<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 Trie:
            def __init__(self):
                self.arr = [None] * 26
                self.isWord = False
            def add(self, word, i):
                if i >= len(word):
                    return
                idx = ord(word[i]) - ord('a')
                if self.arr[idx] == None:
                    self.arr[idx] = Trie()
                if i == len(word)-1:
                    self.arr[idx].isWord = True
                self.arr[idx].add(word,i+1)
        
        root = Trie()
        
        for word in words:
            if not word:
                continue
            root.add(word,0)
        
        dp = {}
        def isValid(word, index, node, wordCount):
            if index == len(word):
                return wordCount>1
            if (index,wordCount) in dp:
                return dp[(index,wordCount)]
            curr = node
            for i in range(index, len(word)):
                idx = ord(word[i])-ord('a')
                if curr.arr[idx] == None:
                    dp[(index,wordCount)] = False
                    return False
                curr = curr.arr[idx]
                if curr.isWord:
                    if isValid(word, i+1, root, wordCount+1):
                        dp[(index,wordCount)] = True
                        return True
            dp[(index,wordCount)] = False
            return False
        
        res = []
        for word in words:
            dp.clear()
            if isValid(word, 0, root, 0):
                res.append(word)
        return res
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