Solution: Sum of All Subset XOR Totals

Explore how to compute the sum of XOR totals for every subset of an integer array using efficient bitwise manipulation techniques. Understand how to avoid exponential complexity by leveraging bitwise OR operations and bit shifts to calculate contributions without enumerating all subsets, improving both time and space efficiency.

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Statement
Solution
- Time complexity
- Space complexity

Statement

Given an array of integers, nums, compute and return the sum of XOR totals for all its possible subsets.

A subset is any combination of elements from the original array, nums. This includes the empty subset (containing no elements) and the subset that includes all array elements.
The XOR total of a subset results from applying the XOR operation to all the elements in that subset.

Note: If the nums array has duplicate elements, then subsets that contain the same elements but with different indexes are treated as separate. Each subset’s XOR total is counted in the final sum.

Constraints:

$1 \leq$ nums.length $\leq12$
$1 \leq$ nums[i] $\leq 20$

Solution

A naive approach to solving the problem would involve generating all possible ...