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"""
1863. Sum of All Subset XOR Totals
"""
"""
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
"""


from typing import List


"""
Runtime: 112 ms
Memory Usage: 14.8 MB
"""


from functools import reduce


class Solution1:
    def subsetXORSum(self, nums: List[int]) -> int:
        arr = []
        while nums:
            num = nums.pop()
            arr += [subarr + [num] for subarr in arr] + [[num]]

        result = 0
        for subarr in arr:
            if len(subarr) == 1:
                result += subarr[0]
            else:
                result += reduce(lambda x, y: x ^ y, subarr)
        return result


"""
Runtime: 116 ms, faster than 35.35% of Python3 online submissions 
Memory Usage: 14.1 MB, less than 82.82% of Python3 online submissions 
"""


from itertools import combinations, accumulate


class Solution2:
    def subsetXORSum(self, nums: List[int]) -> int:
        result = 0
        for i in range(len(nums)):
            for arr in combinations(nums, i):
                result += accumulate(arr, func=lambda x, y: x ^ y)
        return result

"""
1863. Sum of All Subset XOR Totals
"""
"""
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
"""


from typing import List


"""
Runtime: 112 ms
Memory Usage: 14.8 MB
"""


from functools import reduce


class Solution1:
    def subsetXORSum(self, nums: List[int]) -> int:
        arr = []
        while nums:
            num = nums.pop()
            arr += [subarr + [num] for subarr in arr] + [[num]]

        result = 0
        for subarr in arr:
            if len(subarr) == 1:
                result += subarr[0]
            else:
                result += reduce(lambda x, y: x ^ y, subarr)
        return result


"""
Runtime: 116 ms, faster than 35.35% of Python3 online submissions 
Memory Usage: 14.1 MB, less than 82.82% of Python3 online submissions 
"""


from itertools import combinations, accumulate


class Solution2:
    def subsetXORSum(self, nums: List[int]) -> int:
        result = 0
        for i in range(len(nums)):
            for arr in combinations(nums, i):
                result += accumulate(arr, func=lambda x, y: x ^ y)
        return result
1863. Sum of All Subset XOR Totals 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 Runtime: 112 ms Memory Usage: 14.8 MB Runtime: 116 ms, faster than 35.35% of Python3 online submissions  Memory Usage: 14.1 MB, less than 82.82% of Python3 online submissions