How can I generate a binary matrix of permutations

Hi, I'd like to ask for help on generating a binary matrix of permutations given several variables:

The first being the number of "ones" per row (n). The second being the length of each row (m). For example, if I was asked to generate a binary matrix given n = 2 and m = 4 the matrix generated should look like the following:

0011
0101
0110
1001
1010
1100

I've been asked to prepare a list of all permutations to select n=23 items out of a list of m=30.

I first thought of generating a matrix of binary numbers incrementing by 1:

0000
0001
0010
0011...

Then going through each row and checking the sum of ones. If that sum equals n then store that row vector in another variable and build my desired matrix that way. This is not efficient though. I am now thinking of something along the lines of this pseudo-code:

for i = 1 to 2^30
x = convert i to binary
if (count of ones in x) = n then y = x

I hope the problem is correctly phrased and I apologies for the simplicity of this question or if it has previously been asked - I'm a complete novice both in Matlab and in using this forum. Your help would be much appreciated.

Greg

[jgg]

I think it might be easier to do an interative loop.

Start with like (in your example) 1100

Then iterate backwards by "moving" the rightmost-1 to the right.

 1100
 1010
 1001
 0110
 0101
 0011

You should be able to do this by recursion; that's definitely going to be better than try to perform billions of operations.

[Greg]

Agreed. Thanks for getting back to me so quickly jgg. Much appreciated.

Answer 1

[Andrei Bobrov]

n = 2;
m = 4;
ii = nchoosek(1:m,n);
k = size(ii,1);
out = zeros(k,m);
out(sub2ind([k,m],(1:k)'*ones(1,n),ii)) = 1;

[Greg]

Thanks for your quick answer Andrei, much appreciated.

[Mohammad]

How we can generate the binary matrix of 0 , 1 whose row is 2^N and coloumn is N

[DGM]

Other than a binary array, it's unclear what you're asking for, or if it's even related to this thread.

Given that everyone in this thread has been inactive for at least a year, it's not likely they're going to respond. If you have a question, open a new thread and ask a question. Be clear about what you want. Provide an example of your expected inputs and outputs.

[DGM]

Wow. I've had this tab open for over three months. I'm just going to take a wild stab at answering anyway.

I'm going to interpret this as to say that we want a binary, possibly logical array A of size NxN, where the column vector at column n is a binary representation of 2^n. For sake of plausible convention, I'm assuming a zero-based indexing. Each column vector is ordered LSB first.

N = 8; % the number of columns
A = rot90(dec2bin(2.^(0:N)) == '1')

A = 9x9 logical array
   1   0   0   0   0   0   0   0   0
   0   1   0   0   0   0   0   0   0
   0   0   1   0   0   0   0   0   0
   0   0   0   1   0   0   0   0   0
   0   0   0   0   1   0   0   0   0
   0   0   0   0   0   1   0   0   0
   0   0   0   0   0   0   1   0   0
   0   0   0   0   0   0   0   1   0
   0   0   0   0   0   0   0   0   1

This all seems like a sound interpretation of the question, but the fact that this is just

A = eye(N)

A = 8x8

1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1

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... suggests that:

• my interpretation was wrong
• the task was not clearly described
• the solution was truly trivial

or possibly all of the above.