<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 TrieNode:
    def __init__(self):
        self.child = {}
        self.is_end_of_word = False

class Solution:
    def findAllConcatenatedWordsInADict(self, words: List[str]) -> List[str]:
        def insert_word(word):
            node = root
            for char in word:
                if char not in node.child:
                    node.child[char] = TrieNode()
                node = node.child[char]
            node.is_end_of_word = True
        
        def can_form(word, node, start, count):
            if start == len(word):
                return count > 1
            
            current_node = node
            for i in range(start, len(word)):
                if word[i] not in current_node.child:
                    return False
                current_node = current_node.child[word[i]]
                if current_node.is_end_of_word:
                    if can_form(word, root, i + 1, count + 1):
                        return True
            return False
        
        root = TrieNode()
        
        words.sort(key=len)
        
        concatenated_words = []
        
        for word in words:
            if not word:
                continue
            if can_form(word, root, 0, 0):
                concatenated_words.append(word)
            else:
                insert_word(word)
        
        return concatenated_words

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