<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 {
public:
    bool isEnd = false;
    Node *next[26] = {nullptr};
};

class Trie {
public:
    Node *head;

    Trie() {
        head = new Node();
    }

    void insert(string word) {
        Node *tmp = head;
        for (auto c: word) {
            c -= 'a';
            if (tmp->next[c]) {
                tmp = tmp->next[c];
            } else {
                tmp->next[c] = new Node();
                tmp = tmp->next[c];
            }
        }
        tmp->isEnd = true;
    }

    bool search(string word) {
        Node *tmp = head;
        for (auto c: word) {
            c -= 'a';
            if (tmp->next[c]) {
                tmp = tmp->next[c];
            } else {
                return false;
            }
        }
        return tmp->isEnd;
    }
};

class Solution {
public:
    Trie trie;
    int isConcatenated(int index, string word, int pieces, vector<int>& dp) {
        if (index == word.size()) return pieces >= 2;
        else if (dp[index] != -1) return dp[index];

        string curr = "";
        dp[index] = 0;
        for (int i=index; i<word.size(); i++) {
            curr += word[i];
            if (trie.search(curr)) {
                dp[index] |= isConcatenated(i+1, word, pieces + 1, dp);
            }
        }
        return dp[index];
    }
    vector<string> findAllConcatenatedWordsInADict(vector<string>& words) {
        for (auto word: words) {
            trie.insert(word);
        }

        vector<string> ans;
        for (auto word: words) {
            vector<int> dp(word.size(), -1);
            if (isConcatenated(0, word, 0, dp)) {
                ans.push_back(word);
            }
        }
        return ans;
    }
};
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