4.5.1 0/1 Knapsack Problem (Program) - Dynamic Programming

0/1 Knapsack Problem explained using Program

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[willjay]

You are an excellent teacher, sir. Your effort is much appreciated.

[aaronaaronaaron]

I hope this AMAZING channel reachs millions of subscribers, THANKS, sirm you are awesome 🥊

[johnc]

Taught very clearly!
(Perhaps a little mistake at 15:26 ? Reducing i-- before accessing J for weight reduction would seems wrong ?)
Thanks for this brilliant teaching sir

[sampreethrv]

there is small error in the code at 15:11 first we have to write j=j-wt[i] then i=i-1;

[rahulchawla]

Correction :
cout<<K[n][m];
and Sir, Thank uh for this lovely explanation.

[mrkyledescoudres]

I have now understood the meaning of the universe, the key to everything... but I cannot explain it (or give it) to you. You have to find it by yourself...

[sumant]

Breakdown of the formula:
⭐K: DP table which stores values of subproblems

⭐K[i, w]: Maximum profit by considering the first 'i' elements in a bag of weight 'w'

⭐p[i]+ K[i-1, w-wt[i]]: Case when the current object is included(~1) 'p[i]' and the remaining part of the bag 'w-wt[i]' must be filled with the maximum profit possible (stored at 'i-1')

⭐K[i-1, w]: Case when the current object is not included(~0) and the bag with current weight 'w' must be filled with the maximum profit possible (stored at 'i-1')

(~ Hence the name 0/1 knapsack problem)

[flexerfadrigalan]

Awesome content, by far the most understandable and easy to understand. I aspire to be you when explaining a difficult topic.

[mauriciocmarinho]

Best explanation about knapsack algorithm implementation on youtube. Thanks a lot!

[-avnee]

Sr, I have no words for appreciation of your way of teaching. I can't compare it with that of any other course faculties or youtubers. Its Unique ! I am following your course also for dsa from Udemy, i have successfully completed it and it happened first time with me that I am almost 90-95% satisfied with a purchased course and that is also at easily affordable cost. Thankyou So Much for your efforts for us, Sr. I want to pay Respect to you by heart !🙏

[surajsuryawanshi]

No words to describe how excellent your teaching is .

[SaraswatiShelke]

you are just amazing sir as i have problem in english but i understood you explanation you are simply great sir
thank you so much sir
🙏🙏🙏🙏

[phantomvisual]

future viewers, some things to note!!
it's important for p[0] = wt[0] = 0 to exist. in the video, p and wt already have 0 at the start. this makes the table's first row and first column filled with 0.

your implementation may need to change if your table's doesn't have that initial condition. you might see `p[i-1]` and `wt[i-1]` in other implementations, this is because the "p" and "wt" usually don't have 0 instantiated thus you shift everything over by 1 to fit the first row filled with 0 (therefore requiring you to do i-1 to index correctly).

[VanjeAv]

I can't belive how talented you are

[stutisflairs]

This code is stuck in my mind from the way you explained thanks for taking so much efforts for us God bless uhh 🙏

[ntaange-junior]

Thhank you teacher for this lesson and the previous one concrning the knapsack problem it is really well understood and well explained

[Sourav]

on 15:02
It should be
cout<<i<<"=1"; j=j-wt[i]; i--;
not
cout<<i<<"=1"; i--; j=j-wt[i];

[shk]

Thank you sir, been following your videos for DAA and they're very helpful! I had a doubt, I'm not able to understand why 0/1 knapsack has exponential complexity, looking at the code it seems the program has O(n*m) complexity..

[raghavddps]

Sir, you are an excellent teacher. Thanks a lot...

[MANUCRIXZ]

what an explaination brother keep it up!
keep going bro