What is the optimal time complexity of solving Maximum XOR Pair?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Maximum XOR Pair?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Maximum XOR Pair?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Maximum XOR Pair?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Competitive ProgrammingHard

Maximum XOR Pair

Learn how to solve the 'Maximum XOR Pair' problem. This detailed resource details brute force and optimized approaches.

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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

Explanation

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

Example 2

Input

max_xor_pair([8, 10, 2])

Output

Explanation

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

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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