Which modification to the optimal bitmask + trie approach correctly handles this variant?
hard🎤 Interviewer Follow-up Q15 of Q15
Subsets & Combinations - Number of Valid Words for Each Puzzle
Suppose the problem is modified so that puzzles can have repeated letters and words can be counted multiple times if they match multiple subsets of the puzzle letters. Which modification to the optimal bitmask + trie approach correctly handles this variant?
APreprocess puzzles to remove duplicates and apply the original algorithm unchanged.
BModify dfs to not require the puzzle's first letter to be present in the word and allow counting multiple matches per word.
CEnumerate all subsets of puzzle letters including duplicates and sum counts from trie traversal without filtering first letter.
DUse a multiset trie that stores counts for repeated letters and traverse all subsets including duplicates.
Step-by-Step Solution
Step 1: Understand variant requirements
Repeated letters in puzzles and multiple counting per word require handling multisets, not just sets.
Step 2: Modify data structure and traversal
A multiset trie that stores counts for repeated letters and traverses all subsets including duplicates correctly counts all matches.
Step 3: Why other options fail
Ignoring first letter breaks mandatory condition; removing duplicates loses information; naive enumeration is inefficient.
Final Answer:
Option D -> Option D
Quick Check:
Multiset trie handles repeated letters and multiple counts correctly [OK]
Quick Trick:Multiset trie needed for repeated letters and multiple counts [OK]
Common Mistakes:
MISTAKES
Ignoring repeated letters
Removing duplicates incorrectly
Dropping first letter condition
Trap Explanation:
PITFALL
Naive subset enumeration or ignoring first letter looks plausible but breaks correctness or efficiency.
Interviewer Note:
CONTEXT
Tests candidate's ability to adapt algorithm to complex variants involving multisets and counting.
Master "Number of Valid Words for Each Puzzle" in Subsets & Combinations
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