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Consider the following code snippet implementing the trie-based maximum XOR finder. Given the input array [2, 8], what is the return value of findMaximumXOR([2, 8])?

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Bit Manipulation - Maximum XOR of Two Numbers

Consider the following code snippet implementing the trie-based maximum XOR finder. Given the input array [2, 8], what is the return value of findMaximumXOR([2, 8])?

A2

B8

C10

D0

Step-by-Step Solution

Solution:

Step 1: Insert numbers 2 and 8 into trie
2 in binary: 000...0010, 8 in binary: 000...1000. Trie stores bits for both numbers.
Step 2: For each number, find max XOR partner
For 2, try to find bits opposite to 2's bits in trie. At bit 3 (8's highest set bit), toggled bit exists, so max_xor |= 8. At bit 1, toggled bit exists, max_xor |= 2. Total max_xor = 10.
Final Answer:
Option C -> Option C
Quick Check:
2 XOR 8 = 10, which is maximum XOR [OK]

Quick Trick: XOR of 2 and 8 is 10, max XOR found [OK]

Common Mistakes:

MISTAKES

Confusing max_xor with input number
Off-by-one bit indexing
Returning XOR with self

Trap Explanation:

PITFALL

Candidates may forget to check toggled bit first, leading to lower XOR values.

Interviewer Note:

CONTEXT

Tests ability to trace bitwise trie traversal and XOR calculation.

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