No.3224 Introduction to 2×2 Matrices
タグ : / 解いたユーザー数 102
作問者 :
ジュ・ビオレ・グレイス
/ テスター :
👑 
p-adic
Problem Statement
You are given integers $A, B, C, D, A', B', C', D'$ from the input. Define the $2\times 2$ matrices $M, M'$ respectively as
$M = \begin{pmatrix} A & B \\ C & D \end{pmatrix}, \ M' = \begin{pmatrix} A' & B' \\ C' & D' \end{pmatrix}$
. Find the matrix product
$M M' M M' = \begin{pmatrix} W & X \\ Y & Z \end{pmatrix}$
.
About the matrix product
The product of $2 \times 2$ matrices is defined as$\begin{pmatrix} a_{1, 1} & a_{1, 2} \\ a_{2, 1} & a_{2, 2} \end{pmatrix} \begin{pmatrix} b_{1, 1} & b_{1, 2} \\ b_{2, 1} & b_{2, 2} \end{pmatrix} = \begin{pmatrix} a_{1, 1} b_{1, 1} + a_{1, 2}b_{2, 1} & a_{1, 1}b_{1, 2} + a_{1, 2}b_{2, 2} \\ a_{2, 1}b_{1, 1} + a_{2, 2}b_{2, 1} & a_{2, 1}b_{1, 2} + a_{2, 2}b_{2, 2} \end{pmatrix}$
. The matrix product satisfies the associative law. That is, $M(NL) = (MN)L$.
Input
$A \ B \\ C \ D \\ A' \ B' \\ C' \ D'$
All integers given in the input are between $-10^4$ and $10^4$, inclusive.
Output
Output $W, X, Y, Z$ defined in the problem statement in the following format:
$W \ X \\ Y \ Z$Print a newline at the end.
Sample
Sample 1
Input
1 0 0 1 2 3 4 5
Output
16 21 28 37
$\begin{pmatrix} 1 & 0 \\ 0 & 1\end{pmatrix} \begin{pmatrix} 2 & 3 \\ 4 & 5 \end{pmatrix} = \begin{pmatrix}2 & 3 \\ 4 & 5\end{pmatrix},$
$\begin{pmatrix} 2 & 3 \\ 4 & 5 \end{pmatrix} \begin{pmatrix} 2 & 3 \\ 4 & 5 \end{pmatrix} = \begin{pmatrix} 2\times 2 + 3 \times 4 & 2 \times 3 + 3 \times 5 \\ 4 \times 2 + 5 \times 4 & 4 \times 3 + 5 \times 5 \end{pmatrix} = \begin{pmatrix}16 & 21 \\ 28 & 37\end{pmatrix} $
Sample 2
Input
1 -2 3 4 -5 -6 7 8
Output
75 110 -65 -90
Sample 3
Input
10000 9797 1234 9876 9898 8989 1717 7777
Output
18254769490702857 33830675938859763 5942164530811048 12570866016297340
The answer may not fit in a 32-bit integer.
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