動機

複習subset的backtrack

Problem

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.- [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: 28Explanation: 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: 480Explanation: The sum of all XOR totals for every subset is 480.

 

Constraints:

  • 1 <= nums.length <= 12
  • 1 <= nums[i] <= 20

Sol

class Solution:
    def subsetXORSum(self, nums: List[int], acc=0) -> int:
        if not nums:
            return acc
        else:
            return self.subsetXORSum(nums[1:],acc)+self.subsetXORSum(nums[1:],acc^nums[0])