线性规划？

litong

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：

1. 11111110001110000000111000000000000111000000000000000000111000000000000000000000000011111001101001100000100110000000000100110000000000000000100110000000000000000000000011110101010101010000010101000000000010101000000000000000010101000000000000000000000011110010110010110000001011000000000001011000000000000000001011000000000000000000000011001111101000001100100000110000000100000110000000000000100000110000000000000000000010101111010100001010010000101000000010000101000000000000010000101000000000000000000010011110110010000110001000011000000001000011000000000000001000011000000000000000000001101101110001001001000100100100000000100100100000000000000100100100000000000000000001011011110000100101000010010100000000010010100000000000000010010100000000000000000000110111110000010011000001001100000000001001100000000000000001001100000000000000000011001000001111101100100000000011000100000000011000000000100000000011000000000000000010100100001111011010010000000010100010000000010100000000010000000010100000000000000010010010001110110110001000000001100001000000001100000000001000000001100000000000000001100001001101111001000100000010010000100000010010000000000100000010010000000000000001010000101011110101000010000001010000010000001010000000000010000001010000000000000000110000010111110011000001000000110000001000000110000000000001000000110000000000000000001101001101001111000000100010001000000100010001000000000000100010001000000000000000001010101010101111000000010001001000000010001001000000000000010001001000000000000000000110010110011111000000001000101000000001000101000000000000001000101000000000000000000001110001111111000000000100011000000000100011000000000000000100011000000000000011001000001000000000111110110011000100000000000000110000100000000000000110000000000010100100000100000000111101101010100010000000000000101000010000000000000101000000000010010010000010000000111011011001100001000000000000011000001000000000000011000000000001100001000001000000110111100110010000100000000000100100000100000000000100100000000001010000100000100000101111010101010000010000000000010100000010000000000010100000000000110000010000010000011111001100110000001000000000001100000001000000000001100000000000001101000000001000110100111110001000000100000000100010000000100000000100010000000000001010100000000100101010111101001000000010000000010010000000010000000010010000000000000110010000000010011001111100101000000001000000001010000000001000000001010000000000000001110000000001000111111100011000000000100000000110000000000100000000110000000000000000001101001000110100100011111000000000010000100001000000000010000100001000000000000000001010100100101010010011111000000000001000010001000000000001000010001000000000000000000110010010011001001011111000000000000100001001000000000000100001001000000000000000000001110001000111000111111000000000000010000101000000000000010000101000000000000000000000001111000000111111111000000000000001000011000000000000001000011000000011001000001000000000100000000000000111110110011000110000100000000000000000000110000010100100000100000000010000000000000111101101010100101000010000000000000000000101000010010010000010000000001000000000000111011011001100011000001000000000000000000011000001100001000001000000000100000000000110111100110010100100000100000000000000000100100001010000100000100000000010000000000101111010101010010100000010000000000000000010100000110000010000010000000001000000000011111001100110001100000001000000000000000001100000001101000000001000000000100000000110100111110001100010000000100000000000000100010000001010100000000100000000010000000101010111101001010010000000010000000000000010010000000110010000000010000000001000000011001111100101001010000000001000000000000001010000000001110000000001000000000100000000111111100011000110000000000100000000000000110000000000001101001000000000000010000110100100011111100001000000000010000000000100001000000000001010100100000000000001000101010010011111010001000000000001000000000010001000000000000110010010000000000000100011001001011111001001000000000000100000000001001000000000000001110001000000000000010000111000111111000101000000000000010000000000101000000000000000001111000000000000001000000111111111000011000000000000001000000000011000000000000000000000110100100010000110100100010000111111000000000000000100000100000100000000000000000000101010010001000101010010001000111111000000000000000010000010000100000000000000000000011001001000100011001001000100111111000000000000000001000001000100000000000000000000000111000100010000111000100010111111000000000000000000100000100100000000000000000000000000111100001000000111100001111111000000000000000000010000010100000000000000000000000000000011111000000000011111111111000000000000000000001000001111001000001000000000100000000000000100000000000000000000111110110011000110000110000010100100000100000000010000000000000010000000000000000000111101101010100101000101000010010010000010000000001000000000000001000000000000000000111011011001100011000011000001100001000001000000000100000000000000100000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复制代码

erawaliktevi

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

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

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

dingji

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

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

Rickykek

n=5吧。