<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>

from collections import defaultdict
class Solution:
    def findAllConcatenatedWordsInADict(self, words: List[str]) -> List[str]:

        potentials =  defaultdict(lambda : list())

        @cache
        def cat_finder(w, count): 
            if w == '': 
                return True

            for prefix in potentials[w[0]]: 
                if prefix == w[:len(prefix)]: 
                    suffix = w[len(prefix):]
                    # print(prefix, suffix)
                    
                    
                    # if count == 0:
                    #     if len(suffix) == 0: 
                    #         return false
                    #     else:
                            
                    #         return cat_finder(suffix, count + 1)
                    # else:

                    if count == 0 and len(suffix) != 0:
                        if cat_finder(suffix, count + 1): 
                            return True
                    if cat_finder(suffix, count + 1) and count != 0: 
                        return True
                    # return cat_finder(suffix)
            else: 
                return False
        words =sorted(words, key=lambda x: len(x))
        # print(words)
        potentials[words[0][0]].append(words[0])
        # potentials = [words[0]]
        words = words[1:]

        returned_values = []
        for w in words: 
            if cat_finder(w, 0): 
                returned_values.append(w)
            # potentials.append(w)
            potentials[w[0]].append(w)

        return returned_values

        
        

        
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