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);
    }
}

Contact Links

If you found this series helpful, please consider giving the repository a star on GitHub or sharing the post on your favorite social networks 😍. Your support would mean a lot to me!

• LinkedIn
• GitHub