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The feedback mechanism is simple enough but figuring out how to prune the candidate list efficiently after each guess is where I got stuck for a bit.
Clarify the problem constraints (e.g., number of guesses allowed, feedback type) and then propose an information-theoretic approach: each guess should maximize the expected information gain by partitioning the candidate set as evenly as possible. Use a decision tree or minimax strategy to select guesses that minimize the worst-case number of remaining candidates, and prove that the secret word can be found within the limit.
Pro tip: Mention that in practice, you can precompute an optimal decision tree for small candidate sets, but for larger sets, a greedy entropy-based heuristic often works well. Also, discuss trade-offs between optimality and computational feasibility.
Ask about the number of guesses allowed, the size of the candidate list, and whether the secret word is guaranteed to be in the list. Confirm that feedback is only the count of exact matches.
Represent the candidate set and feedback as a decision tree where each node is a guess and edges correspond to possible feedback values. The goal is to minimize the depth of the tree.
Use an information-theoretic approach: for each possible guess, compute the distribution of feedback over the remaining candidates and pick the guess that maximizes entropy (or minimizes the maximum partition size).
Prove that the strategy finds the word within the limit by bounding the number of candidates that can remain after each guess. Discuss the trade-off between optimality and computational cost.
Explain how to implement the strategy efficiently, e.g., using precomputed feedback tables or pruning. Mention that for small candidate sets, exhaustive search for the optimal decision tree is feasible.
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