How to generate all possible ways of dividing up the numbers from 1 to 46 into three groups?

I want to generate all possible ways of dividing up the numbers from 1 to 46 into three groups with at least five numbers in each group. So far, I use the way below:

in1=46;

in2=5;

C1 = nchoosek(1:in1,in2); % Binomial coefficient or all combinations

C1 = [C1,zeros(size(C1,1),in1-in2)]; % Add some zeros to have a full matrix

x = 1:in1; % Number of values

for p = 1:size(C1,1)

t = true(1,in1); % Generate a logical matrix

t(C1(p,1:in2)) = false(1,in2); % Inserd zeros logical values in the pth row

C1(p,in2+1:in1) = x(t); % Insert remaining values into 6:46 indices

end

C2 = nchoosek(1:in1-in2,5); % Binomial coefficient or all combinations

C2 = [C2,zeros(size(C2,1),in1-in2-5)]; % Add some zeros to have a full matrix

x = 1:in1-in2;

for q = 1:size(C2,1)

t = true(1,in1-in2);

t(C2(q,1:in2)) = false(1,in2);

C2(q,in2+1:in1-in2) = x(t);

end

% A = zeros(size(C1,1)*size(C2,1),in1); % Generate a zeros matrix

tic

k = 0;

for p = 1:size(C1,1)

x = C1(p,1:in2);

y = C1(p,in2+1:in1);

for q = 1:size(C2,1)

k = k + 1;

A(k,:) = [x,y(C2(q,:))];

end

end

clear C1 C2 k p q t x y

toc

It takes long time, is there any other faster way to achieve this goal?

Answer 1

[Image Analyst]

You cannot do that. This would be the command:

combinations = perms(1:46);

and then you could generate 3 indexes, at least 5 apart, to extract the 3 groups

But the theoretical number of combinations would be 46 factorial, 5.50262215981209e+57, and that is way too big for your computer to handle.

[Ehsan Modiri]

I see, and due to this fact I ask this question.