我想生成（或计数）满足特定条件的所有可能的二进制矩阵

Question

我想生成（或计数）满足以下条件的所有可能的二进制矩阵。 令A为任意二进制矩阵4 * 4

A=   [0 0 1 1]
     [0 0 1 1]
     [1 1 0 0]
     [1 1 0 0] 

[sum(row1) sum(r2) sum(r3) sum(r4) sum(column1) sum(c2) sum(c3) sum(c4)]

condition: [2 2 2 2 2 2 2 2]
1)how many matrix satisfy above condition?
2)how can i generate them?

answer 1 is:90 
but i want a formula or algorithm ,
because i want to use it for 1024*1024 or upper and every arbitrary condition vector.

Answer 1

蛮力方法：生成所有4x4二进制矩阵并测试其中哪些符合您的条件：

condition = [2 2 2 2 2 2 2 2]; %// desired conditions

matrices = reshape(dec2bin(0:2^16-1,16).'-'0', 4,4,[]); %'// all binary matrices
ind = all(bsxfun(@eq, [squeeze(sum(matrices,1)); squeeze(sum(matrices,2))],...
  condition(:))); %// gives 1 for matrices that fulfill the condition, or else 0
result = matrices(:,:,ind); %// pick solution matrices
number = size(result,3); %// number of solution matrices

解决方案矩阵为result(.,:,1)，result(.,:,2)，......;并且number是解决方案矩阵的数量。

你可以加快一点利用对称性。