How to generate all the permutations of a multiset?

Question

A multi-set is a set in which all the elements may not be unique.How to enumerate all the possible permutations among the set elements?

Answer 1

You can reduce your problem to enumerate all permutations of a list. The typcial permutation generation algorithm takes a list and don't check if elements are equal. So you only need to generate a list out of your multiset, and feed it to your permutation generating algorithm.

For example, you have the multiset {1,2,2}.

You transform it to the list [1,2,2].

And generate all permutations, for example in python:

import itertools as it
for i in it.permutations([1,2,2]):
   print i

And you will get the output

(1, 2, 2)
(1, 2, 2)
(2, 1, 2)
(2, 2, 1)
(2, 1, 2)
(2, 2, 1)

The problem is, that you get some permutations repeatedly. A simple solution would be just to filter them out:

import itertools as it
permset=set([i for i in it.permutations([1,2,2])])
for x in permset:
   print x

Output:

(1, 2, 2)
(2, 2, 1)
(2, 1, 2)