#### Permutations

P
R
```def permute_recursive(nums: list[int]) -> list[list[int]]:
"""
Return all permutations.

>>> permute_recursive([1, 2, 3])
[[3, 2, 1], [2, 3, 1], [1, 3, 2], [3, 1, 2], [2, 1, 3], [1, 2, 3]]
"""
result: list[list[int]] = []
if len(nums) == 0:
return [[]]
for _ in range(len(nums)):
n = nums.pop(0)
permutations = permute_recursive(nums.copy())
for perm in permutations:
perm.append(n)
result.extend(permutations)
nums.append(n)
return result

def permute_backtrack(nums: list[int]) -> list[list[int]]:
"""
Return all permutations of the given list.

>>> permute_backtrack([1, 2, 3])
[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 2, 1], [3, 1, 2]]
"""

def backtrack(start: int) -> None:
if start == len(nums) - 1:
output.append(nums[:])
else:
for i in range(start, len(nums)):
nums[start], nums[i] = nums[i], nums[start]
backtrack(start + 1)
nums[start], nums[i] = nums[i], nums[start]  # backtrack

output: list[list[int]] = []
backtrack(0)
return output

if __name__ == "__main__":
import doctest

result = permute_backtrack([1, 2, 3])
print(result)
doctest.testmod()
```