Given an array of strings words (without duplicates), return all the concatenated words in the given list of words.

concatenated word is defined as a string that is comprised entirely of at least two shorter words in the given array.

Example 1:

Input: words = ["cat","cats","catsdogcats","dog","dogcatsdog","hippopotamuses","rat","ratcatdogcat"]
Output: ["catsdogcats","dogcatsdog","ratcatdogcat"]
Explanation: "catsdogcats" can be concatenated by "cats", "dog" and "cats"; 
"dogcatsdog" can be concatenated by "dog", "cats" and "dog"; 
"ratcatdogcat" can be concatenated by "rat", "cat", "dog" and "cat".

Example 2:

Input: words = ["cat","dog","catdog"]
Output: ["catdog"]


  • 1 <= words.length <= 104
  • 0 <= words[i].length <= 1000
  • words[i] consists of only lowercase English letters.
  • 0 <= sum(words[i].length) <= 105
class Solution:
    def findAllConcatenatedWordsInADict(self, words: List[str]) -> List[str]:
        words = set(words)
        memo = {}
        def dfs(word):
            if word in memo:
                return memo[word]
            memo[word] = False
            for i in range(1, len(word)):
                if word[:i] in words and (word[i:] in words or dfs(word[i:])):
                    memo[word] = True
            return memo[word]

        return [word for word in words if dfs(word)]

Time complexity: O(N \; L^2), where N is the length of the input word list and L is the length of the longest word

Space complexity : O(N + L)

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