1863.go

// Source: https://leetcode.com/problems/sum-of-all-subset-xor-totals
// Title: Sum of All Subset XOR Totals
// Difficulty: Easy
// Author: Mu Yang <http://muyang.pro>

////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// 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
//
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

package main

import (
	"math/bits"
)

// Use bit code
func subsetXORSum(nums []int) int {
	n := len(nums)
	m := 1 << n
	sum := 0
	for mask := 0; mask < m; mask++ {
		sum += _subsetXOR(nums, mask)
	}
	return sum
}

func _subsetXOR(nums []int, mask int) int {
	res := 0
	for i, num := range nums {
		if mask&(1<<i) != 0 {
			res ^= num
		}
	}
	return res
}

// Use gray code
func subsetXORSum2(nums []int) int {
	n := len(nums)
	m := uint(1 << n)

	sum := 0
	xor := 0
	for i := uint(1); i < m; i++ {
		bit := bits.TrailingZeros(i) // flip bit of gray code
		xor ^= nums[bit]
		sum += xor
	}
	return sum
}