algorithm - Using PHP, randomly pair up group of items, not pairing any with itself, no direct pairings

Question

Assume you have a set of items in an array.

A, B, C, D, E, F, G, H

Using PHP, how would you randomly pair the letters together without pairing them with a duplicate of themselves?

Such as this:

 A->pairedLetter = G
 B->pairedLetter = C
 C->pairedLetter = E
 D->pairedLetter = A
 E->pairedLetter = B
 F->pairedLetter = D
 G->pairedLetter = F

and so on...

EDIT: Oh, and also, If A is paired with F, F can NOT be paired with A. So there will have to be as many relationships as there are items.

Answer 1

Does it have to be perfectly random given your constraints? If you were willing to add in another constraint then you could make the problem very simple. If you were willing to make it so that the mappings all formed a single loop then you could just shuffle your array and then make element one pont at two, two point at three and the last element points at the first. You will guarantee that no element can poitn at itself (unless the array only has one element), no element will point at the element pointing at it (unless the array only has two elements) and that no element will be pointed at by more than one item.

You are restricting your results set slightly so losing a certain amount of the random element but if you are happy with this its extremely simpel to do.