Python itertools generating a powerset with replacements - python

I'm trying to generate a powerset of a large list of strings that includes replacements. None of the built-in itertools functions do this (as far as I can tell).
EDIT Maybe using "set" in the title was misleading. Order is important here. 'ca' != 'ac'
Example of what I want:
print( powerset_with_replacement(['abc']) )
# yeilds
('a',)
('b',)
('c',)
('a', 'a')
('a', 'b')
('a', 'c')
('b', 'b')
('b', 'c')
('c', 'c')
('a', 'a', 'a')
('a', 'a', 'b')
('a', 'a', 'c')
('a', 'b', 'b')
('a', 'b', 'c')
('a', 'c', 'c')
('b', 'b', 'b')
('b', 'b', 'c')
('b', 'c', 'c')
('c', 'c', 'c')
I got this far already but it seems messy.. I'm wondering if there is a cleaner or more pythonic way to do this. Any help is much appreciated.
Is there a way to get rid of the flatten function or put that inside the main one?
from itertools import combinations_with_replacement
import collections
def flatten(it):
for x in it:
if (isinstance(x, collections.abc.Iterable) and
not isinstance(x, tuple)):
yield from flatten(x)
else:
yield x
def powerset_with_replacement(list1):
for i in range(1,len(list1)+1):
yield( combinations_with_replacement(list1, i) )
y = flatten(powerset_with_replacement(list('abc')))
for x in y:
print(x)


You can define your own generator and mix in itertools.product to achieve this result:
def combinations_upto(x):
for i in range(len(x)):
yield from itertools.product(x, repeat=i+1)
x = "abc"
combo_list = list(combinations_upto(x))
print(combo_list)


Create a list of cartesian products of size 1 to len(X)
from itertools import product, chain
x = 'abc'
prods = chain.from_iterable(product(x,repeat=n) for n in range(1,len(x)+1))
[print(_) for _ in prods]
Output
('a',)
('b',)
('c',)
('a', 'a')
('a', 'b')
('a', 'c')
('b', 'a')
('b', 'b')
('b', 'c')
('c', 'a')
('c', 'b')
('c', 'c')
('a', 'a', 'a')
('a', 'a', 'b')
('a', 'a', 'c')
('a', 'b', 'a')
('a', 'b', 'b')
('a', 'b', 'c')
('a', 'c', 'a')
('a', 'c', 'b')
('a', 'c', 'c')
('b', 'a', 'a')
('b', 'a', 'b')
('b', 'a', 'c')
('b', 'b', 'a')
('b', 'b', 'b')
('b', 'b', 'c')
('b', 'c', 'a')
('b', 'c', 'b')
('b', 'c', 'c')
('c', 'a', 'a')
('c', 'a', 'b')
('c', 'a', 'c')
('c', 'b', 'a')
('c', 'b', 'b')
('c', 'b', 'c')
('c', 'c', 'a')
('c', 'c', 'b')
('c', 'c', 'c')

Related

List every combination of a list's elements

I'm trying to retrieve every combination of a list's elements in a variable but one at a time,
I used this code that I modified to fit my program :
import itertools
stuff = [1, 2, 3]
for L in range(0, len(stuff)+1):
for subset in itertools.combinations(stuff, L):
print(subset)
in my program, the list "stuff" contains the alphabet and numbers,
but the problem is that I retrieve the combinations like "a", "b",..., "y", "z" and then i would like to get "aa", "ab", "ac",... but it doesn't return "aa", as if it skipped it, it comes to "ab" directly.
I'm new to this forum, it's my first question so it might not be perfect
Thanks for any help :)

You're not looking for combinations of elements from an existing collection, but for all possible products of the elements of that collection:
import itertools
stuff = ['a', 'b', 'c']
for n in range(0, len(stuff) + 1):
for result in itertools.product(stuff, repeat=n):
print(result)
Output:
()
('a',)
('b',)
('c',)
('a', 'a')
('a', 'b')
('a', 'c')
('b', 'a')
('b', 'b')
('b', 'c')
('c', 'a')
('c', 'b')
('c', 'c')
('a', 'a', 'a')
('a', 'a', 'b')
('a', 'a', 'c')
('a', 'b', 'a')
('a', 'b', 'b')
('a', 'b', 'c')
('a', 'c', 'a')
('a', 'c', 'b')
('a', 'c', 'c')
('b', 'a', 'a')
('b', 'a', 'b')
('b', 'a', 'c')
('b', 'b', 'a')
('b', 'b', 'b')
('b', 'b', 'c')
('b', 'c', 'a')
('b', 'c', 'b')
('b', 'c', 'c')
('c', 'a', 'a')
('c', 'a', 'b')
('c', 'a', 'c')
('c', 'b', 'a')
('c', 'b', 'b')
('c', 'b', 'c')
('c', 'c', 'a')
('c', 'c', 'b')
('c', 'c', 'c')
Note: I renamed L to n, because it's generally not a good idea to name variables and functions in Python with capitals and I renamed subset to result because what both combinations and product produce are not sets but tuples.
As #mozway correctly points out, you may consider an example like ('a', 'b') and ('b', 'a') duplicates, in which case you want combinations_with_replacement:
import itertools
stuff = ['a', 'b', 'c']
for n in range(0, len(stuff) + 1):
for result in itertools.combinations_with_replacement(stuff, r=n):
print(result)
Output:
()
('a',)
('b',)
('c',)
('a', 'a')
('a', 'b')
('a', 'c')
('b', 'b')
('b', 'c')
('c', 'c')
('a', 'a', 'a')
('a', 'a', 'b')
('a', 'a', 'c')
('a', 'b', 'b')
('a', 'b', 'c')
('a', 'c', 'c')
('b', 'b', 'b')
('b', 'b', 'c')
('b', 'c', 'c')
('c', 'c', 'c')

Cartesian Product with optional lists

I am creating a program, in python, that allows me to generate NFT Art based on the given assets.
Obviously the number of arts that can be generated varies according to the assets (layers and layer images) and this is precisely the problem, how can I calculate the possible combinations also counting the optional layers?
To be clearer:
for example I have 4 layers:
l1 = ["A","B"]
l2 = ["C"]
l3 = ["D","E"] #optional
l4 = ["F","G"] #optional
where l3 and l4 are optional. So the combinations I expect are:
1. ["A","C"]
2. ["B","C"]
3. ["A","C","D"]
4. ["A","C","E"]
5. ["B","C","D"]
6. ["B","C","E"]
7. ["A","C","F"]
8. ["A","C","G"]
9. ["B","C","F"]
10. ["B","C","G"]
11. ["A","C","D","F"]
12. ["A","C","D","G"]
13. ["A","C","E","F"]
14. ["A","C","E","G"]
15. ["B","C","D","F"]
16. ["B","C","D","G"]
17. ["B","C","E","F"]
18. ["B","C","E","G"]
How can I get to that? I tried with itertools.product but obviusly it take into account all lists

One way to do this is with the powerset recipe from the itertools docs. Chaining together the products of 'required lists' with every subset of the 'optional-list-set' gives a generator that produces each possibility once:
def powerset(iterable):
"""powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)"""
s = list(iterable)
return chain.from_iterable(combinations(s, r) for r in range(len(s) + 1))
def product_with_optional(required_sequences, optional_sequences):
return chain.from_iterable(product(*required_sequences, *optionals)
for optionals in powerset(optional_sequences))
optional_combinations = product_with_optional(required_sequences=[l1, l2],
optional_sequences=[l3, l4])
which gives:
1 ('A', 'C')
2 ('B', 'C')
3 ('A', 'C', 'D')
4 ('A', 'C', 'E')
5 ('B', 'C', 'D')
6 ('B', 'C', 'E')
7 ('A', 'C', 'F')
8 ('A', 'C', 'G')
9 ('B', 'C', 'F')
10 ('B', 'C', 'G')
11 ('A', 'C', 'D', 'F')
12 ('A', 'C', 'D', 'G')
13 ('A', 'C', 'E', 'F')
14 ('A', 'C', 'E', 'G')
15 ('B', 'C', 'D', 'F')
16 ('B', 'C', 'D', 'G')
17 ('B', 'C', 'E', 'F')
18 ('B', 'C', 'E', 'G')

I'm assuming the ordering of the optional layers matter, so you can just iteratively create all combinations of the optional layers, then use itertools.product on the layers + optional_layers to generate the lists.
import itertools
from pprint import pprint
l1 = ["A","B"]
l2 = ["C"]
l3 = ["D","E"] #optional
l4 = ["F","G"] #optional
layers = [l1, l2]
optional_layers = [l3, l4]
results = []
results += itertools.product(*layers)
for i in range(len(optional_layers) + 1):
comb = itertools.combinations(optional_layers, r=i)
for c in comb:
results += itertools.product(*layers, *c)
pprint(results)
Output
[('A', 'C'),
('B', 'C'),
('A', 'C'),
('B', 'C'),
('A', 'C', 'D'),
('A', 'C', 'E'),
('B', 'C', 'D'),
('B', 'C', 'E'),
('A', 'C', 'F'),
('A', 'C', 'G'),
('B', 'C', 'F'),
('B', 'C', 'G'),
('A', 'C', 'D', 'F'),
('A', 'C', 'D', 'G'),
('A', 'C', 'E', 'F'),
('A', 'C', 'E', 'G'),
('B', 'C', 'D', 'F'),
('B', 'C', 'D', 'G'),
('B', 'C', 'E', 'F'),
('B', 'C', 'E', 'G')]

How can I rearrange a set of values into new pattern on python and print results

so I will do my best to explain what I'm looking for,
at the moment I have a 100 item list that I want to repetitively shuffle using a set pattern to first check if the pattern will eventually bring me back to where I began
and 2 to print the result of each loop to a text file.
so using a 3 item list as my example
[a,b,c]
and the shuffle pattern [3 1 2]
where the 3rd item becomes the first.
the first item becomes the second
and the second item becomes the 3rd
on a loop would generate the following patterns
[a,b,c]
[3,1,2]
[c,a,b]
[b,c,a]
[a,b,c]
but I have a list at the moment of 100 items that I need to find every single arrangement for a few different patterns I would like to test out.
does anyone know of a way to do this in python please.

You can define function and call this function multi times like below:
>>> def func(lst, ptr):
... return [lst[idx-1] for idx in ptr]
>>> lst = ['a','b','c']
>>> ptr = [3,1,2]
>>> for _ in range(5):
... lst = func(lst, ptr)
... print(lst)
['c', 'a', 'b']
['b', 'c', 'a']
['a', 'b', 'c']
['c', 'a', 'b']
['b', 'c', 'a']

You could use numpy advanced integer indexing if your list contains a numeric type:
import numpy as np
original_list=[1,2,3]
numpy_array = np.array(original_list)
pattern = [2,1,0]
print(numpy_array[pattern])
>>> array([3, 2, 1])

def rearrange(pattern : list,L:list):
new_list = []
for i in pattern :
new_list.append(L[i-1])
return new_list
print(rearrange([3,1,2],['a','b','c']))
output :
['c', 'a', 'b']

Itertools could be what you need.
import itertools
p = itertools.permutations(['a','b','c', 'd'])
list(p)
Output:
[('a', 'b', 'c', 'd'),
('a', 'b', 'd', 'c'),
('a', 'c', 'b', 'd'),
('a', 'c', 'd', 'b'),
('a', 'd', 'b', 'c'),
('a', 'd', 'c', 'b'),
('b', 'a', 'c', 'd'),
('b', 'a', 'd', 'c'),
('b', 'c', 'a', 'd'),
('b', 'c', 'd', 'a'),
('b', 'd', 'a', 'c'),
('b', 'd', 'c', 'a'),
('c', 'a', 'b', 'd'),
('c', 'a', 'd', 'b'),
('c', 'b', 'a', 'd'),
('c', 'b', 'd', 'a'),
('c', 'd', 'a', 'b'),
('c', 'd', 'b', 'a'),
('d', 'a', 'b', 'c'),
('d', 'a', 'c', 'b'),
('d', 'b', 'a', 'c'),
('d', 'b', 'c', 'a'),
('d', 'c', 'a', 'b'),
('d', 'c', 'b', 'a')]
​

Creating combination on list values

I have a requirement where say i have a list
lis = ['a','b','c','d','e','f']
I have to now create a combination of them eg:
l1 = [a],['b,c,d,e,f]
l2: [b],[a,c,d,e,f]
.
.
l10 [a,b,c],[d,e,f]
.
l11 [a,b,c,d] [e,f]
The repeated elements on the left and right nodes will be removed:
eg: i don't need two lists as:
l1: [b,c] , [a,d,e,f]
l2: [a,d,e,f], [b,c]
Since they are the same
The pseudo code i have in mind is:
for length = 1, i will take one element from list and club others
similar for length=2, will take two element and club others
till length=len(list)-1, will do the clubbing
and then later remove the duplicates.
Any better solution i could try?

This may no be optimal, but is very straightforward:
from itertools import chain, combinations
def power_set(iterable):
"""power_set([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)"""
source = list(iterable)
return chain.from_iterable(combinations(source, r) for r in range(1, len(source) // 2 + 1))
def complement(source, universe):
return tuple(set(universe) - set(source))
lst = ['a', 'b', 'c', 'd', 'e', 'f']
result = set(frozenset({si, complement(si, lst)}) for si in power_set(lst))
for s, c in result:
print(s, c)
Output
('a', 'd', 'e') ('f', 'c', 'b')
('f', 'a', 'c', 'b') ('d', 'e')
('b', 'e') ('d', 'f', 'a', 'c')
('a', 'b', 'f') ('d', 'e', 'c')
('e', 'd', 'a', 'f', 'b') ('c',)
('c', 'f') ('d', 'a', 'e', 'b')
('d', 'f') ('a', 'e', 'b', 'c')
('d',) ('e', 'c', 'a', 'f', 'b')
('f', 'a', 'e', 'c') ('b', 'd')
('e', 'c', 'd', 'a', 'b') ('f',)
('b', 'c', 'd') ('f', 'a', 'e')
('a', 'b', 'e') ('d', 'f', 'c')
('b', 'c') ('d', 'f', 'a', 'e')
('f', 'a', 'b') ('c', 'd', 'e')
('d', 'e', 'b', 'c') ('a', 'f')
('c', 'd', 'f') ('a', 'e', 'b')
('e', 'c', 'd', 'f', 'b') ('a',)
('a', 'c') ('d', 'f', 'e', 'b')
('f', 'e', 'c') ('a', 'b', 'd')
('a', 'd') ('f', 'e', 'b', 'c')
('b', 'c', 'e') ('d', 'f', 'a')
('a', 'c', 'e') ('d', 'f', 'b')
('d', 'e', 'f') ('a', 'c', 'b')
('a', 'c', 'd') ('f', 'e', 'b')
('d', 'f', 'e', 'c') ('a', 'b')
('f', 'a', 'e', 'b') ('c', 'd')
('d', 'a', 'c') ('b', 'e', 'f')
('a', 'e') ('d', 'f', 'c', 'b')
('a', 'b', 'c') ('d', 'f', 'e')
('a', 'd', 'f') ('e', 'b', 'c')
('d', 'e', 'b') ('a', 'c', 'f')
('c', 'd', 'a', 'f', 'b') ('e',)
('b',) ('e', 'c', 'd', 'a', 'f')
('e', 'f') ('d', 'a', 'c', 'b')
('d', 'c', 'b') ('a', 'e', 'f')
('b', 'f') ('d', 'a', 'e', 'c')
('d', 'a', 'e') ('b', 'c', 'f')
('b', 'd', 'e') ('f', 'a', 'c')
('a', 'e', 'c') ('b', 'd', 'f')
('c', 'e') ('d', 'f', 'a', 'b')
('d', 'a', 'b') ('c', 'e', 'f')

All strings with list of characters?

I'm making a specialized utility similar to John the Ripper, and I'd like to use a loop that returns all strings up to x characters that can be formed from the string. For example, if the "seed" string is abcd, it should return:
a
b
c
d
aa
ab
ac
and so on. If the character limit is 10, it would generate aaaaaaaaaa, abcddcbaaa, and so on. Is there a simple for loop to do this, or is it more complicated than that?

I'll self-plagiarize from this answer and add a maximum length:
from itertools import product
def multiletters(seq, max_length):
for n in range(1, max_length+1):
for s in product(seq, repeat=n):
yield ''.join(s)
which gives
>>> list(multiletters("abc", 2))
['a', 'b', 'c', 'aa', 'ab', 'ac', 'ba', 'bb', 'bc', 'ca', 'cb', 'cc']
>>> list(multiletters("abcd", 4))[:8]
['a', 'b', 'c', 'd', 'aa', 'ab', 'ac', 'ad']
and so on.

def all_strings(alphabet, length_limit=None):
n_letters = len(alphabet)
length = 0
n_strings = 1
buf = []
while True:
for i in xrange(0, n_strings):
k = i
for j in xrange(length - 1, -1, -1):
buf[j] = alphabet[k % n_letters]
k /= n_letters
yield ''.join(buf)
length += 1
if length == length_limit:
break
n_strings *= n_letters
buf.append(alphabet[0])
for s in all_strings('abcd', length_limit=4):
print s

As pointed out in the comment's use itertools.premutations or even better take a look #DSM's answer, as this one misses the doubles:
In [194]: from itertools import chain, permutations
In [195]: s = 'abcd'
In [196]: map(''.join,chain.from_iterable(permutations(s,x)
for x in range(1,len(s)+1)))
Out[196]:
['a',
'b',
'c',
'd',
'ab',
'ac',
'ad',
'ba',
'bc',
'bd',
...
'dbca',
'dcab',
'dcba']
Anyway, here's a version of #DSM's answer that returns a list:
from itertools import product
def ms(seq, max_length):
return [''.join(s) for n in range(1, max_length+1)
for s in product(seq,repeat=n)]

Use itertools.permuataions.
for i in range(2,4):
tuples = itertools.permutations('abca' , i)
print( list(tuples))
The example code sequence generates:
[('a', 'b'), ('a', 'c'), ('a', 'a'), ('b', 'a'), ('b', 'c'), ('b', 'a'), ('c', 'a'), ('c', 'b'), ('c', 'a'), ('a', 'a'), ('a', 'b'), ('a', 'c')]
[('a', 'b', 'c'), ('a', 'b', 'a'), ('a', 'c', 'b'), ('a', 'c', 'a'), ('a', 'a', 'b'), ('a', 'a', 'c'), ('b', 'a', 'c'), ('b', 'a', 'a'), ('b', 'c', 'a'), ('b', 'c', 'a'), ('b', 'a', 'a'), ('b', 'a', 'c'), ('c', 'a', 'b'), ('c', 'a', 'a'), ('c', 'b', 'a'), ('c', 'b', 'a'), ('c', 'a', 'a'), ('c', 'a', 'b'), ('a', 'a', 'b'), ('a', 'a', 'c'), ('a', 'b', 'a'), ('a', 'b', 'c'), ('a', 'c', 'a'), ('a', 'c', 'b')]

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