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

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Ehsan Modiri
Ehsan Modiri on 20 Jan 2020
Commented: Ehsan Modiri on 20 Jan 2020
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?

Answers (1)

Image Analyst
Image Analyst on 20 Jan 2020
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.

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