permutations with unique values

Question

itertools.permutations generates where its elements are treated as unique based on their position, not on their value. So basically I want to avoid duplicates like this:

Answer 1

Came across this the other day while working on a problem of my own. I like Luka Rahne's approach, but I thought that using the Counter class in the collections library seemed like a modest improvement. Here's my code:

def unique_permutations(elements):
    "Returns a list of lists; each sublist is a unique permutations of elements."
    ctr = collections.Counter(elements)

    # Base case with one element: just return the element
    if len(ctr.keys())==1 and ctr[ctr.keys()[0]] == 1:
        return [[ctr.keys()[0]]]

    perms = []

    # For each counter key, find the unique permutations of the set with
    # one member of that key removed, and append the key to the front of
    # each of those permutations.
    for k in ctr.keys():
        ctr_k = ctr.copy()
        ctr_k[k] -= 1
        if ctr_k[k]==0: 
            ctr_k.pop(k)
        perms_k = [[k] + p for p in unique_permutations(ctr_k)]
        perms.extend(perms_k)

    return perms

This code returns each permutation as a list. If you feed it a string, it'll give you a list of permutations where each one is a list of characters. If you want the output as a list of strings instead (for example, if you're a terrible person and you want to abuse my code to help you cheat in Scrabble), just do the following:

[''.join(perm) for perm in unique_permutations('abunchofletters')]