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High-Dimensional Vector Correspondence
Let < p1, p2,..., pn > and < q1, q2,..., qn > be two sequences of vectors in the m-dimensional Euclidean space. Is that possible to transform the former using a series of reflections and/or rotations so that it becomes the latter?
The input consists of a single data set given in the format (n, m ≤ 512)
for all 1≤i≤n. All numbers except m and n are floating-point. Blank characters are irrevelant.
It is known that both reflections and rotations are linear transformations, which are represented by squarematrices. In particular, in the m-dimensional Euclidean space, they are represented by m × m matrices. Furthermore, composition of linear transformations is represented by the product of the corresponding matrices. Therefore, if the desire sequence of reflections and rotations exists, you are to output a matrix H in the format
such that Hpi = qi for all 1≤i≤n; otherwise, you only have to output an asterisk ("*"). Blank characters are irrevelant.
2 -0.569248928113214700 0.822165225390831260 0.822165225390831590 0.569248928113214810
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