The counting part felt approachable once I framed it as a DP over positions in the string, basically dp[i] = number of ways to decode the first i characters.
Clarify the problem constraints and edge cases, then propose a dynamic programming solution to count decodings and a modified DP with backtracking to find the lexicographically smallest strings. Discuss trade-offs between time and space, and how to handle the modulo and the top-10 limit.
Pro tip: Mention that you would use a trie or hash map for the custom Morse code mapping to allow efficient prefix checks, and emphasize the importance of modular arithmetic to avoid overflow.
Ask about input size, character set, and whether the mapping is fixed or can have variable-length codes. Discuss edge cases like empty string, no valid decodings, and codes that are prefixes of others.
Define dp[i] as the number of ways to decode the prefix of length i. Transition by checking all possible code lengths ending at i, using the mapping. Apply modulo at each step.
Use DP to store the lexicographically smallest up to 10 strings for each prefix, or use backtracking with memoization to generate them in order. Ensure lexicographic order by sorting characters or codes appropriately.
Analyze time complexity O(n * L) where L is max code length, and space O(n * 10 * avg_length). Suggest optimizations like rolling arrays or pruning if needed.
Walk through a small example to verify correctness. Discuss trade-offs between storing all strings vs. generating on the fly, and how to handle large outputs.
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