Bit Manipulation - Maximum XOR of Two Numbers
What is the overall time complexity of building a binary trie and finding the maximum XOR pair for an array of n integers where each integer fits in W bits?
What is the overall time complexity of building a binary trie and finding the maximum XOR pair for an array of n integers where each integer fits in W bits?
medium📊 Complexity Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Building the trie
Inserting each of the n numbers into the trie takes O(W) time per number, total O(n * W).Step 2: Querying maximum XOR
For each number, traversing the trie to find max XOR also takes O(W), total O(n * W).Step 3: Combine steps
Total time complexity is O(n * W) + O(n * W) = O(n * W).Final Answer:
Option C -> Option CQuick Check:
Linear in n and bit-length W [OK]
Quick Trick: Time proportional to n times bit-length W [OK]
Common Mistakes:
MISTAKES- Assuming quadratic time due to pairwise comparisons
- Confusing W with log n
- Ignoring bit-length factor in complexity
Trap Explanation:
PITFALL- Mistaking pairwise XOR as O(n^2) ignores trie optimization.
Interviewer Note:
CONTEXT- Tests understanding of algorithmic complexity for trie-based XOR.
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