Matrix Chain Multiplication | Dynamic Programming 

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@@QuocDatPhung sure 😊

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@@QuocDatPhung Thank you, I'll go through it

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It's over 2 years since I've taken this course but let's say i = 1 and j = 2. Then this means you're finding the minimal cost multiplying matrix 1 and matrix 2 right? Let's say that matrix 1 multiply matrix 2 costs 30, whereas matrix 2 multiply matrix 1 costs 20. Now, consider i = j. Here you only have 1 matrix. Nothing to multiply to. Therefore, the cost is 0. Let me know if that makes sense.

@@QuocDatPhung ​ thank you very much sir, what about the reason we ignore m[2,1] ; m[3,2] etc? I'm sorry if I ask too much, I just want to understand... thank you in advance sir :)

@@aoyukialquen2835 No worries! Now remember m(2,2) = 0 right? Because there is no cost when you only have a matrix 2 and matrix 2 only. Since there is only one matrix, there is nothing to multiply to so m(2,2) = 0. Now, what about m(2,1)? There wouldn't be any matrix to consider at all. That's why it's left blank. Let me know if that makes sense.

@@QuocDatPhung thank you sir, your video and explanation helped me, please keep going with the youtube videos, i support your channel! God bless you

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Once you complete the table using the formula, the top right value is always the minimum cost. That is how the algorithm works. The proof for the algorithm is long and complex, so it's best just to know that the top right value is the minimum cost. Let me know if that helps.

@@QuocDatPhung Yes. Thank you!

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@@QuocDatPhung I'll surely watch the playlist 😊😊