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Permutation and Combination in Python

  • Difficulty Level : Medium
  • Last Updated : 29 May, 2021

Python provides direct methods to find permutations and combinations of a sequence. These methods are present in itertools package.

Permutation 

First import itertools package to implement the permutations method in python. This method takes a list as an input and returns an object list of tuples that contain all permutations in a list form. 
 

Python3




# A Python program to print all
# permutations using library function
from itertools import permutations
 
# Get all permutations of [1, 2, 3]
perm = permutations([1, 2, 3])
 
# Print the obtained permutations
for i in list(perm):
    print (i)

Output: 

(1, 2, 3)
(1, 3, 2)
(2, 1, 3)
(2, 3, 1)
(3, 1, 2)
(3, 2, 1)

It generates n! permutations if the length of the input sequence is n. 
If want want to get permutations of length L then implement it in this way. 
 

Python3




# A Python program to print all
# permutations of given length
from itertools import permutations
 
# Get all permutations of length 2
# and length 2
perm = permutations([1, 2, 3], 2)
 
# Print the obtained permutations
for i in list(perm):
    print (i)

Output: 



(1, 2)
(1, 3)
(2, 1)
(2, 3)
(3, 1)
(3, 2)

It generates nCr * r! permutations if the length of the input sequence is n and the input parameter is r.

Combination 

This method takes a list and an input r as an input and return an object list of tuples which contain all possible combination of length r in a list form. 
 

Python3




# A Python program to print all
# combinations of given length
from itertools import combinations
 
# Get all combinations of [1, 2, 3]
# and length 2
comb = combinations([1, 2, 3], 2)
 
# Print the obtained combinations
for i in list(comb):
    print (i)

Output: 

(1, 2)
(1, 3)
(2, 3)

 

1. Combinations are emitted in lexicographic sort order of input. So, if the input list is sorted, the combination tuples will be produced in sorted order. 
 

Python3




# A Python program to print all
# combinations of a given length
from itertools import combinations
 
# Get all combinations of [1, 2, 3]
# and length 2
comb = combinations([1, 2, 3], 2)
 
# Print the obtained combinations
for i in list(comb):
    print (i)

Output: 

(1, 2)
(1, 3)
(2, 3)

 

2. Elements are treated as unique based on their position, not on their value. So if the input elements are unique, there will be no repeat values in each combination. 
 



Python3




# A Python program to print all combinations
# of given length with unsorted input.
from itertools import combinations
 
# Get all combinations of [2, 1, 3]
# and length 2
comb = combinations([2, 1, 3], 2)
 
# Print the obtained combinations
for i in list(comb):
    print (i)

Output: 

(2, 1)
(2, 3)
(1, 3)

 

3. If we want to make a combination of the same element to the same element then we use combinations_with_replacement. 
 

Python3




# A Python program to print all combinations
# with an element-to-itself combination is
# also included
from itertools import combinations_with_replacement
 
# Get all combinations of [1, 2, 3] and length 2
comb = combinations_with_replacement([1, 2, 3], 2)
 
# Print the obtained combinations
for i in list(comb):
    print (i)

Output:

(1, 1)
(1, 2)
(1, 3)
(2, 2)
(2, 3)
(3, 3) 

 

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