Sum of All Subset XOR Totals Python Solution

lcpy gen -n 1863   # by problem number
lcpy gen -s sum_of_all_subset_xor_totals   # by problem name

Input: nums = [1,3]
Output: 6
Explanation: The 4 subsets of [1,3] are:
- The empty subset has an XOR total of 0.
- [1] has an XOR total of 1.
- [3] has an XOR total of 3.
- [1,3] has an XOR total of 1 XOR 3 = 2.
0 + 1 + 3 + 2 = 6

Input: nums = [5,1,6]
Output: 28
Explanation: The 8 subsets of [5,1,6] are:
- The empty subset has an XOR total of 0.
- [5] has an XOR total of 5.
- [1] has an XOR total of 1.
- [6] has an XOR total of 6.
- [5,1] has an XOR total of 5 XOR 1 = 4.
- [5,6] has an XOR total of 5 XOR 6 = 3.
- [1,6] has an XOR total of 1 XOR 6 = 7.
- [5,1,6] has an XOR total of 5 XOR 1 XOR 6 = 2.
0 + 5 + 1 + 6 + 4 + 3 + 7 + 2 = 28

Input: nums = [3,4,5,6,7,8]
Output: 480
Explanation: The sum of all XOR totals for every subset is 480.

class Solution:
    # Time: O(n * 2^n)
    # Space: O(n)
    def subset_xor_sum(self, nums: list[int]) -> int:
        def backtrack(index: int, current_xor: int) -> int:
            if index == len(nums):
                return current_xor

            include = backtrack(index + 1, current_xor ^ nums[index])
            exclude = backtrack(index + 1, current_xor)

            return include + exclude

        return backtrack(0, 0)