<p>Given an array of strings <code>words</code> (<strong>without duplicates</strong>), return <em>all the <strong>concatenated words</strong> in the given list of</em> <code>words</code>.</p>

<p>A <strong>concatenated word</strong> is defined as a string that is comprised entirely of at least two shorter words (not necessarily distinct)&nbsp;in the given array.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> words = [&quot;cat&quot;,&quot;cats&quot;,&quot;catsdogcats&quot;,&quot;dog&quot;,&quot;dogcatsdog&quot;,&quot;hippopotamuses&quot;,&quot;rat&quot;,&quot;ratcatdogcat&quot;]
<strong>Output:</strong> [&quot;catsdogcats&quot;,&quot;dogcatsdog&quot;,&quot;ratcatdogcat&quot;]
<strong>Explanation:</strong> &quot;catsdogcats&quot; can be concatenated by &quot;cats&quot;, &quot;dog&quot; and &quot;cats&quot;; 
&quot;dogcatsdog&quot; can be concatenated by &quot;dog&quot;, &quot;cats&quot; and &quot;dog&quot;; 
&quot;ratcatdogcat&quot; can be concatenated by &quot;rat&quot;, &quot;cat&quot;, &quot;dog&quot; and &quot;cat&quot;.</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> words = [&quot;cat&quot;,&quot;dog&quot;,&quot;catdog&quot;]
<strong>Output:</strong> [&quot;catdog&quot;]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= words.length &lt;= 10<sup>4</sup></code></li>
	<li><code>1 &lt;= words[i].length &lt;= 30</code></li>
	<li><code>words[i]</code> consists of only lowercase English letters.</li>
	<li>All the strings of <code>words</code> are <strong>unique</strong>.</li>
	<li><code>1 &lt;= sum(words[i].length) &lt;= 10<sup>5</sup></code></li>
</ul>

class Node(object):
    def __init__(self):
        self.isWord = False
        self.children = {}
        
class Trie(object):

    def __init__(self):
        self.root = Node()
        
    def insert(self, word):
        """
        :type word: str
        :rtype: None
        """
        curr = self.root
        for c in word:
            if c not in curr.children:
                curr.children[c] = Node()
            curr = curr.children[c]
        curr.isWord = True
        
    def search(self, word, include, exclude):
        """
        :type word: str
        :rtype: bool
        """
        curr = self.root
        for i in range(include, exclude):
            c = word[i]
            if c not in curr.children:
                return False
            curr = curr.children[c]
        return curr.isWord
        
    def dfs(self, word, index, visited):
        """
        :type prefix: str
        :rtype: bool
        """
        if index == len(word):
            return True
        if index in visited:
            return False
        visited.add(index)
        for i in reversed(range(index + 1, len(word) + 1 - (index == 0))):
            if self.search(word, index, i) and self.dfs(word, i, visited):
                return True
        return False
    
class Solution:
    def findAllConcatenatedWordsInADict(self, words: List[str]) -> List[str]:
        words = set(words)
        trie = Trie()
        result = []
        for word in words:
            trie.insert(word)
        for word in words:
            visited = set()
            if trie.dfs(word, 0, visited):
                result.append(word)
        return result
   
        
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