Bit Manipulation - Maximum Product of Word Lengths
What is the time complexity of the optimal bitmasking solution that sorts words by length and prunes pairs early when their product cannot exceed the current maximum?
What is the time complexity of the optimal bitmasking solution that sorts words by length and prunes pairs early when their product cannot exceed the current maximum?
medium🪤 Complexity Trap Q5 of Q15
Step-by-Step Solution
Solution:
Step 1: Analyze components
Computing bitmasks takes O(n*k), sorting takes O(n log n), nested loops for pairs take O(n^2).Step 2: Combine and prune
Early pruning reduces unnecessary checks but worst case remains O(n^2), so total is O(n^2 + n*k + n log n).Final Answer:
Option D -> Option DQuick Check:
Sorting + bitmask + pair checks sum to O(n^2 + n*k + n log n) [OK]
Quick Trick: Sorting adds n log n, bitmasking adds n*k, pairs add n^2 [OK]
Common Mistakes:
MISTAKES- Confusing k with n in complexity
- Ignoring sorting cost
- Assuming cubic complexity
Trap Explanation:
PITFALL- Candidates often overestimate complexity as cubic or ignore sorting cost, missing combined terms.
Interviewer Note:
CONTEXT- Tests understanding of combined time complexity with pruning and sorting
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