Find the permutations of an array using recursion

Question

I came up with the following function:

def permutations(elements, arr, index):
    if len(elements) == index:
        print arr
    for i in xrange(index, len(elements)):
        arr[index] = elements[i]
        permutations(elements, arr, index+1)

permutations([1,2,3], [0,0,0], 0)

However, it's printing:

[1, 2, 3]
[1, 3, 3]
[2, 2, 3]
[2, 3, 3]
[3, 2, 3]
[3, 3, 3]

what's wrong with my recursion?

Answer 1

Ok, I found this as a Java String recursive permutation algorithm that I translated to Python. I think it's the best solution:

def permutation(aux, ls):
    if len(ls) == 0: 
        print(aux)
    else:
        for i in range(len(ls)):
            permutation(aux + [ls[i]], ls[0:i] + ls[i+1:len(ls)])

permutation([], [1, 2, 3])

This is the output:

[1, 2, 3]
[1, 3, 2]
[2, 1, 3]
[2, 3, 1]
[3, 1, 2]
[3, 2, 1]

Answer 2

The main problem in your code is that on i-th position only possible values are from (i, n - 1) where is n length of list. Thats why on last index in list you have all 3's. So the solution would be to iterate on all "levels" ( i-th permutation call) from (0, n - 1) . But because you will iterate from (0, n - 1) on all "levels" you must introduce dictionary(used as hashset) where you will keep if some value ( j-th element) is already chosen on previous calls. Easiest solution would be something like:

def perm(elements):
    def inner(arr, index, visited):
        if len(elements) == index:
            print arr
        for i in xrange(0, len(elements)):
            if (i not in visited):
                visited[i] = 1; # mark so same index can not be used later
                arr[index] = elements[i]
                inner(arr, index + 1, visited);
                del visited[i] # free index
    inner([0] * len(elements), 0, {});         

perm([1,2,3])

As @Hooked already mentioned it would be best if you can use permutations function from itertools module . Note that on Python 3, you can put arr and visited outside of function parameters with nonlocal . Also, here you are one more solution, without dictionary, but with additional list which will hold all possible values for i-th level (position) of permutation. In this solution, however order of permutations is not preserved

def perm(elements):
    def inner(arr, index, possible):
        if len(elements) == index:
            print arr
        lenForLevel = len(elements) - index;
        for i in xrange(0, lenForLevel):            
            arr[index] = possible[i]
            (possible[i], possible[lenForLevel - 1]) = (possible[lenForLevel - 1], possible[i])
            inner(arr, index + 1, possible);
            (possible[i], possible[lenForLevel - 1]) = (possible[lenForLevel - 1], possible[i])
    inner([0] * len(elements), 0, list(elements))

perm([1,2,3,4])