What is the optimal time complexity of solving Minimum 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 Minimum 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 Minimum 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 Minimum 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 ProgrammingEasy

Minimum XOR Pair

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

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Problem Statement

Easy

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

Constraints

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

Examples

Example 1

Input

min_xor_pair([9, 5, 3])

Output

Explanation

9^5 = 12, 9^3 = 10, 5^3 = 6. The minimum is 6.

Example 2

Input

min_xor_pair([1, 2, 3, 4])

Output

Explanation

2^3 = 1, which is the minimum XOR sum.

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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