Algorithm for finding multiset permutation given lexicographic index

Question

I am trying to find an efficient algorithm to find permutation of a multiset, given an index.

Ex: given {1, 3, 3}. All permutations in an ascending lexi

Answer 1

# Python 2
from collections import Counter
from math import factorial


def count_permutations(counter):
    values = counter.values()
    return (
        factorial(sum(values))/reduce(lambda a, v: a * factorial(v), values, 1)
    )


def permutation(l, index):
    l = sorted(l)

    if not index:
        return l

    counter = Counter(l)
    total_count = count_permutations(counter)
    acc = 0
    for i, v in enumerate(l):

        if i > 0 and v == l[i-1]:
            continue

        count = total_count * counter[v] / len(l)

        if acc + count > index:
            return [v] + permutation(l[:i] + l[i + 1:], index - acc)

        acc += count

    raise ValueError("Not enough permutations")

Seems to work as expected

In [17]: for x in range(50): print x, permutation([1, 1, 2, 2, 2], x)
0 [1, 1, 2, 2, 2]
1 [1, 2, 1, 2, 2]
2 [1, 2, 2, 1, 2]
3 [1, 2, 2, 2, 1]
4 [2, 1, 1, 2, 2]
5 [2, 1, 2, 1, 2]
6 [2, 1, 2, 2, 1]
7 [2, 2, 1, 1, 2]
8 [2, 2, 1, 2, 1]
9 [2, 2, 2, 1, 1]
10---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
[...]
ValueError: Not enough permutations

Time complexity: O(n^2).