sum of all subsets xor total leetcode 1863 python скачать в хорошем качестве

sum of all subsets xor total leetcode 1863 python

Download 1M+ code from https://codegive.com/1350bd5 certainly! the problem "sum of all subsets xor total" (leetcode 1863) asks us to compute the sum of the xor of all subsets of a given array. problem explanation given an integer array `nums`, we need to find the sum of the xor of all possible subsets of the array. the xor of a subset is calculated by taking the xor of all elements in that subset. key observations 1. **xor properties**: xor is commutative and associative. an element xored with itself results in 0, while xored with 0 results in the element itself. 2. **subset count**: for an array of size `n`, there are `2^n` possible subsets. 3. **element contribution**: each element in the array contributes to the xor total depending on how many subsets it is included in. if an element is included in half of the subsets, it will appear in `2^(n-1)` subsets. 4. **bit contribution**: we can compute the contribution of each bit position separately. for each bit position, we count how many numbers have that bit set and determine how many subsets will have that bit set in the xor. steps to solve 1. for each bit position (from 0 to 31, since we assume 32-bit integers), count how many numbers have that bit set. 2. for the bit position `i`, if `count` is the number of elements with the `i-th` bit set, then the number of subsets where the `i-th` bit contributes to the xor is given by `count * (2^(n-1))` because the remaining `n-1` elements can either be included or excluded independently. 3. the total contribution of the `i-th` bit to the final result is `count * (2^(n-1)) * (1 i)` because `1 i` represents the value of the `i-th` bit. python code example here’s the python code to solve the problem: explanation of the code 1. **input handling**: we take an array `nums` as input. 2. **bit loop**: we loop through each bit position from 0 to 31. 3. **count calculation**: for each bit position, we compute how many numbers have that bit set. 4. **contribution calculation**: ... #LeetCode #Python #windows subsets xor total leetcode bitwise operations combinations dynamic programming optimization algorithms Python binary representation mathematical properties complexity analysis problem-solving