intelligently generating combinations of combinations

Question

Let\'s say I have a class of 30 students and want generate every possible way in which they can be partitioned into groups of 5 (order is irrelevant).

I know how to

Answer 1

You could do some post-processing on the permutations. Some pseudo-code (implement in the language of your choice...):

// We have a list of lists called 'permutations'
// combinations is an (empty) list of lists
for each permutation in permutations
{
   sortedPermutation = permutation.sort()
   if (! combinations.find(sortedPermutation) )
   {
       combinations.add(sortedPermutation);
   }
}

Probably not the most efficient; I'd add the sort & compare to the code that generates the permutations personally.