The example input was patterns ('1*0', 5) and ('*10', 10) with input '110', expected output 10.
Clarify requirements first: pattern semantics (e.g., '.' matches exactly one bit, '*' matches any sequence including empty), precedence when multiple patterns match, and expected scale. Then design a solution that balances simplicity and efficiency, such as a trie with wildcard handling or dynamic programming, and discuss trade-offs.
Pro tip: Proactively discuss how to handle overlapping patterns and define deterministic precedence (e.g., longest match or pattern order) to avoid ambiguity, and mention that '*' can be optimized by precomputing transitions or using memoization to avoid exponential blowup.
Ask about pattern semantics, input size, number of patterns, and expected performance. Confirm how conflicts are resolved (e.g., first match, longest match, or priority).
Decide between a trie-based approach for efficiency or dynamic programming for simplicity. Consider that '*' introduces non-determinism, so a trie may need to branch or use backtracking.
If using a trie, each node represents a bit (0 or 1) and may have special edges for '.' and '*'. For DP, define a state (pattern index, input index) and transitions.
Write pseudocode for the matching algorithm, handling '.' as a single-bit wildcard and '*' as a multi-bit wildcard. Ensure correct handling of empty matches and backtracking.
Discuss time and space complexity. For DP, it's O(P * N) where P is pattern length and N is input length. For trie, it can be O(N * branching factor) but may degrade with many '*'. Suggest optimizations like memoization or precomputation.
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