1863. Sum of All Subset XOR Totals

1863. Sum of All Subset XOR Totals

Easy

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: 28
• 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:

class Solution {

    /**
     * @param Integer[] $nums
     * @return Integer
     */
    function subsetXORSum($nums) {
        return array_reduce($nums, function($carry, $item) {
            return $carry | $item;
        }) << (count($nums) - 1);
    }
}

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