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描述
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.
Note:
1 <= nums.length <= 12
1 <= nums[i] <= 20
解析
根据题意，就是找出所有的 nums 的子集，然后计算出每个子集的元素异或值，将所有的异或值加起来的和。这里用到的内置函数直接找所有的子集，直接进行计算。高手应该要自己求所有子集，而不是学我用内置函数这种低级水平。
解答
class Solution(object):
def subsetXORSum(self, nums):
"""
:type nums: List[int]
:rtype: int
"""
result = 0
for i in range(len(nums)+1):
for j in itertools.combinations(nums,i):
t = 0
for k in j:
t ^= k
result += t
return result
运行结果
Runtime: 56 ms, faster than 68.31% of Python online submissions for Sum of All Subset XOR Totals.
Memory Usage: 13.2 MB, less than 93.43% of Python online submissions for Sum of All Subset XOR Totals.
解析
不用内置函数找 nums 子集，直接通过前向遍历找出所有的子集，然后将不为空的子集进行异或运算，将所有子集进行异或运算之后的结果相加。
解答
class Solution(object):
def subsetXORSum(self, nums):
"""
:type nums: List[int]
:rtype: int
"""
result = 0
subsets = [[]]
for num in nums:
subsets += [subset+[num] for subset in subsets]
for subset in subsets:
if subset:
result += functools.reduce(lambda x,y:x^y,subset)
return result
运行结果
Runtime: 100 ms, faster than 39.20% of Python online submissions for Sum of All Subset XOR Totals.
Memory Usage: 14 MB, less than 12.21% of Python online submissions for Sum of All Subset XOR Totals.
原题链接：leetcode.com/problems/su…
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