2527

2527. Find Xor-Beauty of Array (Medium)

You are given a 0-indexed integer array nums.

The effective value of three indices i, j, and k is defined as ((nums[i] | nums[j]) & nums[k]).

The xor-beauty of the array is the XORing of the effective values of all the possible triplets of indices (i, j, k) where 0 <= i, j, k < n.

Return the xor-beauty of nums.

Note that:

• val1 | val2 is bitwise OR of val1 and val2.
• val1 & val2 is bitwise AND of val1 and val2.

 

Example 1:

Input: nums = [1,4]
Output: 5
Explanation: 
The triplets and their corresponding effective values are listed below:
- (0,0,0) with effective value ((1 | 1) & 1) = 1
- (0,0,1) with effective value ((1 | 1) & 4) = 0
- (0,1,0) with effective value ((1 | 4) & 1) = 1
- (0,1,1) with effective value ((1 | 4) & 4) = 4
- (1,0,0) with effective value ((4 | 1) & 1) = 1
- (1,0,1) with effective value ((4 | 1) & 4) = 4
- (1,1,0) with effective value ((4 | 4) & 1) = 0
- (1,1,1) with effective value ((4 | 4) & 4) = 4 
Xor-beauty of array will be bitwise XOR of all beauties = 1 ^ 0 ^ 1 ^ 4 ^ 1 ^ 4 ^ 0 ^ 4 = 5.

Example 2:

Input: nums = [15,45,20,2,34,35,5,44,32,30]
Output: 34
Explanation: The xor-beauty of the given array is 34.

 

Constraints:

• 1 <= nums.length <= 105
• 1 <= nums[i] <= 109

Companies: Amazon

Related Topics:
Array, Math, Bit Manipulation

Similar Questions:

• Decode XORed Permutation (Medium)

Solution 1.

See https://leetcode.com/problems/find-xor-beauty-of-array/solutions/3015014/why-just-xor-of-all-numbers-works/

// OJ: https://leetcode.com/problems/find-xor-beauty-of-array
// Author: github.com/lzl124631x
// Time: O(N)
// Space: O(1)
class Solution {
public:
    int xorBeauty(vector<int>& A) {
        int ans = 0;
        for (int n : A) ans ^= n;
        return ans;
    }
};