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Permutation and Combination in Python
• Difficulty Level : Easy
• Last Updated : 19 Nov, 2020

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 permutation in a list form.
 `# 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.

 `# 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 generate nCr * r! permutations if length of input sequence is n and input parameter is r.

Combination

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

```(2, 1)
(2, 3)
(1, 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.
 `# 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:

```(1, 1)
(1, 3)
(1, 3)
```
3. If we want to make combination of same element to same element then we use combinations_with_replacement.
 `# 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) ```