[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: 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

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