I knew memoized backtracking was the move but fumbled the explanation for a minute.
Use recursion with memoization to explore all possible segmentations of the string, checking at each position whether a prefix exists in the dictionary. For each valid prefix, recursively solve the remaining suffix and combine the results. This naturally handles word reuse and returns all valid sentences.
Pro tip: Clarify edge cases upfront (empty string, empty dictionary, no valid segmentation) and discuss how memoization avoids exponential recomputation. Also mention that the order of sentences depends on the order of dictionary checks, which may matter for testing.
Confirm that words can be reused, that the dictionary is a set for O(1) lookups, and that the output should be all possible sentences. Ask about empty inputs, case sensitivity, and whether spaces should be inserted between every word.
Design a function that takes a starting index and returns all valid sentences for the substring from that index. At each step, try every possible end index, check if the substring is in the dictionary, and if so, recurse on the remainder.
Use a memo dictionary mapping start index to list of sentences to cache results for each suffix. This reduces time complexity from exponential to O(n^2 * k) where k is average sentence length, by reusing overlapping subproblems.
When the start index reaches the end of the string, return a list containing an empty string to represent a valid complete sentence. For each valid word, prepend it to each sentence from the recursive call, separated by a space.
Discuss time and space complexity, noting that output size can be exponential in worst case. Walk through a small example to verify correctness and consider optimizations like pruning if dictionary is large.
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