My first instinct was recursion, which technically works but blows up on longer inputs.
Clarify the problem constraints (string length, dictionary size, word lengths) and edge cases, then propose a dynamic programming solution where dp[i] indicates if the first i characters can be segmented. Discuss time/space complexity and possible optimizations like using a trie or BFS, and relate it to real-world ML applications such as tokenization.
Pro tip: Mention that this problem is analogous to word segmentation in NLP tokenizers, and highlight the trade-off between DP and BFS with memoization; also note that using a trie can reduce lookup time from O(n) to O(L) where L is max word length.
Ask about input constraints (string length, dictionary size, word length limits), whether the dictionary can contain duplicates, and if the empty string is considered breakable. Confirm that words can be reused.
Define dp[i] as whether the substring s[0:i] can be segmented. Initialize dp[0] = true, then for each i from 1 to n, check all j < i where dp[j] is true and s[j:i] is in the dictionary. Return dp[n].
The naive DP is O(n^2 * L) where L is average word length due to substring hashing. Optimize by using a trie for dictionary lookups, reducing to O(n * L_max) or using BFS with memoization to avoid redundant checks.
Compare DP with BFS/DFS + memoization, and mention that BFS can find the minimum number of words if needed. Also note that if the dictionary is large, a trie or hash set is preferable.
Connect the problem to tokenization in NLP models (e.g., WordPiece, BPE) and discuss how efficient word segmentation impacts model inference speed and memory usage.
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