3681 - Maximum XOR of Subsequences.

Hard

You are given an integer array nums of length n where each element is a non-negative integer.

Select two subsequences of nums (they may be empty and are allowed to overlap ), each preserving the original order of elements, and let:

• X be the bitwise XOR of all elements in the first subsequence.

• Y be the bitwise XOR of all elements in the second subsequence.

Return the maximum possible value of X XOR Y.

Note: The XOR of an empty subsequence is 0.

Example 1:

Input: nums = 1,2,3

Output: 3

Explanation:

Choose subsequences:

• First subsequence [2], whose XOR is 2.

• Second subsequence [2,3], whose XOR is 1.

Then, XOR of both subsequences = 2 XOR 1 = 3.

This is the maximum XOR value achievable from any two subsequences.

Example 2:

Input: nums = 5,2

Output: 7

Explanation:

Choose subsequences:

• First subsequence [5], whose XOR is 5.

• Second subsequence [2], whose XOR is 2.

Then, XOR of both subsequences = 5 XOR 2 = 7.

This is the maximum XOR value achievable from any two subsequences.

Constraints:

• <code>2 <= nums.length <= 10⁵</code>

• <code>0 <= numsi<= 10⁹</code>