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You are given an array of integers and need to find two numbers whose XOR is the maximum possible. Which approach guarantees an optimal solution for this problem?

easy🔍 Pattern Recognition Q11 of Q15

Bit Manipulation - Maximum XOR of Two Numbers

You are given an array of integers and need to find two numbers whose XOR is the maximum possible. Which approach guarantees an optimal solution for this problem?

ABuild a binary trie of all numbers and traverse it to find the maximum XOR pair.

BUse a dynamic programming approach to build XOR values incrementally.

CUse a greedy approach by iteratively guessing the maximum XOR bit from the most significant bit down.

DUse brute force nested loops to check XOR of every pair and track the maximum.

Step-by-Step Solution

Solution:

Step 1: Understand problem constraints
We want to find two numbers maximizing XOR, which requires bitwise comparisons across all numbers.
Step 2: Evaluate approaches
Brute force works but is O(n²), greedy bit-by-bit can fail on some inputs due to incomplete prefix checks, while trie-based stores bits for all numbers and efficiently finds complementary bits to maximize XOR.
Final Answer:
Option A -> Option A
Quick Check:
Trie-based approach is optimal and guaranteed to find max XOR [OK]

Quick Trick: Trie stores bits for efficient max XOR search [OK]

Common Mistakes:

MISTAKES

Believing greedy bit-by-bit always works
Thinking DP applies here
Assuming brute force is optimal

Trap Explanation:

PITFALL

Greedy bit-by-bit looks correct but can miss pairs due to incomplete prefix sets.

Interviewer Note:

CONTEXT

Tests if candidate can identify the best algorithm beyond brute force or greedy heuristics.

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