<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:
    def __init__(self):
        self.arr = {}
        self.is_word = False

class Trie:
    def __init__(self):
        self.root = Node()

    def insert(self, word):
        cur = self.root
        for ch in word:
            if ch not in cur.arr:
                cur.arr[ch] = Node()
            cur = cur.arr[ch]
        cur.is_word = True
    
    def search(self, word):
        cur = self.root
        for ch in word:
            if ch not in cur.arr:
                return False
            cur = cur.arr[ch]
        return cur.is_word

class Solution:
    def findAllConcatenatedWordsInADict(self, words: List[str]) -> List[str]:
        # trie = Trie()
        min_length = math.inf
        # lengths = set()
        for word in words:
            min_length = min(min_length, len(word))
        #     lengths.add(len(word))
        #     trie.insert(word)
        dictionary = set(words)
        ans = []
        for word in words:
            # if len(word) < 2 * min_length: 
            #     continue
            dp = [False] * (len(word) + 1)
            dp[0] = True
            for i in range(len(word) + 1):
                for j in range(i - 1, -1, -1):
                    if dp[j] is True:
                        subword = word[j:i]
                        if subword != word and subword in dictionary:
                            dp[i] = True
            if dp[-1] is True:
                ans.append(word)
        return ans
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