1863. Sum of All Subset XOR Totals

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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.
- [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

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.
- [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

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

Solution

Backtracking approach

1. By exaustive enumeration generate a subSequence

2. operate the XOR sum operation in on that subSequence

3. Add that value to the total

4. Choice: every value fater the current one to form the subSequence

5. Constraint: If no more values after the current one then return

6. Goal: With a valid subSequence calculate the XOR sum and add to the the accumulator for result