Minimum XOR Pair
Detailed guide and Python implementation for the 'Minimum XOR Pair' problem.
1. Concept Overview
The 'Minimum XOR Pair' problem is a key challenge in the Trie section.
This implementation focuses on easy-level logic in Python.
We prioritize technical accuracy and code readability in our provided solutions.
2. Real-World Applications
3. Visual Intuition
Visualizing the logic flow for Minimum XOR Pair.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Minimum XOR Pair carefully.
2. Formulate brute force
Draft a simple iterative solution.
3. Identify inefficiency
Look for redundant calculations.
4. Optimize search path
Use hashing or sorting to speed up the process.
5. Final Implementation
Clean up the code for production standards.
Problem Statement
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.
- •2 <= len(arr) <= 10^5
- •0 <= arr[i] <= 10^9
Examples
min_xor_pair([9, 5, 3])
6
9^5 = 12, 9^3 = 10, 5^3 = 6. The minimum is 6.
min_xor_pair([1, 2, 3, 4])
1
2^3 = 1, which is the minimum XOR sum.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
Ready to Solve?
Open the problem in PyRun's browser-based Python editor. Your code runs fully offline — no server required.
Interview Insights & Variations
Complexity Analysis Breakdown
Why Time: Directly evaluates all possibilities.
Why Space: Uses standard local memory.
Why Time: Optimized paths reduce total operations.
Why Space: May trade memory for speed.
Optimized Solution Python Code
Optimized Solution Python Code
def min_xor_pair_opt(arr):
arr.sort(); res = float('inf')
for i in range(len(arr) - 1): res = min(res, arr[i] ^ arr[i+1])
return resBrute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def min_xor_pair_brute(arr):
res = float('inf')
for i in range(len(arr)):
for j in range(i + 1, len(arr)):
res = min(res, arr[i] ^ arr[j])
return resAlgorithm Pattern Checklist
When dealing with Trie data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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