Divide list of numbers into 3 groups in matlab - matlab

Question

I have a list of numbers, [1:9], that I need to divide three groups. Each group must contain at least one number. I need to enumerate all of the combinations (i.e. order does not matter). Ideally, the output is a x by 3 array. Any ideas of how to do this in matlab?

Answer 1

Is this what you want:
x = 1:9;
n = length(x);
T=3;
out = {};
%// Loop over all possible solutions
for k=1:T^n
s = dec2base(k, T, n);
out{k}{T} = [];
for p=1:n
grpIndex = str2num(s(p))+1;
out{k}{grpIndex} = [out{k}{grpIndex} x(p)];
end
end
%// Print result. size of out is the number of ways to divide the input. out{k} contains 3 arrays with the values of x
out

Answer 2

Maybe this is what you want. I'm assuming that the division in groups is "monotonous", that is, first come the elements of the first group, then those of the second etc.
n = 9; %// how many numbers
k = 3; %// how many groups
b = nchoosek(1:n-1,k-1).'; %'// "breaking" points
c = diff([ zeros(1,size(b,2)); b; n*ones(1,size(b,2)) ]); %// result
Each column of c gives the sizes of the k groups:
c =
Columns 1 through 23
1 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 4 4 4 4 5
1 2 3 4 5 6 7 1 2 3 4 5 6 1 2 3 4 5 1 2 3 4 1
7 6 5 4 3 2 1 6 5 4 3 2 1 5 4 3 2 1 4 3 2 1 3
Columns 24 through 28
5 5 6 6 7
2 3 1 2 1
2 1 2 1 1

Answer 3

This produces what I was looking for. The function nchoosekr_rec() is shown below as well.
for x=1:7
numgroups(x)=x;
end
c=nchoosekr_rec(numgroups,modules);
i=1;
d=zeros(1,modules);
for x=1:length(c(:,1))
c(x,modules+1)=sum(c(x,1:modules));
if c(x,modules+1)==length(opt_mods)
d(i,:)=c(x,1:modules);
i=i+1;
end
end
numgroups=[];
for x=1:length(opt_mods)
numgroups(x)=x;
end
count=0;
for x=1:length(d(:,1))
combos=combnk(numgroups,d(x,1));
for y=1:length(combos(:,1))
for z=1:nchoosek(9-d(x,1),d(x,2))
new_mods{count+z,1}=combos(y,:);
numgroups_temp{count+z,1}=setdiff(numgroups,new_mods{count+z,1});
end
count=count+nchoosek(9-d(x,1),d(x,2));
end
end
count=0;
for x=1:length(d(:,1))
for y=1:nchoosek(9,d(x,1))
combos=combnk(numgroups_temp{count+1},d(x,2));
for z=1:length(combos(:,1))
new_mods{count+z,2}=combos(z,:);
new_mods{count+z,3}=setdiff(numgroups_temp{count+z,1},new_mods{count+z,2});
end
count=count+length(combos(:,1));
end
end
function y = nchoosekr_rec(v, n)
if n == 1
y = v;
else
v = v(:);
y = [];
m = length(v);
if m == 1
y = zeros(1, n);
y(:) = v;
else
for i = 1 : m
y_recr = nchoosekr_rec(v(i:end), n-1);
s_repl = zeros(size(y_recr, 1), 1);
s_repl(:) = v(i);
y = [ y ; s_repl, y_recr ];
end
end
end