I started with the obvious: just iterate through all 26 letters for each of the 5 positions, call check() each time, done.
Start by describing a brute-force approach that systematically checks each position with all 26 letters, then optimize by leveraging letter and position frequency data from a dictionary to prioritize likely candidates. Emphasize the trade-offs between worst-case guarantees and average-case efficiency, and discuss how to adapt the strategy based on feedback.
Pro tip: Demonstrate awareness of real-world constraints: the checker function may be expensive, so minimizing calls is crucial. Also, mention that the dictionary may not contain the target word, so the algorithm should gracefully handle that case.
Ask clarifying questions: Is the dictionary known? Can we preprocess it? How many queries can we make? What is the cost of each query? This ensures you understand the problem scope.
Propose a simple algorithm: for each position (1 to 5), try all 26 letters until a match is found. This guarantees finding the word in at most 5*26 = 130 queries, but is inefficient.
Preprocess the dictionary to compute letter frequencies per position. Then, for each position, query letters in descending order of frequency. This reduces the expected number of queries significantly.
Consider using a decision tree or information gain to choose queries that maximize expected information. Discuss trade-offs: precomputation time vs. query efficiency, and handling words not in the dictionary.
Analyze worst-case and average-case query counts. Discuss edge cases: repeated letters, words with rare letters, and the possibility that the word is not in the dictionary.
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