main.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 {
	subsetXOR := func(mask int) int {
		xor := 0
		for i, num := range nums {
			if mask&(1<<i) != 0 {
				xor ^= num
			}
		}
		return xor
	}

	n := len(nums)
	m := 1 << n

	sum := 0
	for mask := range m {
		sum += subsetXOR(mask)
	}

	return sum
}

// Use gray code
func subsetXORSum2(nums []int) int {
	n := len(nums)
	m := uint32(1 << n)

	sum := 0
	xor := 0
	for i := uint32(1); i < m; i++ {
		bit := bits.TrailingZeros32(i) // flip bit of gray code
		xor ^= nums[bit]
		sum += xor
	}

	return sum
}