I'm having trouble drawing a recursion tree for the following permutation code:
def permut(array):
if len(array) == 1:
return [array]
res = []
for permutation in permut(array[1:]):
print permutation, array
for i in range(len(array)):
res.append(permutation[:i] + array[0:1] + permutation[i:])
return res
Let's say my array is 'mick' then I get the following print outs for permutation and array:
k and ck
ck and ick
kc and ick
ick and mick
I understand it until 'k' and 'ck' (as when array = 'ck' len(arraw[1:]) == 1) but how do we ever get 'ick' as an array in the recursion? Could you visualize this anyhow? Thanks a lot for any tips!
permut('Mick') # recursion: for permutation in permut('ick')
permut('ick') # recursion: for permutation in permut('ck')
permut('ck') # recursion: for permutation in permut('k')
permut('k') # return ['k']
permut('ck') # continue from the loop
# print each element of ['k'] with 'ck'
# return res, which is ['ck', 'kc']
permut('ick') # continue from the loop
# print each of ['ck', 'kc'] with 'ick'
# return res, which is ['ick', 'cik', 'cki', 'ikc', 'kic', 'kci']
permut('Mick') # continue from loop
# print each of the above elements + 'Mick' individually
# return res, which is... long
The above basically permutes all letters in the word, which can be simply achieved with
>>> import itertools as it
>>> res = list(''.join(p) for p in it.permutations('Mick'))
>>> print res
['Mick', 'Mikc', 'Mcik', 'Mcki', 'Mkic', 'Mkci', 'iMck', 'iMkc', 'icMk', 'ickM', 'ikMc', 'ikcM', 'cMik', 'cMki', 'ciMk', 'cikM', 'ckMi', 'ckiM', 'kMic', 'kMci', 'kiMc', 'kicM', 'kcMi', 'kciM']