All Combinations For A List Of Objects

Prerequisite: Python Itertools

There are several ways to get all combinations for a list of objects in python. This problem has already a recursive solution. Python has an itertools module that provides two functions named combinations() and combinations_with_replacement() which make our work a lot easier. Below are the two methods:

1. Using itertools.combinations():

Syntax : itertools.combination(iterable, r) 

Where r is the length of output tuples.

This function returns subsequences(tuples) of length r from the input iterable. It takes a list of objects and the length of the output tuples(r) as input. But there are a few things to notice about this function like:

• The combination tuples are emitted in lexicographic order. So, if the input iterable is in sorted order the combined output will also be produced in sorted order.
• Elements are treated as unique based on their positions not on their values. So, if the input elements consist of duplicate values there will be duplicate values in the output.
• The number of items returned is nCr = n! / (r! * (n-r)!) when 0 <= r <= n; and zero when r > n.

All combinations without replacement

Below is the implementation:

Python3

# code
from itertools import combinations

# m = list of objects.
# same method can be applied
# for list of integers.
m = ['GFG', 'GeeksforGeeks', 'Geeks']
# display
for i in range(len(m)):
  print(list(combinations(m, i+1)))

Output:

[('GFG',), ('GeeksforGeeks',), ('Geeks',)]
[('GFG', 'GeeksforGeeks'), ('GFG', 'Geeks'), ('GeeksforGeeks', 'Geeks')]
[('GFG', 'GeeksforGeeks', 'Geeks')]

If the input has duplicate elements:

Python3

# code
from itertools import combinations

# m = list of objects.
# 1st and 3rd elements are same.
# same method can be applied
# for list of integers.
m = ['GFG', 'GeeksforGeeks', 'GFG']

# output : list of combinations.
for i in range(len(m)):
  print(list(combinations(m, i+1)))

Output:

[('GFG',), ('GeeksforGeeks',), ('GFG',)]
[('GFG', 'GeeksforGeeks'), ('GFG', 'GFG'), ('GeeksforGeeks', 'GFG')]
[('GFG', 'GeeksforGeeks', 'GFG')]

2. Using itertools.combinations_with_replacement():

Syntax: itertools.combination_with_replacement(iterable, r) 

 Where r is the length of output tuples.

This function works same as itertools.combinations(). But this function returns r length subsequences including individual elements repeated more than once. There are also some points to note:

• The combination tuples are emitted in lexicographic order. So, if the input iterable is in sorted order the combined output will also be produced in sorted order.
• Elements are treated as unique based on their positions not on their values. So, if the input elements consist of duplicate values there will be duplicate values in the output.
• The number of items returned is (n+r-1)! / r! / (n-1)! when n > 0.

Combinations with replacement.

Below is the implementation:

Python3

# code
from itertools import combinations_with_replacement

# m = list of objects.
# same method can be applied
# for list of integers.
m = ['GFG', 'GeeksforGeeks', 'Geeks']

# output : list of combinations.
for i in range(len(m)):
  print(list(combinations_with_replacement(m, i+1)))

Output:

[(‘GFG’,), (‘GeeksforGeeks’,), (‘Geeks’,)]
[(‘GFG’, ‘GFG’), (‘GFG’, ‘GeeksforGeeks’), (‘GFG’, ‘Geeks’), (‘GeeksforGeeks’, ‘GeeksforGeeks’), (‘GeeksforGeeks’, ‘Geeks’), (‘Geeks’, ‘Geeks’)]
[(‘GFG’, ‘GFG’, ‘GFG’), (‘GFG’, ‘GFG’, ‘GeeksforGeeks’), (‘GFG’, ‘GFG’, ‘Geeks’), (‘GFG’, ‘GeeksforGeeks’, ‘GeeksforGeeks’), (‘GFG’, ‘GeeksforGeeks’, ‘Geeks’), (‘GFG’, ‘Geeks’, ‘Geeks’), (‘GeeksforGeeks’, ‘GeeksforGeeks’, ‘GeeksforGeeks’), (‘GeeksforGeeks’, ‘GeeksforGeeks’, ‘Geeks’), (‘GeeksforGeeks’, ‘Geeks’, ‘Geeks’), (‘Geeks’, ‘Geeks’, ‘Geeks’)]