All possible grouping combination for different package

Hi,

I want to group items in different packages and have all possible combinations. On the other hand, there must not be repetition with the same elements in a different order for the same package.

There are X elements that I would like to divide into Y groups with all possible combinations. For example, for X=5 elements: A, B, C, D, E and Y=2 groups, this should be as follow:

Group 1, Group 2

Combination 1: {A, B, C} , {D, E}

Combination 2: {A, B, D} , {C, E}

Combination 3: {A, D, E} , {B, C}

…

However, all grouping combination with the same element should be avoided, such as A,B,C or A,C,B.

Thanks

Answer 1

[Walter Roberson]

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

S = {'A', 'B', 'C', 'D', 'E'}

S = 1×5 cell array
    {'A'}    {'B'}    {'C'}    {'D'}    {'E'}

Group1 = nchoosek(S, 3)

Group1 = 10×3 cell array
    {'A'}    {'B'}    {'C'}
    {'A'}    {'B'}    {'D'}
    {'A'}    {'B'}    {'E'}
    {'A'}    {'C'}    {'D'}
    {'A'}    {'C'}    {'E'}
    {'A'}    {'D'}    {'E'}
    {'B'}    {'C'}    {'D'}
    {'B'}    {'C'}    {'E'}
    {'B'}    {'D'}    {'E'}
    {'C'}    {'D'}    {'E'}

and in each case, Group2 is setdiff(S) and the corresponding elements of group 1.

[Yannick Pratte]

Hi,

Thanks for the answer. But I think it works only if Y groups = 2. I would like to have expandable methods.

The final idea is to select boxes (packaging) with different products. Each possible solution will be sent to an optimization function. I would like to evaluate the 2, 3, 4 combinations of boxes.

[Torsten]

https://stackoverflow.com/questions/58079910/find-all-ways-to-partition-a-set-into-given-sized-subsets

Prune's answer seems promising.

[Walter Roberson]

https://www.mathworks.com/matlabcentral/fileexchange/24133-set-partition gives code to partition into a fixed number of non-empty sets. In itself, it is not designed for fixed set sizes. Perhaps @Bruno Luong has an adaptation for that purpose.