Interval Scheduling Maximization (Proof w/ Exchange Argument) 

Table of Contents: Introduction 0:00 - 1:22 Greedy Algorithm Walkthrough 1:22 - 5:14 What We Want To Prove 5:14 - 7:03 Exchange Arguments 7:03 - 7:33 The Proof 7:33 - 11:30 Trying To Exchange 11:30 - 16:20 Finishing The Argument 16:20 - 19:24 Conclusion 19:24 - 20:17

This is an award-winning explanation if one considers the patience, thoughtfulness and elocution with which it has been done. God bless your continued efforts in education!

I have never seen so in-depth understanding of Interval Scheduling ANYWHERE! Keep killing it!!! THANKS, A LOT! "By the very nature we are doing something, there can be no conflict" hit me the most.

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Can you believe that I have attended two 2 hour lectures about greedy algorithm and I have just understood it in this 20 minutes video! Thank you!

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This man has helped me with my algo class more than anyone else

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I have an Algorithms Midterm tomorrow and I found this video to be super helpful! I could understand everything you were saying! Simple and straightforward explanations are the best!!! Thank you for this!

These videos of him are amazing! He explains perfectly well and understandable. Thanks for that!

been watching all your videos for my final and man you explain 16 weeks of school better in a 20 min video.

You're such a talented teacher, than you for these wonderful videos!

Excellent! As a person with a background in math who now works as a software dev who’s looking for a new job, this was great. Underneath it all, at its fundamental level, i think this a proof by induction. Very well explained!

This makes good sense. I had to picture in my head the diagram or examples as you explained all the WHY's, to convince myself that it's always true. And indeed it is. It's hard to think about application of this to other algorithms though.

Duuuude! The best explanation I've found on Exchange Argument! God bless you!

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Crystal clear!!!! Thank you!

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This helps me a lot. Thank you

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Incredible video! Thank you!

Very good explanation, thank you!

Love this. Wish it would show a written proof with induction. Only saying this because there was a lot of talking, but putting this into a written proof is a bit mind bending. However, absolutely thumbs up and subscribed!

Thank you so much.

Great explanation!

Thanks, this is best explanation of the proof

Thank you so much!!!

Good job. Well explained

MAN was this video well made, thank you.

Very hard to build an intuition for this, but this video is closest I have seen.

great explanation thank you :)

such a great and clear explain, even though I am poor at English can understand.

Jesus Christ what an incredibly fresh cut

Very clear explanation!

great work

Nice explanation :)

I wish you were my professor. This is sooo helpful

thank you sir

watching this tonight coz i have finals tomorrow.thanks for such a great explanation. Have u done interval partitioning as well?

thanks i get it now bro

aaammaazzinggg...got it perfectly

I really should have watch this video before my midterm

Thanks for these amazing videos . could you also add the question link, so that we can try

so good

Subscribed.

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I am a little confused. Does an exchange mean that ur are sawing 2 events? Or are u inserting one and still keeping the other? For ex, gk and bk, did u put gk in optimal set and still keep bk after it or did u replace bk by gk?

you save me thanks

You got a subscriber

Consider a variant of this question. We are supposed to find intervals giving the max cardinality as before. But the added constraint is that in the case of two solutions having the same cardinality, we need to pick the solution where the length of time covered by all the intervals is lowest. What modifications (if any) to the current algo would be required?

Hero !

Nice video, could you do a video on Weighted Interval Scheduling?

I dont understand, so everything is the same from G to O until k-1 but k is where everything diverge ? how can you say that the finishing time fo G(k)

cool and nice

godlike!!

Hey John Legend! Keep up the Good work my man!!

i had a similar problem, but i cant find a solution to this anywhere. in fact, i cant even find the problem anywhere (i originally saw this problem on my university test). the problem is, u r given n jobs with start and finish times, and u have to find the minimum number of processors that can finish all jobs. a processor can only do disjoint jobs (jobs that don't overlap). Sample test case: There are 5 jobs (with start and end time given respectively): 1 11 2 3 3 6 4 6 10 13 The answer is you need a min of 3 processors to complete all the jobs. processor 1: 1-11 processor 2: 2-3 4-6 10-13 processor 3: 3-6

Is there also a greedy method for maximization of the intervals length instead of the amount of intervals?

I understood the first part (the algorithm explanation) but not the one where you compare the Optimal vs the Greedy one. I guess I need to see it more times. Haha. Anyways, awesome work!

how you can say that fgk

He spoke of the code in the description, but I cannot find it

Well I was not cleared how you made sure your greedy solution is the optimal solution. Is it possible to share more information?

I need to rob my University, take all what I've paid them, and hand it all to you

so this looks like a combo of greedy and dynamic programming right???

can we say Greedy Exchange is the most efficient solution?

Why sort by finish time and not by start time? I sorted by start time and it cost me a coding round :(

What is your leetcode username?

too late :'(

I think I kinda got what optimal substructure means here ..

where the heck is the code? 🤔

شكرا صاح! عمال ساعة بحاول افهم بس انت راجل صح الصح وفهمت خلاص الحمد لله.

waiting for your video

sup bro?

Good explanation :|

bro the implementation ? the code?

Great explanation but why does he explain this like a tech bro hahaha

unclear!!!!!!!!!!!!!!!!!

very much thanks sir