All possible combinations (subgroups vary in size) of elements in a vector

Hey,

I am trying to find a solution for the following problem:

I want to generate every possible combination of elements in a vector. The vector elements should always be split up in 2 groups. The groups can vary in size (number of elements), but all elements have to been included in the groups. The number of elements in a vector varies from 3 to 12.

Vector1 = [1 2 3 4]

Possible subgroups:

1 vs. 2,3,4

   2 vs. 1,3,4 
   3 vs. 1,2,4 
   4 vs. 1,2,3 
  1,2, vs. 3,4 
   1,3  vs. 2,4 
   1,4 vs. 2,3

Vector2 =[1 2 3 4 5 6]

Size Subgroup1 = 1, Subgroup2 = 5

  1 vs. 2,3,4,5,6
  2 vs. 1,3,4,5,6
  …
        6 vs  1,2,3,4,5

Size Subgroup1 = 2, Subgroup2 = 4

   1,2 vs. 3,4,5,6 
   1,3 vs. 2,4,5…
   …

Size Subgroup1 = 3, Subgroup2 = 3

   1,2,3 vs 4,5,6
        1,2,4 vs 3,5,6

Size Subgroup1 = 4, Subgroup2 = 2

     …

Size Subgroup1 = 5, Subgroup2 = 1

…

I have searched for a solution but I haven´t found one yet. Thanks!

Stephan

[Andrea Ferrari Braga]

Hi, I'm searching for the solution of this problem too.

Do you find anything useful in this months ?

Thanks.

Andrea

Answer 1

[Matt Fig]

This might be what you are looking for:

partitions

>> C = partitions(4);
>> partdisp(C)

The 15 partitions of set {1 2 3 4}:
{1 2 3 4} 
{1 2 3} {4} 
{1 2 4} {3} 
{1 2} {3 4} 
{1 2} {3} {4} 
{1 3 4} {2} 
{1 3} {2 4} 
{1 3} {2} {4} 
{1 4} {2 3} 
{1} {2 3 4} 
{1} {2 3} {4} 
{1 4} {2} {3} 
{1} {2 4} {3} 
{1} {2} {3 4} 
{1} {2} {3} {4}

[Andrea Ferrari Braga]

Thanks a lot !!!

Answer 2

[drawer]

Thanks for your responses. I found a solution, but it is too embarassing to post it since there is also a very easy way to solve the problem. thanks again!

[James]

You sound an awful lot like Fermat here. :-)