# LeetCode 1863. Sum of All Subset XOR Totals

## Description

https://leetcode.com/problems/sum-of-all-subset-xor-totals/

The XOR total of an array is defined as the bitwise `XOR` of all its elements, or `0` if the array is empty.

• For example, the XOR total of the array `[2,5,6]` is `2 XOR 5 XOR 6 = 1`.

Given an array `nums`, return the sum of all XOR totals for every subset of `nums`

Note: Subsets with the same elements should be counted multiple times.

An array `a` is a subset of an array `b` if `a` can be obtained from `b` by deleting some (possibly zero) elements of `b`.

Example 1:

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

Example 2:

```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.
-  has an XOR total of 5.
-  has an XOR total of 1.
-  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
```

Example 3:

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

Constraints:

• `1 <= nums.length <= 12`
• `1 <= nums[i] <= 20`

## Explanation

Find all subsets. Then get xor total of all subsets.

## Python Solution

``````class Solution:
def subsetXORSum(self, nums: List[int]) -> int:
subsets = []

self.find_subsets(nums, 0, [], subsets)

results = 0

for subset in subsets:
if not subset:
results += 0

else:
xor_total = reduce(lambda x, y: x ^ y, subset)
results += xor_total

return results

def find_subsets(self, nums, start, combination, results):
results.append(list(combination))

for i in range(start, len(nums)):
num = nums[i]
combination.append(num)
self.find_subsets(nums, i + 1, combination, results)
combination.pop()
``````
• Time Complexity: O(N).
• Space Complexity: O(N).