Competitive ProgrammingHard

Maximum XOR Pair

Detailed guide and Python implementation for the 'Maximum XOR Pair' problem.

Problem Statement

Hard

Write a function max_xor_pair(arr) that takes an array of non-negative integers arr and returns the maximum XOR sum of any two elements in the array.

Constraints
  • 2 <= len(arr) <= 10^5
  • 0 <= arr[i] <= 10^9

Examples

Example 1
Input
max_xor_pair([3, 10, 5, 25, 2, 8])
Output
28
Explanation

The maximum XOR is obtained by pairing 5 and 25 (5^25 = 28).

Example 2
Input
max_xor_pair([8, 10, 2])
Output
10
Explanation

The maximum XOR is obtained by pairing 8 and 2 (8^2 = 10).

Need a Hint?
Consider using Trie-specific data structures like sets or heaps.
Edge Cases to Watch
  • Empty input structures
  • Single element inputs
  • Large numerical bounds

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