Fast algorithm to get combinations in Matlab? - matlab

Question

I need to adjust the following algorithm in Matlab because the double loop in step (2) takes to much time when n is large (I should be able to run the algorithm for n=15). Any ideas?
n=3;
% (1) construct A: list of DISPOSITIONS of the elements of the set {0,1} in n
%places (organise 2 elements in n places with possibility of repetitions and the order matters)
A=makeindex(n); %matrix 2^n x n (FAST)
% (2) modify A: it should give the list of COMBINATIONS of the elements of the set
%{0,1} in n-1 places (organise 2 elements in n-1 places with repetitions and the
%order does NOT matter), repeated twice:
% once when the n-th element is 0, the other when the n-th element is 1
Xr=A(:,n);
m=sum(A,2); %vector totalx1
%each element is the total number of ones in the
%corresponding row
drop=false(2^n,1); %logical vector totalx1
for i=1:2^n
parfor j=1:2^n
if j>i
if m(i)==m(j) && Xr(i)==Xr(j) %(VERY SLOW)
drop(j)=true;
end
end
end
end
A(drop,:)=[];
The function makeindex is
function [index]=makeindex(k) %
total=2^k; %
index=zeros(total,k); %
for i=1:k %
ii=1; %
cc=1; %
c=total/(2^i); %
while ii<=total %
if cc <=c %
index(ii,i)=1; %
cc=cc+1; %
ii=ii+1; %
else %
ii=ii+c; %
cc=1; %
end %
end %
end %
%
end

Answer 1

Here my solution if that's what you want:
A=zeros(n,2*n);
A(:,1)=1;
for i=2:2:n*2-1
A(:,i-1)=circshift(A(:,i-1),[-1 0]);
A(:,i)=A(:,i-1);
A(end,i)=0;
A(:,i+1)=A(:,i);
end
A(:,end-1)=circshift(A(:,end-1),[-1 0]);
A=A';
For n = 10:
Elapsed time is 0.000976 seconds.
Old code:
Elapsed time is 32.804602 seconds.
n=15:
Elapsed time is 0.000866 seconds.
Old code:
... still calculating... ;)