Given an array of integers, nums, compute and return the sum of XOR totals for all its possible subsets.
A subset is any combination of elements from the original array, nums. This includes the empty subset (containing no elements) and the subset that includes all array elements.
The XOR total of a subset results from applying the XOR operation to all the elements in that subset.
Note: If the
numsarray has duplicate elements, then subsets that contain the same elements but with different indexes are treated as separate. Each subset’s XOR total is counted in the final sum.
Constraints:
nums.length
nums[i]
A naive approach to solving the problem would involve generating all possible subsets, calculating the XOR for each, and summing the results. However, with up to
To overcome this inefficiency, we use bitwise operations to determine how each number in the array contributes to the XOR total without generating all subsets. We can achieve this by using the properties of subset generation, binary numbers, and bitwise manipulation. The solution can be divided into two main parts:
Given an array of integers, nums, compute and return the sum of XOR totals for all its possible subsets.
A subset is any combination of elements from the original array, nums. This includes the empty subset (containing no elements) and the subset that includes all array elements.
The XOR total of a subset results from applying the XOR operation to all the elements in that subset.
Note: If the
numsarray has duplicate elements, then subsets that contain the same elements but with different indexes are treated as separate. Each subset’s XOR total is counted in the final sum.
Constraints:
nums.length
nums[i]
A naive approach to solving the problem would involve generating all possible subsets, calculating the XOR for each, and summing the results. However, with up to
To overcome this inefficiency, we use bitwise operations to determine how each number in the array contributes to the XOR total without generating all subsets. We can achieve this by using the properties of subset generation, binary numbers, and bitwise manipulation. The solution can be divided into two main parts: