# Permutations between 2 lists

## Question:

From 2 list i would like to know an optimal way in Python to do a sort of "indexed permutation".

This is how this would look like :

input :

```
list2 = [3,4,5]
list1 = [0,1,2]
```

output

```
[[0,1,2], [0,1,5], [0,4,2], [3,1,2],
[3,4,5], [3,4,2], [3,1,5], [0,4,5],
]
```

So each element of the lists remains in the same index.

## Answers:

You basically want two variables: `list_to_pick`

, which can vary in `range(number_of_lists)`

, and `index_to_swap`

which can vary in the `range(-1, len(list1))`

. Then, you want the *product* of these two ranges to decide which list to pick, and which item to swap. When `index_to_swap`

is `-1`

, we won’t swap any items

```
import itertools
source = [list1, list2]
result = []
for list_to_pick, index_to_swap in itertools.product(range(len(source)), range(-1, len(source[0])):
# Make a copy so we don't mess up the original list
selected_list = source[list_to_pick].copy()
# There are only two lists, so the other list is at index abs(list_to_pick - 1)
other_list = source[abs(list_to_pick - 1)]
# We swap only if index_to_swap >= 0
if index_to_swap >= 0:
selected_list[index_to_swap] = other_list[index_to_swap]
result.append(selected_list)
```

Which gives:

```
[[0, 1, 2],
[3, 1, 2],
[0, 4, 2],
[0, 1, 5],
[3, 4, 5],
[0, 4, 5],
[3, 1, 5],
[3, 4, 2]]
```

The order is not the same as your required list, but all the "permutations" are there. If you want the same order as in your question, you will have to define the second argument to `itertools.product`

as:

```
swap_indices = [-1] + list(range(len(source[0])-1, -2, -1))
```