litong 发表于 2024-2-4 03:04:08

线性规划？

一个84*84的表格中填满了0和1，其中每行或每列的1的个数都是19个。
如何选择最少的n行组成n*84的新表格，使得每列至少有一个1.
示例数据如下：1111111000111000000011100000000000011100000000000000000011100000000000000000000000001111100110100110000010011000000000010011000000000000000010011000000000000000000000001111010101010101000001010100000000001010100000000000000001010100000000000000000000001111001011001011000000101100000000000101100000000000000000101100000000000000000000001100111110100000110010000011000000010000011000000000000010000011000000000000000000001010111101010000101001000010100000001000010100000000000001000010100000000000000000001001111011001000011000100001100000000100001100000000000000100001100000000000000000000110110111000100100100010010010000000010010010000000000000010010010000000000000000000101101111000010010100001001010000000001001010000000000000001001010000000000000000000011011111000001001100000100110000000000100110000000000000000100110000000000000000001100100000111110110010000000001100010000000001100000000010000000001100000000000000001010010000111101101001000000001010001000000001010000000001000000001010000000000000001001001000111011011000100000000110000100000000110000000000100000000110000000000000000110000100110111100100010000001001000010000001001000000000010000001001000000000000000101000010101111010100001000000101000001000000101000000000001000000101000000000000000011000001011111001100000100000011000000100000011000000000000100000011000000000000000000110100110100111100000010001000100000010001000100000000000010001000100000000000000000101010101010111100000001000100100000001000100100000000000001000100100000000000000000011001011001111100000000100010100000000100010100000000000000100010100000000000000000000111000111111100000000010001100000000010001100000000000000010001100000000000001100100000100000000011111011001100010000000000000011000010000000000000011000000000001010010000010000000011110110101010001000000000000010100001000000000000010100000000001001001000001000000011101101100110000100000000000001100000100000000000001100000000000110000100000100000011011110011001000010000000000010010000010000000000010010000000000101000010000010000010111101010101000001000000000001010000001000000000001010000000000011000001000001000001111100110011000000100000000000110000000100000000000110000000000000110100000000100011010011111000100000010000000010001000000010000000010001000000000000101010000000010010101011110100100000001000000001001000000001000000001001000000000000011001000000001001100111110010100000000100000000101000000000100000000101000000000000000111000000000100011111110001100000000010000000011000000000010000000011000000000000000000110100100011010010001111100000000001000010000100000000001000010000100000000000000000101010010010101001001111100000000000100001000100000000000100001000100000000000000000011001001001100100101111100000000000010000100100000000000010000100100000000000000000000111000100011100011111100000000000001000010100000000000001000010100000000000000000000000111100000011111111100000000000000100001100000000000000100001100000001100100000100000000010000000000000011111011001100011000010000000000000000000011000001010010000010000000001000000000000011110110101010010100001000000000000000000010100001001001000001000000000100000000000011101101100110001100000100000000000000000001100000110000100000100000000010000000000011011110011001010010000010000000000000000010010000101000010000010000000001000000000010111101010101001010000001000000000000000001010000011000001000001000000000100000000001111100110011000110000000100000000000000000110000000110100000000100000000010000000011010011111000110001000000010000000000000010001000000101010000000010000000001000000010101011110100101001000000001000000000000001001000000011001000000001000000000100000001100111110010100101000000000100000000000000101000000000111000000000100000000010000000011111110001100011000000000010000000000000011000000000000110100100000000000001000011010010001111110000100000000001000000000010000100000000000101010010000000000000100010101001001111101000100000000000100000000001000100000000000011001001000000000000010001100100101111100100100000000000010000000000100100000000000000111000100000000000001000011100011111100010100000000000001000000000010100000000000000000111100000000000000100000011111111100001100000000000000100000000001100000000000000000000011010010001000011010010001000011111100000000000000010000010000010000000000000000000010101001000100010101001000100011111100000000000000001000001000010000000000000000000001100100100010001100100100010011111100000000000000000100000100010000000000000000000000011100010001000011100010001011111100000000000000000010000010010000000000000000000000000011110000100000011110000111111100000000000000000001000001010000000000000000000000000000001111100000000001111111111100000000000000000000100000111100100000100000000010000000000000010000000000000000000011111011001100011000011000001010010000010000000001000000000000001000000000000000000011110110101010010100010100001001001000001000000000100000000000000100000000000000000011101101100110001100001100000110000100000100000000010000000000000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erawaliktevi 发表于 2024-2-4 03:04:18

EXCEL表如下：84x84.xls(73.5 KB, 下载次数: 1)2010-5-9 14:18 上传
点击文件名下载附件

kutnfeuwunaxo 发表于 2024-2-4 03:04:44

最小顶点覆盖问题，NPC的，不过本题用类似双向搜的方法，有可能在O(n^4)求解。

DJWilliamstada 发表于 2024-2-4 03:05:35

\(f(1,1) = \begin{pmatrix}
0& 1 \\
1 & 0\end{pmatrix}
f(2,1) = \begin{pmatrix}
0& 1&0 \\
0 & 0&1\\1&0&0\end{pmatrix}
f(3,2) = \begin{pmatrix}
1 & 0&0&0&1 \\ 0 & 1&0&1&0\\0&0&1&1&0\\1&0&1&0&0\\0&1&0&0&1\end{pmatrix}\)

dingji 发表于 2024-2-4 03:05:44

\( 如果将一矩形（长宽不相等）的位置状态规定0为纵放，1为横放。则如图： \)

\( f(65,19)=? \)

Rickykek 发表于 2024-2-4 03:06:28

n=5吧。

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