My first instinct was to track just the minimum cost per index, which is basically the standard word break DP.
First, clarify the problem and edge cases, then propose a dynamic programming solution that tracks the two smallest costs for each prefix. Explain how to compute the second-smallest cost efficiently and analyze time/space complexity, including optimizations for large inputs.
Pro tip: Mention that you can use a trie to optimize dictionary lookups and that tracking the two smallest costs avoids storing all segmentations, which is crucial for large inputs.
Restate the problem to ensure understanding, and discuss edge cases such as empty string, no valid segmentation, and exactly one valid segmentation.
Define dp[i] as the two smallest costs to segment the prefix of length i. For each i, iterate over all j < i where the substring s[j:i] is in the dictionary, and update dp[i] using dp[j].
Use a trie or a hash set for O(1) or O(L) substring lookups, and consider precomputing all valid substrings to avoid repeated checks.
Time complexity is O(n^2 * L) with naive substring checks, but can be O(n^2) with a trie. Space complexity is O(n) for dp and O(total characters) for the trie.
For large inputs, use a trie to reduce lookup time, consider memory limits, and possibly use a sliding window or BFS with pruning to avoid unnecessary computations.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.