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Solution: Sum of All Subset XOR Totals

Explore how to efficiently calculate the sum of XOR totals from all possible subsets of an integer array by using bitwise OR and left-shift operations. Understand the role of XOR in subset calculations without enumerating all subsets and learn a method with linear time complexity and constant space usage.

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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 ...