Thank you Mr. Roy, I cannot express just how important it has been to find your upload... Gus, London.

Nicely put! Thanks for the explanation. It's great that you take an example and go through the problem step by step. Keep up the good work! :)

I finally see it, 2 years after I learnt my algorithm class. Thank you.

After 8 years, still so much better than our computer science teachers. Thank you for the video. -Turkey

nice video gautam gambhir

Tushar, THANK YOU!!!! This was a great explanation. I wish my class material was as clear as this.

This is the THIRD video I've watched on the Knapsack problem and the ONLY one that helped me understand it. Thank you so much for sharing this!

Great video. The way you draw out the tabulation and go through it very clearly is very helpful.

Very nice, became a fan of you. best online teacher I have ever found. plz keep making video like this, the new generation student will be benefited.. Thank you..

Best 0/1 Knapsack tut on the Internet! Keep up the good work! :)

Amazing tutorial, you explained the process in a very understandable and complete way. Great job man.

You are really doing a great job. Because of you , people are learning tough concepts so easily and getting good jobs . Keep it up tushar :)

@Tushar Roy, we need more teachers like you. Your virtues: your videos are well paced unlike many other indian videos, which keeps a person interested, no extraneous content -- everything is precise and to the point (extremely helpful) at times while revising concepts. I wish you all the best for your future endeavours. Wish I could meet you some day personally for your autograph. Thanks a lot for your efforts, you are just amazing!! :)

Amazing videos man. Like Sal Khan (founder of Khan academy), you have a unique knack for teaching extremely complex concepts. I have learnt so much from your videos. Thank you once again!!

I spent 2 whole days trying to understand 0-1 knapsack problem until I stumbled upon this video. This video explains more than just arriving on a mathematical equation. Many thanks for making this video.

this changed my life. Best tutorial out there, i grok after only 5 min where many written tutorials failed

It's far better than 90% videos available on the same topic + you cover the basics... Keep up the good work !🤘

Your videos are so good! I skipped nearly all the lectures for algorithms class this semester cuz I know you'll explain it better than my prof. Thank you Tushar!

Tushar, your tutorials and explanations are awesome! Keep it coming mate!

Thanks a ton for this video and your complete channel! You are truly gifted, you're a great teacher. Thanks again

one of the best explanations , not just filling the table using the formula ;)

Thanks a lot for explanation.. I finally understood the algorithm. I have just one suggestion ,you should have 0th column also so that you have its row(top row) with all 0s.I got little bit lost :) with your explanation when you said for the first column with weight 1 that best we can do is 1 (for weight 0 to 7). If you had the top row (with 0s) you could have applied the max formula and shown everyone why each value ended up being 1 (like you did with other three items). The reason I mentioned this is because while writing a computer program we need the top row with 0s in order to make the max formula work for 1st item. But again thanks a lot.. :)

Thanks Tushar Roy for your simple way in teaching and your best way in delivering the main idea of the Algorithm

I can't stop seeing your videos!!! You are simply awesome....and it's of course the best video as far as 0-1 knapsack prob is concerned!!!

I like the video. Super helpful. Two things though, I would have loved to see a list of few questions which can be solved using 0/1 Knapsack. Also, in the second part of the video where you explain the formula, it would have been easier to understand if you could have used variable names as row and column instead of i,j.

Best tutorial on the 0-1 knapsack problem that I ever saw. Thanks!

You saved my butt big time on understanding this algorithm man! Good work on the tutorial!

By far the best explanation about knapsack algorithm I 've seen on youtube. Great job!

Great! Finally spent an hour on this and All I can say is maybe dynamic programming isn't for me :(

Hi Tushar... Your method is so simple. Easy to understand some complex DP problems. Thanks..

It is the best tutorial of the Knapsack.I'm very thankful for you Tushar

It was a nice discussion on 0-1 knapsack. I clearly understood all of it. Thank you for this .

This is the exact same problem I got on my final algorithmics exam. God bless you!

Thanks, helped me prepare for final exams! Greeting from Prague.

Excellent video Tushar. I never understood this properly in my Masters, but you are way too good. Thanks !

Really clear explanation and step by step instruction - no obfuscation - thanks for the great video!

Thanks man! I wished I had a teacher like you when I had my first algorithms class.

Hey Tushar , Many many thanks for doing such a wonderful job of explanining dynamic programming problems in such a lucid way!!. Kudos to you. However in your videos I find one little thing missing and thats is how you arrive at the optimal substructure property of a given example ( which IMO is the crux for nailing down new dyn problems). Like you directly start solving the probem by drawing a 2D /1D array, process of filling the array and then writing down the recurrence at the very end. It would be really helpful if you could spend time in discussing the thorught process to approach the problem first which will really help listeners to develop a knack of solving new dyn problems. As a very specific example , in this video , before even we start to solve the knapsack problem, discussing the optimal substructure property linguistically like : The maximum value that can be obtained from n items is max of following two values. 1) Maximum value obtained by n-1 items and W weight (excluding nth item). 2) Value of nth item plus maximum value obtained by n-1 items and W minus weight of the nth item (including nth item). If weight of nth item is greater than W, then the nth item cannot be included and case 1 is the only possibility. would have been really useful. Thanks again for such a wonderful job!!

First i watched MIT's video , didnt understand, and seriously after watching this whole funda has been cleared with ur explanation of formula. Hats off!!!!

Thanks a lot for the helpful tutorial friend! Good work! Will spent this new year holiday watching playlist full of yours!

For those who are having trouble understanding how the table is generated; for me it helped the most to carefully listen from 8:15 to about 8:45

BEST TUTORIAL EVER!!!! !!! I have watched so many tutorials i didn't understand anythything, that T[0][0] thing helped me understood... others just keep saying ith ith idiots. THis is the best, you are the best!!!

Best explanation I've seen for this type of problem, thank you

Very helpful! Struggled with knapsack before seeing this, thank you for posting!

Sir ,I think first recursive approach should be taught then memoize the repeated sub problems.

Solving my question by 15min comparing my professor by 3 hours...

Hello Tushar sir, thank you very much for your tutorials. Before I watched them, dynamic programming was looking magical. And now, its lucid and amazing. Please continue your good work. Would like to see more tutorials of yours on Trees section.

Thank you for posting this video. After watching the first part before you dove into the code. I was able to form an algo for myself that works! :)

For people who are asking about intuition and to explain why does he go up and left. This is what is the crux of DP. It's called memoization. For example, let's see the point where you have 1,3 and 4 weights and w=7 at 8:49. Now you have two choices: 1. Use 4 If you use 4, then you are left with 7-4=3 total knapsack size and 1 and 3 as remaining weights available to you. Now the question can be rephrased as "you have a knapsack of size 3 and 1, 3 wights, available, give me the optimal total value". This is where memoization comes into picture, you have already solved this subproblem and you already have an optimal solution for it i.e optimal value = 4. That is what basically he is doing by going up and left at t[1][3] 2. Do no use 4 Again question becomes, you have a total knapsack of size 7 and two wegiths of size 1 and 3, give optimal value. We have already solved this sub problem as well. It's 5 (t[1][7])

the world goes silent when thushar starts thalking.

Very good explanation. In my school i was only confused but with your example its simply and clear. Thanks a lot!!!

thank you very much, i am very happy learning this, i was having a lot of pblm before i watched this video

hi Tushar, thanks for one more good video!! m = Total_weight, n is size of wt/val array. Time: O(m*n), Space: O(m*n) ( Correct me , If i'm wrong ) If total_wt is say, 1000. then we would need to 1000 columns to solved this problem?? Is there a way to optimise further??

If anyone hers to learn DP and has fear for DP .. please avoid this sway of learning..... you should learn DP with recursive tree ----> memorization ----> Top down..... please please draw Recursive tree in pen and paper.. else whole life you will fear this sshit........

you're great man, really appreciate all that you do

I was sure that I was going to fail on the quiz on Sunday. You gave me a little hope man. Thanks.

Just one problem. The 2D array size should be T[total_item+1][total_weight+1]. First Row and First column should be initialized to ZERO.

I dont get the up and going to the left part.

sir, tmr is my exam and you have no idea how much this video helped me. thank you so much, from the bottom of my heart.

Your explanation did provide the nice insight into why we are going back in the previous row while calculating max. Thanks for the explanation and nice video indeed.

Tau ye bhi bata dia kro ki DP ku lagani hai Bs "Yes we will use dynamic programming for this solution" ye to keetab bhi bata deti hai

You're the best thank you

You did your best in helping me understanding the solution!. Thanks Tushar!!

I love the way you explain. simple and effective.

awesome sir!!

My exam is 2 days away and I'm still lurking on youtube for answers.. I'm so screwed

this video finally ended my hunt to find a video which explains me knapsack perfectly

Very Nicely Explained! Thank you for this amazing tutorial!

You completely didn't explain how the re-trace to find out which items are included works. How do you know whether to move up or to the side in the matrix? You only said "it's obviously not coming from x" but didn't explain why.

Is this the Indian version of Ray William Johnson?

You explain it way better than my prof does! Thank you.

Crystal clear explanation, So easy to understand.I must appreciate your effort.

didn't understood anything!!😟

Gautam Gambhir

Thank you Sir....This really helped me when i m preparing at 11th hour.

You're amazing dog, your tutorials are really easy to understand.

man, why are you in so much hurry... it all went above my head...didn't get anything..

Making the most easier topic the most complicated one Totally not satisfied

Excellent, cleared up my misconception about picking individual higher weight items from a set of items to get closest to target value.

You my good sir, are an excellent instructor! Accept my deepest gratitude for saving my ass as I couldn't make heads or tails of this particular algorithm until i stumbled upon your tutorial.

Did i m the only one who noticed the mistake at row 3 that should be 01145689

The best part is 9 is the winner😂😂😂 at 11:15

bro i didn't learn like this from anybody else, what a simple way of explaining!!

thank you for your teaching, this really saves me from the hard-reading lecture note.

most confusing explanation

You're a good teacher, but you need to slow down. English is my first language and you're going too fast.

Thank you, finally got a grasp of dynamic programming thanks to you.

That's pretty clearly with your explanation! Thanks a lot! Pretty helpful for my homework!

you are teaching like we know everything and we are just rehearsing the topic from your tutorial.. dude its so bad..

this is the hardest way i have ever see... make it more easy......

As always, another great video!

Superb! Much better than my Algorithm teacher in Uni, thank you very much!

useless explanation very hard to understand

You do a nice job your video is quick short Which is very reliable at exam time to do learn in minimum time Thank you

Very nicely explained. Understood the algorithm very well. Thanks Tushar!

The power of explaining the same thing over and over, but in the most fundamental way. Helps me understand a lot, because I can pause the video and try to understand what he is saying. I am also motivated to pause and ponder because I know that was he is saying is correct!

awesome training! thank you so much! no one could teach it better than this! :)

That was a very clean and crisp explanation! Thanks Tushar

You are wonderful Tushar! Thanks for the videos! They are very easy to understand.

I tried two other videos before finding this one. Much clearer explanation than the others I tried. Thank you.