#### All possible permutations of a set of distinct integers

This problem is about finding all possible permutations of a set of distinct integers. For example, if the input is [1, 2, 3], then the output should be [[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]].

#### Problem

```Given a set of distinct integers, return all possible permutations.
Example input:
[1, 2, 3]
Example output:
[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]```

#### Solution

This solution is in Python. Our A.I. can create solutions in multiple languages.
```# Solution:
# The solution is to use a recursive function that takes in a list of integers and returns a list of lists of integers.
# The function will take the first integer in the list and add it to the beginning of each list in the list of lists returned by the recursive function.
# The recursive function will be called on the list of integers without the first integer.
# The base case is when the list of integers is empty. In this case, the function returns a list containing an empty list.
# The solution is optimal because it is O(n!) time complexity and O(n!) space complexity.

def permute(nums):
if len(nums) == 0:
return [[]]
else:
first = nums
rest = permute(nums[1:])
result = []
for l in rest:
for i in range(len(l) + 1):
result.append(l[:i] + [first] + l[i:])
return result

print(permute([1, 2, 3]))```

A.I. Evaluation of the Solution

The candidate's solution is complete and solves the problem. The approach is recursive and uses a backtracking algorithm. The time and space complexity of the solution is O(n!).

Evaluated at: 2022-11-24 14:16:07