I started with the naive recursive approach, enumerate all words that match the current digit prefix, recurse on the remainder.
Clarify the problem constraints and define the T9 mapping. Then present a recursive backtracking solution that builds word sequences by matching dictionary words against prefixes of the digit string, and discuss optimizations using a trie or DP with prefix pruning.
Pro tip: Mention that the DP approach can be framed as counting or listing paths in a DAG, and that memoization on the digit index avoids redundant work, especially when the dictionary contains many words sharing prefixes.
Ask about input size, dictionary size, whether words can be reused, and if the output should be all combinations or just count. Confirm the T9 mapping (e.g., 2=ABC, 3=DEF, etc.).
Convert each dictionary word to its T9 digit sequence and store in a hash map or trie for fast lookup. This allows O(1) or O(prefix length) checks during recursion.
At each digit index, try all dictionary words whose T9 encoding matches a prefix of the remaining digits. If a match, recurse on the next index and add the word to the current path. Base case: index reaches end of digit string.
Use a trie to prune branches early: traverse the trie along the digit string, and whenever a node marks a word end, recurse. Alternatively, use DP where dp[i] = list of word sequences for digits[i:], building from the end.
Compare recursion (simple, but may recompute subproblems) vs DP (avoids recomputation, but uses extra space). Trie reduces prefix checks but adds memory. Mention time/space complexity and when each is preferable.
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