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3681. Maximum XOR of Subsequences

Description

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:

  • 2 <= nums.length <= 105
  • 0 <= nums[i] <= 109

Solutions

Solution 1

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