how to add combinatorics function in matlab with n different objects divided into r groups and each group get at least 1 object

I have 7 machines which I want to group in 3 cells such that each cell contain atleast 1 machine the numeric formula for this is

3^7−3⋅2^7+3=2187−3⋅(128)+3=1806

I want to generate a matrix with each combination and run loop over that. is there any way I can code this? for example the 1st array is 1 1 1 1 2 3 1 and running the 2nd time loop give another value for example 1 1 1 2 1 1 3

Answer 1

[Roger Stafford]

C = zeros(r^n,n);
t = 0;
for k = 0:(r^n)-1
  s = dec2base(k,r,n);
  if length(unique(s))==r
    t = t+1;
    C(t,:) = s-‘0’+1;
  end
end
C = C(1:t,:);

[summyia qamar]

thankyou sir..can you please explain this?how dec2base is used and why? why k=0:(r^n)-1

[Roger Stafford]

Using your values r = 3 and n = 7, the range of k = 0:(3^7)-1 is exactly the range of numbers that in base 3 can be represented as a 7-digit number:

0000000
0000001
0000002
0000010
....
2222222

There are 3^7 such base 3 numbers, and they are created by Matlab’s ‘dec2base’ function. See:

https://www.mathworks.com/help/matlab/ref/dec2base.html

The requirement “length(unique(s))==r” forces each of the three groups to have at least one digit representing it. (Actually the digits will be one below the corresponding group number.) Hence, for example, '0010121' is accepted but '0010111' is not.

[summyia qamar]

thankyou sir