Bit Manipulation - Maximum XOR of Two Numbers
What is the space complexity of the trie-based maximum XOR algorithm for an input array of size n, where each number fits in W bits?
What is the space complexity of the trie-based maximum XOR algorithm for an input array of size n, where each number fits in W bits?
medium🪤 Complexity Trap Q6 of Q15
Step-by-Step Solution
Solution:
Step 1: Each inserted number creates up to W nodes in the trie.
In worst case, all numbers differ in all bits, so total nodes ≈ n * W.Step 2: Thus, space complexity is O(n * W).
O(n^2) is incorrect, O(n) ignores W, O(W) ignores n.Step 3: Since W is fixed (e.g., 32 bits), O(n * W) ≈ O(n), but strictly it's O(n * W).
Final Answer:
Option A -> Option AQuick Check:
Trie size grows with n and W bits [OK]
Quick Trick: Trie stores up to n*W nodes [OK]
Common Mistakes:
MISTAKES- Ignoring bit width or recursion stack space
Trap Explanation:
PITFALL- Candidates pick O(n) ignoring bit dimension or O(n^2) confusing time with space.
Interviewer Note:
CONTEXT- Tests understanding of auxiliary space in bitwise tries.
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