My first instinct was pure recursion and I coded it up fast, felt good about it.
Use recursion with memoization to explore all valid segmentations of the string, where at each step you try every prefix that is a valid word and recurse on the remainder. Collect all valid sentences by combining the chosen word with the results from the suffix. This approach efficiently handles overlapping subproblems and avoids redundant computation.
Pro tip: Emphasize that the number of valid sentences can be exponential, so it's crucial to discuss time and space complexity and consider optimizations like memoization or dynamic programming. Also, clarify whether the output should be a list of sentences or just the count, as this affects the solution.
Confirm that words can be reused, character order is preserved, and the output should be all possible valid sentences. Discuss edge cases like empty string, no valid segmentation, and very long strings.
At each index, try all possible prefixes that are in the dictionary, and recursively solve for the remaining substring. Combine the word with each valid sentence from the suffix.
Use a hash map to cache results for each starting index to avoid recomputing the same suffix multiple times. This reduces time complexity from exponential to polynomial in the number of subproblems.
Explain that the time complexity is O(n * 2^n) in the worst case without memoization, but with memoization it becomes O(n * L) where L is the number of valid sentences, which can still be exponential. Space complexity is O(n + L) for recursion stack and output storage.
Write clean code with helper functions, and walk through a small example like 'catsanddog' with dictionary ['cat','cats','and','sand','dog'] to demonstrate correctness. Mention potential follow-ups like returning the count or handling large inputs.
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