2961：Sylvester construction

题目描述

A Hadamard matrix of order n is an n x n matrix containing only 1s and -1s, called H_n, such that H_nH_n^T = nI_n where I_n is the n x n identity matrix. An interesting property of Hadamard matrices is that they have the maximum possible determinant of any n x n matrix with elements in the range [-1, 1]. Hadamard matrices have applications in errorcorrecting codes and weighing design problems.

The Sylvester construction is a way to create a Hadamard matrix of size 2n given H_n. H_2n can be constructed as:

for example:

and so on.

In this problem you are required to print a part of a Hadamard matrix constructed in the way described above.

输入解释

The first number in the input is the number of test cases to follow. For each test case there are five integers: n, x, y, w and h. n will be between 1 and 2⁶² (inclusive) and will be a power of 2. x and y specify the upper left corner of the sub matrix to be printed, w and h specify the width and height respectively. Coordinates are zero based, so 0 ≤ x,y < n. You can assume that the sub matrix will fit entirely inside the whole matrix and that 0 < w,h ≤ 20. There will be no more than 1000 test cases.

输出解释

For each test case print the sub matrix followed by an empty line.

输入样例

3
2 0 0 2 2
4 1 1 3 3
268435456 12345 67890 11 12

输出样例

1 1
1 -1

-1 1 -1
1 -1 -1
-1 -1 1

1 -1 -1 1 1 -1 -1 1 1 -1 -1
-1 -1 1 1 -1 -1 1 1 -1 -1 1
1 1 1 -1 -1 -1 -1 1 1 1 1
-1 1 -1 -1 1 -1 1 1 -1 1 -1
1 -1 -1 -1 -1 1 1 1 1 -1 -1
-1 -1 1 -1 1 1 -1 1 -1 -1 1
-1 -1 -1 -1 -1 -1 -1 1 1 1 1
1 -1 1 -1 1 -1 1 1 -1 1 -1
-1 1 1 -1 -1 1 1 1 1 -1 -1
1 1 -1 -1 1 1 -1 1 -1 -1 1
-1 -1 -1 1 1 1 1 1 1 1 1
1 -1 1 1 -1 1 -1 1 -1 1 -1

该题目是Virtual Judge题目，来自北京大学POJ

题目来源 Svenskt Mästerskap i Programmering/Norgesmesterskapet 2004

源链接： POJ-2961

最后修改于 2020-10-29T06:48:36+00:00 由爬虫自动更新

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时间上限	内存上限
1000	65536