Bird
Raised Fist0

Given an array of integers, which data structure is most efficient to use for finding two numbers that produce the maximum XOR?

easy💻 Programming Q1 of Q15
Bit Manipulation - Maximum XOR of Two Numbers
Given an array of integers, which data structure is most efficient to use for finding two numbers that produce the maximum XOR?
AA stack to keep track of maximum and minimum elements
BA balanced binary search tree storing the integers
CA hash map storing frequency counts of numbers
DA binary trie (prefix tree) built from the binary representation of numbers
Step-by-Step Solution
Solution:

  1. Step 1: Represent numbers in binary

    Convert each integer to its binary form to analyze bitwise differences.

  2. Step 2: Build a binary trie

    Insert each binary number into a trie where each level represents a bit position.

  3. Step 3: Find maximum XOR pair

    Traverse the trie to find the number that differs most at the highest bit positions, maximizing XOR.

  4. Final Answer:

    Option D -> Option D

  5. Quick Check:

    Trie efficiently exploits bit patterns for XOR [OK]
Quick Trick: Use a binary trie for bitwise maximum XOR [OK]
Common Mistakes:
MISTAKES
  • Using sorting or BSTs which don't optimize bitwise XOR
  • Relying on frequency counts which don't help XOR calculation
  • Using stacks which are unrelated to XOR computations
Trap Explanation:
PITFALL
  • Other data structures don't efficiently exploit bitwise properties for XOR.
Interviewer Note:
CONTEXT
  • Tests understanding of appropriate data structures for bitwise XOR problems.
Master "Maximum XOR of Two Numbers" in Bit Manipulation

3 interactive learning modes - each teaches the same concept differently

Try ItSolutionTrace

Want More Practice?

15+ quiz questions · All difficulty levels · Free

Free Signup - Practice All Questions
More Bit Manipulation Quizzes
Bitwise AND of Numbers Range - Bitwise AND of Numbers Range - Quiz 3easy Find Two Missing Numbers - Find Two Missing Numbers - Quiz 10hard Generate All Permutations Using Bitmask DP - Generate All Permutations Using Bitmask DP - Quiz 6medium Maximum Product of Word Lengths - Maximum Product of Word Lengths - Quiz 14medium Reverse Bits - Reverse Bits - Quiz 10hard Reverse Bits - Reverse Bits - Quiz 1easy Single Number III (Two Singles) - Single Number III (Two Singles) - Quiz 7medium Subsets Using Bitmask - Subsets Using Bitmask - Quiz 15hard Sum of Two Integers Without + Operator - Sum of Two Integers Without + Operator - Quiz 14medium UTF-8 Validation - UTF-8 Validation - Quiz 13medium