Solution: Sum of All Subset XOR Totals

Explore how to compute the sum of XOR totals of all possible subsets of an integer array using bitwise OR and shifting techniques. Understand the underlying concept that each bit's contribution can be scaled by considering its presence in half the subsets. This lesson helps you grasp an efficient approach to tackle subset XOR problems without generating all subsets, improving performance from exponential to linear time complexity.

We'll cover the following...

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 ...