<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 Trie:
    def __init__(self):
        self.vals = [None] * 26
        self.full_word = False

class Solution:
    def findAllConcatenatedWordsInADict(self, words: List[str]) -> List[str]:
        base_trie = Trie()
        for word in words:
            curr = base_trie
            for char in reversed(word):
                pos = ord(char) - 97
                if curr.vals[pos]:
                    curr = curr.vals[pos]
                else:
                    new_trie = Trie()
                    curr.vals[pos] = new_trie
                    curr = new_trie
            curr.full_word = True

        def check_word(word, index, trie, dp):
            if trie is None:
                return 0
            
            if trie.full_word and (index == -1 or dp[index]):
                return 1 if index == -1 else dp[index] + 1
            elif index == -1:
                return 0

            return check_word(word, index - 1, trie.vals[ord(word[index]) - 97], dp)

        
        output = []
        for word in words:
            dp = [0] * len(word)
            for i in range(len(word)):
                dp[i] = check_word(word, i, base_trie, dp)
            if dp[-1] > 1:
                output.append(word)
        return output
            
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