How to Solve Sum of All Subset X O R Totals Problem
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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, retu...
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Problem Statement
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.
Sum of All Subset XOR Totals
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Examples
nums = [1,3]
6
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
nums = [5,1,6]
28
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
nums = [3,4,5,6,7,8]
480
The sum of all XOR totals for every subset is 480.
Constraints
1 <= nums.length <= 12
1 <= nums[i] <= 20
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