Python | All possible permutations of N lists

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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