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Welcome back.

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In the previous video we have seen that in this example which is given to us, we can multiply the three

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matrices involved in these two ways.

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Over here we are first multiplying the first and second matrix, and the output of this will be multiplied

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with the third matrix.

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Over here we are first multiplying the second and third matrices, and the output of this and the first

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matrix are getting multiplied.

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Now let's take a look at the number of multiplications involved in these two ways of multiplying the

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three matrices.

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Just so that we clearly understand what the question demands from us.

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Now, to multiply these two matrices, we know that the number of multiplications involved is 20 into

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ten into five.

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That's equal to 1000 okay.

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And the dimension of this matrix, once these two are multiplied will be 20 into five okay.

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So we have a matrix of size 20 into five.

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And when we multiply this matrix with this matrix over here the multiplications involved will be 20

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into five into 30 okay.

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So that would be equal to 3000.

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And therefore the total number of multiplications involved is 1000 plus 3000.

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Which is equal to 4000.

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And again, notice we don't have any multiplications involved to reduce this part to a single matrix

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because it's already a single matrix.

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And that's why it's just zero.

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So we could say that the number of multiplications involved is 1000 plus 3000 plus zero, which is equal

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to 4000.

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Now what about this way of multiplying the three matrices involved.

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So initially we have one matrix.

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So there's no multiplication involved to reduce this to a single matrix because it's already a single

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matrix.

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Now to multiply these two matrices the number of multiplications involved is ten into five into 30,

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which is equal to 1500.

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And the size of this matrix, once these two are multiplied, would be ten into 30.

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Okay.

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And to multiply these two matrices, which are of size 20 into ten and ten into 30, the number of multiplications

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involved is 20 into ten into 30.

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And that's equal to 6000.

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So the total number of multiplications involved in the second way would be 1500 plus 6000, which is

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equal to 7500.

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Now notice over here we just had to do 4000 multiplications.

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But in the second way we have to do almost double which is 7500 multiplications.

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So in this case this is the most efficient way of multiplying the three matrices which are given to

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us.

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And we'll have to return this value.

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So that would be the expected output.

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All right.

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So we have thoroughly understood the question at hand.

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Now as always remember when you are given a coding interview question, it's very important that you

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ask any clarifying questions that you may want to ask.

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So a possible question that you could ask in this case is what if I am given an array with just one

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element?

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Now the issue with this is if there is just one element in the array which is given, you are not able

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to form any matrix, right?

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You need at least two elements to form a matrix.

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And let's say the interviewer replies the array will have at least two elements.

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All right.

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So we have understood the question.

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We've reviewed all that we need to know about matrix multiplication.

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And we have also asked clarifying questions in the next video.

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Let's build the intuition required to solve this problem.