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.
• [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

class Solution:
    def subsetXORSum(self, nums: List[int]) -> int:
        bits = 0
        for a in nums:
            bits |= a
        return bits * int(pow(2, len(nums)-1))

Explanation:

-total number of subsets of an array is 2**(len(nums)-1). -so we took xor of all element using for loop and |=. -then we multiplied xor of all elements with total number of subsets. *Runtime: 32 ms, faster than 100.00% of Python3 online submissions for Sum of All Subset XOR Totals. *Memory Usage: 14.1 MB, less than 100.00% of Python3 online submissions for Sum of All Subset XOR Totals.