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 finding the maximum product of word lengths with no common letters?
What is the time complexity of the optimal bitmasking solution that sorts words by length and prunes pairs early when finding the maximum product of word lengths with no common letters?
medium🪤 Complexity Trap Q13 of Q15
Step-by-Step Solution
Step 1: Analyze preprocessing steps
Computing bitmasks takes O(n*k) where k is average word length. Sorting masks by length takes O(n log n).Step 2: Analyze nested loops with pruning
Nested loops run O(n^2) in worst case, but pruning reduces unnecessary checks. Bitwise AND checks are O(1).Final Answer:
Option C -> Option CQuick Check:
Combining all steps yields O(n^2 + n*k + n log n) [OK]
Quick Trick: Bitmask checks are O(1), pruning reduces pairs [OK]
Common Mistakes:
MISTAKES- Assuming O(n^2*k) due to character checks per pair
- Ignoring sorting cost
- Confusing recursion stack space with iterative solution
Trap Explanation:
PITFALL- Many think each pair requires O(k) character checks, but bitmasking reduces this to O(1), making O(n^2) dominant.
Interviewer Note:
CONTEXT- Tests understanding of bitmasking impact on complexity and pruning benefits.
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