# Understanding Python Permutations function with examples

Permutations means different orders by which elements can be arranged. The elements might be of a string, or a list, or any other data type. It is the rearrangement of items in different ways. Python has different methods inside a package called itertools, which can help us achieve python permutations.

For example, if we have three balls – RED BLUE YELLOW

We can make different arrangements for this ball.

• RED BLUE YELLOW
• RED YELLOW BLUE
• YELLOW RED BLUE
• YELLOW BLUE RED
• BLUE RED YELLOW
• BLUE YELLOW RED

These all are possible arrangements where the order is essential and there is no repetition, and this is known as permutation.

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## Syntax of python permutations

Python has a package called ‘itertools’ from which we can use the permutations function and apply it on different data types. The number of total permutation possible is equal to the factorial of length (number of elements). In our case, as we have 3 balls, 3! = 3*2*1 = 6.

To import permutations() – from itertools import permutations

### Parameters-

1. Iterable – Here, we have to pass the iterable of whose permutations we want. Example of iterables- list, tuple, string, etc.
2. Size- In this parameter, we have to specify the number of elements in each permutation.

## Example for Simple Python Permutation

```from itertools import permutations
a=permutations ([1,2,3],2)
for i in a:
print(i)
```
```Output-
(1, 2)
(1, 3)
(2, 1)
(2, 3)
(3, 1)
(3, 2) ```

If we do not pass any argument in the second parameter, the default value is set as the length of the iterable.

For example-

```from itertools import permutations
a=permutations([1,2,3])
for i in a:
print(i)
```
```Output-
(1, 2, 3)
(1, 3, 2)
(2, 1, 3)
(2, 3, 1)
(3, 1, 2)
(3, 2, 1) ```

You must be wondering why we are saving the result in a variable and printing the result using a ‘for’ loop. Let’s see what if we print the variable.

```from itertools import permutations
a=permutations([1,2,3])
print(a)
```
```Output-
<itertools.permutations object at 0x00000265E51F1360>  ```

We are getting this object as an output. So, we have to use a for loop to iterate through this variable and get the result.

Another way to get the output is making a list and then printing it.

```from itertools import permutations
print(list(permutations([1,2,3])))
```
```Output-
[(1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), (3, 2, 1)] ```

## Using Python Permutations function on a String

If we want to find different orders in which a string can be arranged, we can use the permutations function. Let us see how-

```string="ASHU"
a=permutations(string)
for i in list(a):
# join all the letters of the list to make a string
print("".join(i))
```
```Output-
ASHU
ASUH
AHSU
AHUS
AUSH
AUHS
SAHU
SAUH
SHAU
SHUA
SUAH
SUHA
HASU
HAUS
HSAU
HSUA
HUAS
HUSA
UASH
UAHS
USAH
USHA
UHAS
UHSA ```

If we want to order these elements in the group of two, we can do the following-

```string="ABC"
a=permutations(string,2)
for i in list(a):
# join all the letters of the list to make a string
print("".join(i))
```
```Output-
AB
AC
BA
BC
CA
CB ```

You can notice that the total number of results are equal to the factorial of the size we are giving to 2nd parameter.

## Find the order in lexicographical sorted order

If we want to find all the permutations of a string in a lexicographically sorted order means all the elements are arranged in alphabetical order and if the first element is equal then sorting them based on the next elements and so on.

```from itertools import permutations
string,n = input(“Enter string and size”).split()
print(*[''.join(i) for i in permutations(sorted(string),int(n))],sep='\n')
```
```Output
Enter the string and size BAC 2
AB
AC
BA
BC
CA
CB ```

## Using python permutations function on a list

Now, if we want to find all the possible orders in which a list can be arranged, we can use the similar approach as we did for string.

```a=permutations([1,2,3,4],2)
for i in a:
print(i)
```
```Output-
(1, 2)
(1, 3)
(1, 4)
(2, 1)
(2, 3)
(2, 4)
(3, 1)
(3, 2)
(3, 4)
(4, 1)
(4, 2)
(4, 3) ```

We can also find the number of ways in which we can reorder the list using a single line of code-

```print(len(list(permutations([1,2,3,4],4))))
```
```Output-
24 ```

## Python Permutation without built-in function for String

If we do not want to use the built-in function, we can make some function to achieve this goal.

```answer=[]
def permutation(string, i, length):
if i == length:
else:
for j in range(i, length):
string[i], string[j] = string[j], string[i]

#keep increasing i by 1 till it becomes equal to 0
permutation(string, i + 1, length)
string[i], string[j] = string[j], string[i]
permutation(list(string), 0, len(string))
string="ABC"
```
```Output-
['ABC', 'ACB', 'BAC', 'BCA', 'CBA', 'CAB'] ```

## Python Permutation without built-in function for Lists

```def permutation(list1):
# If the length of list=0 no permuataions possible
if len(list1) == 0:
return []
# If the length of list=1, return that element
if len(list1) == 1:
return [list1]
l = []
for i in range(len(list1)):
m = list1[i]
# Extract list1[i] or m from the list. remlist1 is
# remaining list
remlist1 = list1[:i] + list1[i+1:]
# Generating all permutations where m is first
# element
for p in permutation(remlist1):
l.append([m] + p)
return l
if __name__=="__main__":
print(list(permutation([1,2,3,4])))
```
```Output-
[[1, 2, 3, 4], [1, 2, 4, 3], [1, 3, 2, 4], [1, 3, 4, 2], [1, 4, 2, 3], [1, 4, 3, 2], [2, 1, 3, 4], [2, 1, 4, 3], [2, 3, 1, 4], [2, 3, 4, 1], [2, 4, 1, 3], [2, 4, 3, 1], [3, 1, 2, 4], [3, 1, 4, 2], [3, 2, 1, 4], [3, 2, 4, 1], [3, 4, 1, 2], [3, 4, 2, 1], [4, 1, 2, 3], [4, 1, 3, 2], [4, 2, 1, 3], [4, 2, 3, 1], [4, 3, 1, 2], [4, 3, 2, 1]] ``` 