation when this video appeared in my recommendation and it clears out everything!! Many Thanks!
I started coding two years ago after watching your videos, now I'm back and still getting so much out of your content. Thanks so much for creating this content.
Thanks Bro, I just cleared an interview with the help of this video. Love you from India
Hey Dojo. It's been a pleasure learning from u. Plz upload the complete explanation for Big O Notation (log, limits etc).
you simplified the concept in a way that we don't memorize anything but understand them.
thank you so much for your clear explanation 🙏
One of the best in the world, I found you on my first teaching python using Jupiter notebook. It was unfortunate in my school they were using wing as IDE. Two years later I found you again and I'm fortunate we use the same concept of Data Structure.
You're a fantastic teacher! Thanks for explaining it so clearly.
Read multiple books and watched several videos on this subject and i didn't understand anything until I stumbled upon this video.
This guy is a legend.
If anyone has a hardtime understanding the big O notation, they only need to watch this video!
I love the way you teach stuff. It is clear, crisp and insightful. Thank you CS Dojo :)
The mathematical rigorous explanation of Big O Notation would be much appreciated, brother. Thank your for the videos. :D
Big(omega)
Great video, I finally understand Big O and how to get it for my programs, the ending was exactly what I was wondering about, what if there's two equally growing highest terms.
Someone correct me if I got the wrong expression but since O(2n^2)=O(n^2) I think it's safe to simplify the initialization, addition and return of variables to O(1) when non scientifically determining the big O notation as it will probably never increase the notation more than it would have been anyway
Your explanations are the best I found online regards the topic you cover. Thanks a lot for the effort you put. It is cool that you concentrate on basic concepts and think logically. That is far more important than watching ML videos were they just use libraries. You teach us to be creative and how to be analytical.
This video has literally cleared all my concepts on this topic. Thank you so very much CS Dojo!
Having just learned to make a sorting algorithm and hash table in C I love when he said “I implemented it in Python” but the pseudo code he wrote is perfectly valid Python already
I am fond of the way of your teaching.
You finally made Big O click for me in the first 11 minutes of your video over some of the other 1 hr lectures I tried listening to. THANK YOU SO MUCH
I am not a computer science student, I have been struggling to understand BIG O Notation for month, this solve this in the simplest best of way. thanks a million
Hi CS Dojo really love your content!! Please make more content on python for people coming from other languages like java,c++ gives the differences in syntax, structure in OOP, control statements, inbuilt data structures and important libraries in it. Also missed you for so long !!!😻
Okay sounds good. Thank you for saying that!
CS Dojo my pleasure 😇 YK!! Thanks for making videos!!!
I really would love to see a explanation on the mathematical details!:) When i wrote programms for maths class I always myself how I could figure out how much time a certain Programm would Take to run and if it's even worth to wait for a result! Thank you for your video
Here is the more accurate mathematical definition of O(something):
Let be U(n) and V(n) two sequences then U(n)=O(V(n)) if and only if U(n)=W(n)×V(n) where W(n) is a bounded sequence in other words it exists a natural number 'N' and a real number 'M>0' where for every natural number 'n' with n>N then | w(n) | < M
This ( O( ) ) is used to approximate the behavious of a sequence with an other , in other words _ and in the case of time complexity _ the graph of execution time for an algorithms is very similar to the one of the expression inside the parentheses after big O.
Okay! Sorry I just saw this comment - I'll see if I can make it after my trip :)
++++++
I would love so too
same here
Your teaching style is unmatched. Thank you for this video.
Finally someone who knows what he's talking about and knows how to explain! Thanks very much! Reminds me of organic chemistry tutor, also an excellent teacher
In the first function in 'pseudocode' if you remove each it will be a good python code:)
Haha yes, I noticed it, too :)
Python IS pseudocode
@@vikrantsingh47 thats why its amazing
@@azizalaliq8 I loveee Python 😍
Hi, awesome video as always.
Thanks for putting this together. I enjoyed your method of blocking out the equations, and revealing them later. It's very clean. Keep up the good work!
Amazing video. I've just started out in Python Programming having had no prior experience and I can confidently say I understand time complexity well enough thanks to this video. Thank you SO MUCH for taking the time to create this content! :)
Hey CS Dojo Really love your teaching and content ...I hope you make a lot of videos on Data Structures ..I have watched your other videos ...Awesome Work ..God bless you :)
Fairoz Ahmed yes plz data structure n algorithm analysis... more videos on BIG O plz discuss its each n every aspect
My drug is back!
お久しぶりY.Kさん!
I started watching your videos recently! Its been grt n I have never been through so many programming stuffs in a shorter period any time in my entire life...keep up the grt work (y)
Thank you so much! This was so easy and straight forward. No book has ever explained it to me in a way that i got it right away! Thank you and keep up the good work!
The box approach is kinda cool, really helps not throw all the stuff at you in one go
Hey Sugi! Thanks for this wonderful tutorial. You just nailed it.....Simple, precise and easy to understand. Go ahead, you're doing excellent :)
#CSDojo
Best tutorial on Big O on this planet. Everything clicked with this video. Far superior than Hacker Rank
This is by far the best explanation I have come across regarding Big O and time complexity.
Thanks buddy
yes, please make formal definition video. Thank you for posting.
this is a great video!
one small correction: for the first find_sum function, i believe total should be total += array[i], rather than i.
other than that, great video! kudos to you.
It's a shame for me that I have worked with various types of projects but I don't know basic things like this, thank you, you just made my day! :)
THANK YOU FOR THIS VIDEO CANT UNDERSTAND MY PROFESSOR BUT BRO YOU NAILED IT!
"I use pseudocode for demonstration."
> shows python
😎
HAHAHAH my thoughts exactly, but then that could be his level of pseudo-code.
Volvox I KNOW ROGHTTTT
Python :am i joke to u ?
"for each" is not Python. :)
I just knew this topic because I have to take an exam for a job application but he explained it very well! I didn't know I can watch, listen and learn from a youtube video this easy. Omg thank you!
Sir your way of teaching is fabulous. Any novice person will become expert from your way of teaching.Hats off to you for this endeavour and fantastic way of teaching. Lots of Thanks to you Sir.
please make video on O(logn) and O(nlogn)
Thank u so much for your nice explanation
Please were you able to find a series that explained the O(logn) and O(nlogn) properly?? if yes can you please share as i could not find the series that covers this on YK's channel. Thank You
pls make a video about formal mathematical definition of Big O!! I need it very much, so do the rest of us. Very nice video btw, keep up the good work!!!! Love you dawg, see you in heaven ;)
Unbelievable how simple the explanation is. Thank u
I’ve been struggling with this concept but you explained it better than most!
14:41 if you're removing all the coefficients then the 1 will also be removed.Instead of that you may write the function as
0.115 * x to the power 0 so that variable x remains according to the rule(anything to the power zero is 1).
Well, you are stuck in an infinite loop there.
ruclips.net/video/vrnzAj9jnoE/видео.html
1 is not the coefficient. 0.115 is.
Thanks
I really understand more much better bigO now with your explaination than my lecturer did in college. I wish i knew your video several years ago and i hope i can achieve my dream for being a lecturer then teach these to my student so they can understand as much as i did. Thank you so much, may god bless you.
Where have you been all my life? You summed up in less that one hour what I have been struggling for weeks to learn. TY!
The array_2d example solution is incorrect. The input data size is N=Row*Row, since it's generated outside of the function and irrelevant to the function's own complexity. The actual complexity would be O(N) because the function itself is going through each element of the input only once.
It's easier to understand if you consider that the same function can be implemented with accepting a one dimensional array (with the same number of elements as the example). Thus the actual function complexity would be O(N).
You are rigth.
If 2d_Array.shape is (n , n), then he: O(n^2) is correct, you are wrong.
If 2d_Array.size = n, then you: O(n) are correct, he is wrong.
yeah I'm pretty sure he was basing it on the 2d array on the left where it was size n by n.
He put the other n by m there to explain rows and columns.
Do you happen to know why the formula for stupid_function, is T^2? I understand that its runtime is O(N), but do not know why Time was written as T^2.
Actually it's better to say O(n*m), because N is the time it takes to traverse the first array and M is the time it takes to traverse the nested array. But yes theoretically O(N) is also correct.
hello brother,
in the video, you mentioned that the second function's(the one with for loop calculating sum near 22:35) time complexity as n(O(1)), and T2= O(1)+ n(O(1))+ O(1)...but there is a CONDITION in the FOR loop to check the ENTRY of program control(until i is less than number of items in array), why you didn't consider the TIME TAKEN in evaluating that condition??? can you please explain that??
Because he was trying to keep this as simple as possible. Explaining loop terminating conditions isn't necessary to understand how this time complexity notation works.
He also excluded the time difference between passing the array as a value versus a reference. When estimating scalable performance times, that could be a bigger factor than the loop itself.
A very good and detailed explanation of Big O notation and time complexity. I'm a college student and I took Data Structure course before but the professor was suck so that I end up did not learn any knowledge about Data Structure. After I watched this video, I really hope that you were my professor at the time that I was learning Data Structure. Excellent video.
It's been a while since I did this - so came here for a refresher. Very helpful and neatly explained. Quite liked the way you illustrated the concept. Keep 'em coming! :)
Please put formal mathematical definition video for O(n)
+++++
Thanks for the great videos! I'm currently using several of them in the classes I teach. The example below is from Blue Pelican Java Lesson 38 by Charles Cook. Your last example with the 2D Array and the example below look like the same idea. However, Cook explains that the Big O value is O(n) because you are essentially adding each element of the 2D array once, that is O(r*c) where r is the number of rows, and c is the number of columns. Could you explain what the difference is?
public static int[] addStuff(int x[ ][ ])
{
int row, col;
int b[] = new int[x.length];
for(row =0; row < x.length; row++)
{
for(col= 0; col < x[row].length; col++)
{
b[row] += x[row][col];
}
}
return b;
}
Yes, this one is a bit more complicated than the previous ones. Let’s assume we call
this method with the following code:
int dfg[][] = { {1,2,...},
{0,4,...},
... };
//Assume this array has r rows and c columns for a
int newArray[] = addStuff(dfg);
//total of rc = n elements
Studying the addStuff method, we note that we go through the outer loop x.length
times which is the number of rows, r. For the inner loop we go through x[row].length
which is the number of columns, c. Therefore, the total number of times through the
code in the inner loop is rc, which in turn is just the number of elements in the entire
matrix, n. We can write the Big O value as either O(rc) or O(n).
From my understanding I think it's because in his example we always have n squared number of elements(number of rows = number of columns), that's why the time complexity is increased. In your example the number of rows and columns are two different variables O(rc) hence O(n). They seem 2 different cases to me that I could easily mix up, if you didn't point this 😀
I tried to understand this concept on Stack Overflow but had no success. I have a better understanding now. Great explanation! Thank you.
This is by far the best explanation about such topic. Really thanks!
Please make a video talking about "how maths important for programming"
You need to know addition at the very MINIMUM!
Shouldn't the "for each i in given_array:" be 0(n) at 22:28 ?
Depends on how you look at it, if you look at the for loop as a compound statement that repeats everything inside n times , you could say it is O(n). Or you could like at the statements inside the for loop and determine their big O notation. Since you repeat those statements n times, you get the big O of the for loop as n times the big O of what’s inside the for loop. So it’s the same thing, the perspective is just a little different. :)
@@oliviervanlier4947 I get what he is saying in the video but isn't it wrong to write n x O(1)? Because mathematically speaking n x O(1) could be written as O(1) + O(1) + O(1) .. n times + O(1) and as we know O(1) + O(1) is still O(1). I just want to make sure I understand, not throwing any hands. :))
This is a great course! Clear, detailed, and understandable. Much better than all my professors at the University, especially my supervisor...
A simple and clear way to explain Big O annotation. Fantastic video, congrats! 👏👏👏
Where the hell was this guy when I was doing my CS Degree !!!!!!!
Hi..sir hello. I am a student from India. I am doing Btech 2 nd year now.ECE streem. What should I do now for getting job in product based company.
I would say continue improving your coding skills and work on personal projects!
If you can make a project that gets popular, I think that will be really good.
CS Dojo will u suggest me how to learn coding. Seriously I don't still to code. And give me ideas about projects. Pls..sir
Get some keywords about the domains you like. May be embedded systems, IoT, Machine Learning, etc. Try to search for introductory videos on them. If you find any of them interesting enough, you can then look for groups on LinkedIn, or courses on coursera, udemy, etc. You will also find many blogs and content which you can practise to further hone your skills in that domain. The more your get yourself attached to a field, the more ideas will pop up. Set up github to showcase your work.
search for similar questions and ask your questions on quora
My professor, who has been teaching programming for 35 years, could not explain this concept properly and you just made it look so simple in just 30 minutes. Not all heroes wear capes, indeed.
I really enjoyed this video. Great Job!! It was a good refresher for me before I started interviewing. I was given some problems to solve as part of an interview and I nailed it.
"I'm gonna use pseudocode to explain this..."
...
...
...
NAH... *uses Python*
17:41 - how to find time complexity
Great stuff as usual! Going to make sure to watch all the vids on this Data Structures & Algorithms Series
Sincerely, what a tremendous talent!
Took me 36 minutes to understand everything that I have been struggling to understand for weeks.
Thanks YK
Fuck that ***pp
What if the row and column are not equal will it be O(mn)??
Stupid function 👌😂😂
My exact question too! And I think it would be linear O(n) where n = rows * columns
This was a seriously good explanation of big O notation. Excellent work, dude!