Detect words formed by multiple dictionary parts

Given an array words of up to 100,000 non-empty lowercase strings (total characters ≤ 1,000, 000), return all strings that can be formed by concatenating at least two other strings from the same array. Component strings may be reused multiple times. Describe two approaches (hash-set with dynamic programming, and trie with DFS plus memoization), analyze time and space complexity, and explain how to avoid counting a word as itself unless it is split into smaller parts. Discuss edge cases such as very short words, repeated components, and large inputs.