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What is the time complexity of the optimal bitmask + trie solution for the Number of Valid Words for Each Puzzle problem, given W words with average length L, and P puzzles?

medium🪤 Complexity Trap Q13 of Q15
Subsets & Combinations - Number of Valid Words for Each Puzzle
What is the time complexity of the optimal bitmask + trie solution for the Number of Valid Words for Each Puzzle problem, given W words with average length L, and P puzzles?
AO(W * L + P * M), where M is the average number of trie nodes traversed per puzzle
BO(W * P * L), since each word is checked against each puzzle
CO(W * 2^7 + P * 7), enumerating all subsets of puzzle letters for each puzzle
DO(W * L * 26 + P * 26), traversing trie nodes for all letters
Step-by-Step Solution

  1. Step 1: Analyze word insertion

    Each word is converted to a bitmask and inserted into trie in O(L) time, total O(W * L).

  2. Step 2: Analyze puzzle queries

    For each puzzle, dfs traverses trie nodes corresponding to subsets of puzzle letters, average M nodes, total O(P * M).

  3. Final Answer:

    Option A -> Option A

  4. Quick Check:

    Matches known optimal complexity [OK]
Quick Trick: Trie traversal depends on subsets of puzzle letters, not all words [OK]
Common Mistakes:
MISTAKES
  • Assuming brute force complexity
  • Confusing 2^7 subsets with trie traversal nodes
  • Ignoring average trie traversal cost
Trap Explanation:
PITFALL
  • Option C looks plausible due to 2^7 subsets but trie traversal is often less than full enumeration, making A correct.
Interviewer Note:
CONTEXT
  • Checks if candidate understands complexity beyond brute force and bitmask subset enumeration.
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