Python | All possible permutations of N lists

Last Updated : 04 Jan, 2019

Computing permutations is always a necessary task in many of the practical applications and a concept widely used in Mathematics to achieve solutions to many practical problems. Lets discuss certain ways in which one can perform the task of getting all the permutations of N lists.

Method #1 : Using list comprehension
List comprehension can be used to convert the naive method task into a single line, hence more compact. This method checks for each element available elements and makes pairs accordingly.

# Python3 code to demonstrate 
# to compute all possible permutations
# using list comprehension 
  
# initializing lists
list1 = [1, 3, 4]
list2 = [6, 7, 9]
list3 = [8, 10, 5]
  
# printing lists 
print ("The original lists are : " + str(list1) +
                               " " + str(list2) + 
                               " " + str(list3))
  
# using list comprehension 
# to compute all possible permutations
res = [[i, j, k] for i in list1 
                 for j in list2
                 for k in list3]
  
# printing result
print ("All possible permutations are : " +  str(res))

Output :

The original lists are : [1, 3, 4] [6, 7, 9] [8, 10, 5]
All possible permutations are : [[1, 6, 8], [1, 6, 10], [1, 6, 5], [1, 7, 8], [1, 7, 10], [1, 7, 5], [1, 9, 8], [1, 9, 10], [1, 9, 5], [3, 6, 8], [3, 6, 10], [3, 6, 5], [3, 7, 8], [3, 7, 10], [3, 7, 5], [3, 9, 8], [3, 9, 10], [3, 9, 5], [4, 6, 8], [4, 6, 10], [4, 6, 5], [4, 7, 8], [4, 7, 10], [4, 7, 5], [4, 9, 8], [4, 9, 10], [4, 9, 5]]

Method #2 : Using itertools.product()
Using product function, one can easily perform this task in more pythonic and concise manner. This is most recommended method to perform this task of computing cartesian product.

# Python3 code to demonstrate 
# to compute all possible permutations
# using itertools.product() 
import itertools
  
# initializing list of list 
all_list = [[1, 3, 4], [6, 7, 9], [8, 10, 5] ]
  
# printing lists 
print ("The original lists are : " + str(all_list))
  
# using itertools.product()  
# to compute all possible permutations
res = list(itertools.product(*all_list))
  
# printing result
print ("All possible permutations are : " +  str(res))

Output :

The original lists are : [[1, 3, 4], [6, 7, 9], [8, 10, 5]]
All possible permutations are : [(1, 6, 8), (1, 6, 10), (1, 6, 5), (1, 7, 8), (1, 7, 10), (1, 7, 5), (1, 9, 8), (1, 9, 10), (1, 9, 5), (3, 6, 8), (3, 6, 10), (3, 6, 5), (3, 7, 8), (3, 7, 10), (3, 7, 5), (3, 9, 8), (3, 9, 10), (3, 9, 5), (4, 6, 8), (4, 6, 10), (4, 6, 5), (4, 7, 8), (4, 7, 10), (4, 7, 5), (4, 9, 8), (4, 9, 10), (4, 9, 5)]

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Python | All possible permutations of N lists