"Everyday Learning" codevs1287 matrix multiplication

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First question.

Title Description Description

Xiao Ming recently has a headache for linear algebra, and linear algebra is really abstract (and boring), but his teacher is talking about this section of matrix multiplication.
Of course, Xiao Ming dozing in class is no problem, but the linear algebra exercise is very scary. Xiao Ming wants you to help him finish the task.

Now give you an AI row AJ column matrix and a bi row BJ column matrix for you to find the product of their multiplication (and of course the matrix).
(Input data guarantee AJ=BI, no need to judge)

Definition of matrix multiplication:

1. When matrix A is multiplied by B, the number of columns of a =b must be required, otherwise the multiplication can not be performed. Therefore, matrix multiplication also does not satisfy the commutative law.

2. Set A is the matrix of X*n, B is the matrix of n*y, and each row of a is multiplied by each column of B to obtain a x*y matrix. For a row multiplied by a column, we call it a vector operation, where each number in the corresponding position is multiplied and then summed.

Written as a formula and:

C[I,J] = Sigma (a[i,k] * b[k,j])

Enter a description input Description

The input file has ai+bi+2 rows, and all of the input numbers are integers (within a long long range).
Line 1th: AI and AJ
Line 2~ai+2: All elements of matrix A
Line ai+3: Bi and BJ
Line ai+3~ai+bi+3: All elements of Matrix B

outputs description output Description

Product of the output matrix A multiply matrix B (Matrix C)

sample input to sample

2 2
12 23
45 56
2 2
78 89
45 56

Sample output Sample outputs

1971 2356
6030 7141

data size & Hint

Matrix Size <=200*200

The topic itself is very simple, here just to say the application of matrix multiplication.

Yesterday in the Zhucheng a summer camp listening to the Gao Tianyu predecessors, matrix multiplication can be combined with the multiplication of ideas to increase the multiplication of repeated calculations to a number of levels of complexity. Since the matrix multiplication satisfies the binding law, the transfer matrix can be doubled with the same fast power and then multiplied with the original matrix, which can greatly improve the running efficiency.

As for how to construct the transfer matrix = = The room is closing quickly too late to say = = if there is anyone (estimated no one) to see this article want to know (no one) can be private message I exchange =

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"Everyday Learning" codevs1287 matrix multiplication