I knew word break immediately, done it before.
Use dynamic programming to determine if the string can be segmented, then backtrack to reconstruct one valid decomposition. Start by defining a DP array where dp[i] indicates if the prefix of length i is segmentable, and populate it by checking all possible last words. For reconstruction, store the starting index of the last word for each reachable position, then follow the links backward to build the list.
Pro tip: After presenting the DP solution, mention that for very large inputs, you can optimize by limiting the maximum word length considered or using a trie to reduce unnecessary checks, showing awareness of practical scalability.
Restate the problem to ensure understanding, including constraints like reuse allowed and returning any valid decomposition. Ask about input size, character set, and dictionary size to guide complexity analysis.
Define dp[i] as whether the prefix of length i can be segmented. Initialize dp[0] = true, and for each i from 1 to n, check all j < i where dp[j] is true and substring(j, i) is in the dictionary.
During DP, store the starting index of the last word for each reachable i (e.g., in a parent array). After filling DP, if dp[n] is true, backtrack from n to 0 using the parent array to build the list of words.
Time complexity is O(n^2 * L) where n is string length and L is average word length for substring checks, or O(n * m) if using a trie with m as max word length. Space complexity is O(n) for DP and parent arrays, plus O(n) for the result.
Mention optimizations like using a trie for faster lookups, limiting j to max word length, or using BFS/DFS with memoization. Discuss trade-offs between time and space, and when to choose one approach over another.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.