<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 {
private:
    struct TrieNode {
        TrieNode* children[26];
        bool isEnd;
        TrieNode() : isEnd(false) {
            for (int i = 0; i < 26; i++) {
                children[i] = nullptr;
            }
        }
    };

    TrieNode* root;

    void insert(const string& word) {
        TrieNode* node = root;
        for (char c : word) {
            int index = c - 'a';
            if (!node->children[index]) {
                node->children[index] = new TrieNode();
            }
            node = node->children[index];
        }
        node->isEnd = true;
    }

    bool isConcatenated(const string& word, int start, int count) {
        if (start == word.length() && count > 1) return true;
        
        TrieNode* node = root;
        for (int i = start; i < word.length(); i++) {
            int index = word[i] - 'a';
            if (!node->children[index]) return false;
            node = node->children[index];
            if (node->isEnd) {
                if (isConcatenated(word, i + 1, count + 1)) return true;
            }
        }
        return false;
    }

public:
    vector<string> findAllConcatenatedWordsInADict(vector<string>& words) {
        root = new TrieNode();
        vector<string> result;

        // Sort words by length
        sort(words.begin(), words.end(), [](const string& a, const string& b) {
            return a.length() < b.length();
        });

        for (const string& word : words) {
            if (word.empty()) continue;
            if (isConcatenated(word, 0, 0)) {
                result.push_back(word);
            } else {
                insert(word);
            }
        }

        return result;
    }
};
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