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Python itertools.combinations_with_replacement() Function

The Python itertools.combinations_with_replacement() function is used to generate all possible unique combinations of elements from a given iterable, allowing elements to be repeated in each combination.

This function is useful in combinatorial problems where selecting subsets with repetition is required, such as generating lottery numbers with repeated values, coin change problems, or rolling dice combinations.

Following is the syntax of the Python itertools.combinations_with_replacement() function −

itertools.combinations_with_replacement(iterable, r)

This function accepts the following parameters −

• iterable: The input iterable whose elements will be combined.
• r: The length of each combination.

This function returns an iterator that produces tuples representing all possible unique combinations, allowing repetition of elements.

Following is an example of the Python itertools.combinations_with_replacement() function. Here, we generate all unique pairs from a list of numbers, allowing repetition −

import itertools

numbers = [1, 2, 3]

result = itertools.combinations_with_replacement(numbers, 2)
for item in result:
   print(item)

Following is the output of the above code −

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

Here, we specify a combination length of 3, generating unique triplets from the given set while allowing repetition −

import itertools

letters = ['A', 'B', 'C']

result = itertools.combinations_with_replacement(letters, 3)
for item in result:
   print(item)

Output of the above code is as follows −

('A', 'A', 'A')
('A', 'A', 'B')
('A', 'A', 'C')
('A', 'B', 'B')
('A', 'B', 'C')
('A', 'C', 'C')
('B', 'B', 'B')
('B', 'B', 'C')
('B', 'C', 'C')
('C', 'C', 'C')

Now, we use itertools.combinations_with_replacement() function to generate all possible 2-letter combinations from a string while allowing repetition −

import itertools

word = "XY"

result = itertools.combinations_with_replacement(word, 2)
for item in result:
   print(''.join(item))

The result obtained is as shown below −

XX
XY
YY

When working with numerical combinations, the itertools.combinations_with_replacement() function can help generate all possible sum pairs including repeated values −

import itertools

numbers = [1, 2, 3, 4]

result = itertools.combinations_with_replacement(numbers, 2)
for pair in result:
   print(pair, "Sum:", sum(pair))

The result produced is as follows −

(1, 1) Sum: 2
(1, 2) Sum: 3
(1, 3) Sum: 4
(1, 4) Sum: 5
(2, 2) Sum: 4
(2, 3) Sum: 5
(2, 4) Sum: 6
(3, 3) Sum: 6
(3, 4) Sum: 7
(4, 4) Sum: 8

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