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Use backtracking to explore all possible segmentations, leveraging a trie or hash set for O(1) word lookups. Optimize with memoization to avoid redundant computations on overlapping subproblems, and discuss time/space complexity.
Pro tip: Clarify whether words can be reused (yes) and whether the output should be deduplicated; also mention that memoization can drastically reduce runtime for strings with many repeated prefixes.
Confirm that words can be reused, the dictionary is a set for O(1) lookups, and handle empty string, no valid segmentation, and duplicate words in dictionary.
Use a hash set for the dictionary for O(1) lookups, or a trie for prefix-based pruning. Use a list to collect results and a memo to cache failed or successful segmentations.
Define a function that takes the current index and builds a path. At each step, try all substrings starting at the index; if a substring is in the dictionary, recurse on the next index.
Cache results for each starting index to avoid recomputing the same suffix. If a suffix yields no valid segmentations, store an empty list to skip future exploration.
Discuss time complexity: O(2^n) worst-case without memoization, but with memoization it's O(n * L) where L is max word length. Test with examples like 'catsanddog' and edge cases.
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