generate the binary sequence

I have a code to generate the binary sequence that only contains m zeros and n ones. For example, m=n=2. then the number of combinations of the binary sequence is 6,nchoosek(4,2). My code was fine to output the 6 combinations, but mostly 2 combinations are the same. My question is how to avoid a combination of sequence show twice?

The code is following:

%  clear all;
m = input('How many zeroes do you need \n');
n = input('how many ones do you need\n');
lnk=nchoosek(m+n,n);
i=n+m;
for kk=1:lnk
   % m = input('How many zeroes do you need \n');
   % n = input('how many ones do you need\n');
   if i<=1
        disp('size of binary sequence is out of range');
   else 
        %Binary sequence contains m zeros and n ones in any order
        x1=zeros(1,i);
        x1(randperm(i,n))=1
        %count down the number of switches in such a Binary sequence x1;
        switches=0;
        for k=1:length(x1)-1
            if x1(k)==0 && x1(k+1)==1
                switches= switches+1;
            elseif x1(k)==1 && x1(k+1)==0 
                switches=switches+1;
            end
        end  
        Av(kk)=switches;
   end   
end

Also, my result shows like:
How many zeroes do you need 
2
how many ones do you need
2

x1 =

     0     0     1     1
x1 =
     0     0     1     1
x1 =
     0     1     1     0
x1 =
     1     0     1     0
x1 =
     1     1     0     0
x1 =
     1     1     0     0
Av =
     1     1     2     3     1     1

tot_combination =

     6

[Bear]

again, my output is wrong, because it's missing one or two combinations. Therefore I want to correct this code and output the unique 6 combinations. I hope someone could help me to correct this code.

Answer 1

[Guillaume]

Maybe I'm misunderstanding something but to me it looks like your code is wrong, it's missing for ex. 0 1 0 1 as an output.

The simplest way to obtain all unique permutations of a sequence is:

m = 2; n = 2;

seqs = unique(perms([zeros(1, m) ones(1, n)]), 'rows')

There are indeed 6 combinations, but not the ones you return in your example.

[Bear]

Yes, it's missing one or two combinations. Therefore I want to correct this code and output the unique 6 combinations.

[Guillaume]

As per my answer, it's simply

m = 2; n = 2; %for example
seqs = unique(perms([zeros(1, m) ones(1, n)]), 'rows')

[Bear]

This works for me, but answer is not likely in vector. The answer I think is in a matrix, and the codes below, To count down the numbers of switches , will not give me correctly results.

[Guillaume]

There's nothing stopping you from iterating over the rows or transforming the rows into a cell array, or whatever data structure you wish.

Or you could just use diff to detect the transitions between columns (transition will show up as either -1 or 1) and sum these up:

m = 2; n = 2; %for example
seqs = unique(perms([zeros(1, m) ones(1, n)]), 'rows')
transitions = sum(abs(diff(seqs, [], 2)), 2)

[Bear]

I see what you mean now, thanks for your great help again.