Max Contiguous Subarray Sum - Cubic Time To Kadane's Algorithm ("Maximum Subarray" on LeetCode) 

Table of Contents: The Problem Introduction 0:00 - 0:31 What I Think Immediately 0:31 - 0:55 What Is A Contiguous Subarray 1:00 - 1:52 Jumping To The Brute Force Quickly 1:52 - 2:34 Search Contig. All Subarrays: Birth of Brute Force 2:34 - 3:01 Cubic Time Approach 3:01 - 4:30 Cubic and Quadratic Solutions Search All Windows 4:30 - 4:35 Why The Cubic Solution Is Slower 4:35 - 5:34 Bottlenecks, Unnecessary Work, Duplicate Work 5:34 - 6:04 How To Compute Subarray Sums Better 6:04 - 7:32 Can We Improve To Linear Time? 7:32 - 7:54 Establishing The Fundamental Subproblems 7:54 - 10:32 Establishing Our Fundamental Choice 10:32 - 13:23 Walking Through The Dynamic Programming Table 13:23 - 17:54 We Are Done Filling The Table Out 17:54 - 18:14 The Best Answer To Our Question 18:14 - 18:30 This Does Not Need To Sink In At Once 18:30 - 18:46 Time & Space Complexity 18:46 - 18:58 Wrap Up 18:58 - 19:18 The code is in the description fully commented for teaching purposes.

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The curiosity and excitement in the way you teach took my interest to another level

The best explanation of kadanes algo on the whole internet. thanks alot.

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all other people I have watched explained the code directly, but you made me write it after this video. Kudos man!

Never thought of n^3 solution to this problem. The key to understand DP from n^2 is to understand how we got to n^2 from n^3. WOW!

I read 5 different articles and watched 3 different videos to try and wrap my head around Kadane's algorithm. This video is the one that finally made it click. Great job, and thank you for sharing!

Such a good explanation, and I appreciate how you walked through the cubic and quadratic solutions as well, it made it easier to understand the linear solution. Thanks!

Just want to let you know I truly appreciate the simplification of these types of problems opposed to portraying these algorithms/problems/solutions with a steep learning curve in a demeaning manner. Really wish I saw these earlier, but all I can control is watching these now! Keep up the excellent work and hope you have a great day.

I have read and watched so many explanations for this problem and I have to say this video is the best. Others seem like they're just repeating someone else without fully understanding the WHY. I could finally understand why the O(n) solution is written that way. Thank you so much!

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I have always known about Kadane's Algorithm and implemented it so many times but never understood the intuition behind it and that it was actually DP. Hats off to you for making me understand this.

Got an interview tomorrow so I was looking for an explanation to Kadane's. Sleepy af right now and yet I still managed to understand the algorithm thanks to you. God damn man, you really do know how to explain complex subjects so that everyone can understand. Best of luck with your endeavours and keep making awesome videos!

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Countless lectures, dozens of RU-vid guides, but thanks to you I've finally got it! Thanks

If you are at this video, you will not have to look for other video. You are the master of explaining with ease and breakdown. Thank you!

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You are one of the best teachers I have encountered on RU-vid. You broke the solution effortlessly as if it was an easy one. Thanks for all the effort and keep making videos. Cheers!

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Bought cracking the code interview and never really understood this problem. This was the best explanation I've seen so far, I can even code it by myself

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More then Kaden's problem you just explained me dynamic programming in the best way i could ever learn . I guess i can feel dynamic programming now

This video right here is GOLD!! it literally forced the concepts of dynamic programming into my skull. I appreciate this.

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Explanation was good enough for me to write the code. I work in the industry, and I was never whiteboard tested, so I have no experience with whiteboard interviews. Now I didn't pick up on how to solve this until I saw you explaining this, and then came up with the code to make it work. I hope in a future interview, the interviewer will help me out a little bit, to get me on the right track if I were to quit my job.

Thank you for patiently explaining each step right up to the end. I am sure I will never ever forget this algorithm again.

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Just the words "Kadane's Algorithm" should already won you a medal, not to mention the expended explanation! Kudo! A O(n^2) can still pass LeetCode test if you memorize the previous result. But nothing beat O(n)!!

Your video about Kadane's Algorithm is the best one ever! Thank you!

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brilliant.. props to the man and his human teaching style

Way better than some professor from college. Keep going. You have all my support.

OMG BEST video on KADANE's algorithm.TYSM

I have looked for such an explanation for long. Thanks for making our lives easy!!!! Appreciate it.

Respect from a fellow coder! Your explanation and energy are unparalleled.

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When you say best choice among these two, I remember this dialogue in Captain america: Winter soldier which is like - The best we can do is to start over. It fits well in this solution. XD

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Cool，the clearest explanition both in all the English and Chinese videos. You deserve a lot more subs.

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I struggle with codewars and solving such challenges a lot but I must admit, the way you explain is the best I've seen so far. Thank you for this

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Absolutely phenomenal explanation for a complex problem!

Very good explaination and the whole video leads us to think instead of just telling us answer! Thanks!

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Thank you so much bro, you are the first one explained that why get max between (current_sum+i, i) instead of get max between (current_sum+i, current_sum).

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wow this is an amazing explanation of kadane's algorithm

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absolutely lovely. the best explanation of the ones I've seen on the internet.

The best explanation of kadane's algorithm !

I wasn't understanding Kadane's algorithm for the life of me but this video really cleared everything up. Thank you sir!

Hands down the best and most intuitive explanation of Kadane's algo. Awesome!

Was struggling to grasp the solution intuitively until you explicitly pointed out what the sub-problem being solved at each step is! Thanks :))

I think the entire video was beautifully summed up in the time slice 16:45-16:50 ... beautiful.

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This guy is brillant!! Kudos to your effort!! Thank you!

Appreciate that! I can tell this video has taken a lot of time! The thing I did not understand was the key to this strategy of DP: subproblem should be what is the maximum END of this index instead of what is the maximum has the length of the end at this index. Thanks a lot!

U can have all the Phd's in the world but if you lack passion about teaching and what you teach, you wont achieve anything. Thank you sir, for doing what my proffesor dreams of.

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Really appreciate your efforts to make your audience understand!

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14 mins in and im starting to understand. Thank you!!!!!!!

The DP solution is amazingly taught!

The best explanation I ever found

Please keep it up.. Your explanation is really helpful to computing science student like me, who is not that smart on solving problems but yet still hoping to challenge myself to make it through the interview! Keep it up man!

Very detailed explanation with a big array! Thank you .

I see how we get 6 as the maximum sum, but how do we get the subarray? In other words, once we get 6, how do we know that 6 is the sum of these four numbers [4, -1, 2, 1]? Edit: nvm, the problem does not require us to return the subarray. Thank you, this is the best, easiest to understand explanation on youtube.

I love the way he tells how to approach the question

Awesome video! You always do an excellent job of breaking down difficult concepts into an easy to understand fashion. . If anyone was wondering, you can also return the range of values that add up to the maximum subsequence sum like this (In Python): def maxSubArraySum(inputArr): currentMaxSum = inputArr[0] seqStartVal = inputArr[0] . for i in range(1, len(inputArr), 1): #for(i=1; i seqStartVal + inputArr[i]): seqStartVal = inputArr[i]; maxSubSeqStart = i else: seqStartVal += inputArr[i] . if (seqStartVal > currentMaxSum): currentMaxSum = seqStartVal maxSubSeqEnd = i . All we are doing is opening up the "max" function to allow for more logic where we can update the values of TWO MORE variables that track the value of the start and stop points of the max subsequence. Then simply print the values between those two points inclusively via another loop and you will output all the values involved in coming up with the maximum sum.

There no way to give a 100 likes .... but you deserve it, man.....!!

Amazing Amazing. These kind of resources motivate me to do more of CP.

Good to see you are providing tushar's video too..

This is a great video. I'd like to see a video on the thought process of how you arrive at the definition for your subproblem

loved ur gist code , got everything ezly.... thank u. LOVE FROM INDIA

Thank you, sir! You explained it with great energy and clarity.

At least I thought of the Brute Force approach correctly. I was also close to the approach you showed but it was taking too much time so I just decided let's take little help. Thanks, Brother !!!

Hey I was struggling to wrap my head around this problem but this video perfectly clarrified everything!

Wonderful teaching skills Brother, Love from India. Keep up your good work.

This video really helps! Thanks for making it :)

Wanna say thank you for the great explanation.

Thank you so much. I just started codewars and this problem popped up. I've never encountered any dynamic programming before. Watched your video twice and managed to bang out Kadane's Algorithm in python. Onto the next question...

I really like the way you teach, thank you very much!!

Great explanation! Kudos for adding table of contents. This is a good video for jumping into DP problems.

I was kind of skeptical at the start because I couldn't understand you well. But after a rewatch, you've cleared up the concept really well. Thanks a ton!

This is the best explanation on kadanes algorithm u got a subscriber