Question

I have N data elements (say, 1:N) that I want to distribute into two distinct groups. I do not know what the best distribution is, so I want to test every possible pairing, but ignore symmetric results.

I need a function that has such a result:

>> pairings(1:2)
{
  [1], [2]
}

>> pairings(1:3)
{
  [1], [2,3]
  [2], [1,3]
  [3], [1,2]
}

>> pairings(1:4)
{
  [1], [2,3,4]
  [2], [1,3,4]
  [3], [1,2,4]
  [4], [1,2,3]
  [1,2], [3,4]
  [1,3], [2,4]
  [1,4], [2,3]
}

Of course an algorithm that employs a lot of looping would be easy enough to write, but I guess there is a solution that does feel more like matlab.

Answer 1

This is essentially a power set enumeration problem. Assume that the element 1 is in the first of the two sets. Enumerate the power set of the elements 2 .. N. This can be done by looping through the binary numbers from 1 .. 2^(N-1). Add the element 1 to the result set as the first set in the pair. Take the complement of the result set as your other set. Toss away the empty set as a subset if it’s not relevant for your problem.