Permutation and Combination in Python

In this post, you will learn how to find the permutation and combination in Python. Python has predefined methods to find the permutation and combination of the given sequence. These methods are available in the itertools package.

Python Permutation

In mathematics, a permutation is an arrangement of the numbers so that a particular set can be arranged. It is used for a list of data where the order of the data matters.

To implement the permutation in Python, first we need to import the itertools packages.

import itertools

This module provides an inbuilt method permutations() that takes a list as an input and returns an object list of tuples that contains all permutations. In the given example, we are finding the permutation of a list of three items.

from itertools import permutations  
seq = permutations([4, 2, 8])  
print(seq)  
for i in list(seq):  
   print(i)

(4, 2, 8)
(4, 8, 2)
(2, 4, 8)
(2, 8, 4)
(8, 4, 2)
(8, 2, 4)

Length of Permutation

We can find the permutation of the fixed length set where we only take a specified number of each element permutation in the given way.

# Find permutations of the given length
from itertools import permutations
 
# Get all permutations of length 2
seq = permutations([4, 2, 8], 2)
 
# Print the obtained permutations
for i in list(seq):
    print (i)

(4, 2)
(4, 8)
(2, 4)
(2, 8)
(8, 4)
(8, 2)

Python Combination

In mathematics, a combination is the number of possible arrangements in a collection of items. It is used for a group of data where the order of data doesn't matter.

The itertools module provides combinations() method to calculate the combination of given data. In the given example, we are finding the combinations of the fixed length set.

from itertools import combinations
 
# Get all combinations of  length 2
comb = combinations([11, 21, 9], 2)
 
# Print the obtained combinations
for i in list(comb):
    print (i)

(11, 21)
(11, 9)
(21, 9)

Combinations for letters in a word

If we want to find all combinations containing exactly 2 letters from the given word, then the code will be-

from itertools import combinations 
    
seq = "HAPPY"  
    
com_seq = combinations(seq, 2)  
    
for c in com_seq:  
    print(c)  

('H', 'A')
('H', 'P')
('H', 'P')
('H', 'Y')
('A', 'P')
('A', 'P')
('A', 'Y')
('P', 'P')
('P', 'Y')
('P', 'Y')

Python Combinations with replacements

If we want to make a combination of same element to same element then we use combinations_with_replacement. This method allows values to be combined with themselves. The given code snippet demonstrates how these methods work:

#Import itertools package
from itertools import combinations_with_replacement

combi = combinations_with_replacement(['e','t','p'], 2)

for c in list(combi):
   print(c)

('e', 'e')
('e', 't')
('e', 'p')
('t', 't')
('t', 'p')
('p', 'p')

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