<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 Solution:
    def findAllConcatenatedWordsInADict(self, words: List[str]) -> List[str]:
        class TrieNode:
            def __init__(self):
                self.child = [None] * 26
                self.isEnd = False
        
        class Trie:
            def __init__(self):
                self.root = TrieNode()

            def insert(self,st):
                tempHead =  self.root
                p = 0
                while p < len(st):
                    chIdx = ord(st[p]) - ord('a')
                    if tempHead.child[chIdx] == None:
                        tempHead.child[chIdx] = TrieNode()
                    tempHead = tempHead.child[chIdx]
                    p+=1
                tempHead.isEnd = True
                return True
            
            def find(self,st):
                tempHead = self.root
                p = 0
                while p <= len(st) - 1:
                    chIdx = ord(st[p]) - ord('a')
                    if tempHead.child[chIdx] == None:
                        return False
                    tempHead = tempHead.child[chIdx]
                    p += 1
                return True
            
            @cache
            def recHelp(self, root, key, index, count):
                if index >= len(key):
                    return count > 1
                curr = root
                for i in range(index, len(key)):
                    p = ord(key[i]) - ord('a')
                    if not curr.child[p]:
                        return False
                    curr = curr.child[p]
                    if curr.isEnd:
                        if self.recHelp(root, key, i+1, count+1):
                            return True
                return False
                
                
            def recFind(self,st):
                return self.recHelp(self.root,st,0,0)
                

        trie = Trie()
        for word in words:
            trie.insert(word)
        
        ans = []
        for i in range(len(words)):
            if trie.recFind(words[i]):
                ans.append(words[i])
        
        return ans

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