Which modification to the optimal bitmasking approach correctly handles this variant?
hard🎤 Interviewer Follow-up Q15 of Q15
Bit Manipulation - Maximum Product of Word Lengths
Suppose the problem changes: you want to find the maximum product of word lengths where words can be reused multiple times (i.e., pairs can be the same word twice if allowed). Which modification to the optimal bitmasking approach correctly handles this variant?
APrecompute bitmasks and lengths, then for each word, consider its square length if it has no repeated characters, else zero; finally, check pairs as before including identical indices.
BRemove the pruning condition and check all pairs including identical indices without overlap check.
CAllow i and j to be equal in the nested loops and check bitmask overlap as before.
DUse a frequency map of words and multiply lengths by frequency to find maximum product.
Step-by-Step Solution
Step 1: Understand reuse of words
Reusing the same word twice is only valid if the word has no repeated characters (so no overlap with itself).
Step 2: Modify approach
Precompute bitmasks and lengths; for each word, consider its length squared if it has unique characters (bitmask check for duplicates). Then check pairs including identical indices.
Step 3: Why other options fail
Allowing i=j without checking duplicates or removing pruning leads to incorrect or inefficient results; frequency map is irrelevant here.
Final Answer:
Option A -> Option A
Quick Check:
Considering squares for unique words and pairs covers reuse correctly [OK]
Quick Trick:Reuse allowed only if word has unique chars [OK]
Common Mistakes:
MISTAKES
Allowing reuse without checking duplicates in word
Removing pruning causing inefficiency
Using frequency maps which don't apply here
Trap Explanation:
PITFALL
Naively allowing i=j breaks correctness unless uniqueness is checked; pruning is still needed for efficiency.
Interviewer Note:
CONTEXT
Tests candidate's ability to adapt bitmasking approach to problem variants with reuse.
Master "Maximum Product of Word Lengths" in Bit Manipulation
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