# [LeetCode]#1863. Sum of All Subset XOR Totals

Environment: Python 3.8

Key technique: |, pow

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: 6Explanation: The 4 subsets of [1,3] are:- The empty subset has an XOR total of 0.-  has an XOR total of 1.-  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: 28Explanation: The 8 subsets of [5,1,6] are:- The empty subset has an XOR total of 0.-  has an XOR total of 5.-  has an XOR total of 1.-  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`

Analysis:

1. Observe example 2, we can see all sunsets are 1, 2, 3, 4, 5, 6, 7.
2. We can covert it by formula (all bits) x 2^(n-1). n is list number.

Solution:

`class Solution(object):    def subsetXORSum(self, nums):        n=len(nums)        bits=0        for i in range(n):            bits |=nums[i]        ans=bits * math.pow(2,n-1)        return int(ans)`

Submissions:

Reference:

https://leetcode.com/problems/sum-of-all-subset-xor-totals/discuss/1333272/Using-OR-operator