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1863. Sum of All Subset XOR Totals

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Description

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

Solutions

Python3

class Solution:
    def subsetXORSum(self, nums: List[int]) -> int:
        def dfs(nums, depth, prev):
            self.res += prev
            for num in nums[depth:]:
                prev ^= num
                depth += 1
                dfs(nums, depth, prev)
                prev ^= num

        self.res = 0
        dfs(nums, 0, 0)
        return self.res

Java

class Solution {
    private int res;

    public int subsetXORSum(int[] nums) {
        dfs(nums, 0, 0);
        return res;
    }

    private void dfs(int[] nums, int depth, int prev) {
        res += prev;
        for (int i = depth; i < nums.length; ++i) {
            prev ^= nums[i];
            dfs(nums, ++depth, prev);
            prev ^= nums[i];
        }
    }
}

JavaScript

/**
 * @param {number[]} nums
 * @return {number}
 */
var subsetXORSum = function (nums) {
    let res = [];
    let prev = 0;
    dfs(nums, 0, prev, res);
    return res.reduce((a, c) => a + c, 0);
};

function dfs(nums, depth, prev, res) {
    res.push(prev);
    for (let i = depth; i < nums.length; i++) {
        prev ^= nums[i];
        depth++;
        dfs(nums, depth, prev, res);
        // bracktrack
        prev ^= nums[i];
    }
}

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