<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>

struct node{
    node* links[26];
    bool flag=false;

    bool contains(char ch){
        return links[ch-'a']!=NULL;
    }

    void put(char ch,node* temp){
        links[ch-'a']=temp;
    }

    node* get(char ch){
        return links[ch-'a'];
    }

    void setflag(){
        this->flag=true;
    }

    bool retflag(){
        return this->flag;
    }

};

class Trie{
    private: node* root;
    public:
    Trie(){
        root=new node();
    }

    void insert(string word){
        node* temp=root;
        for(int i=0;i<word.size();i++){
            if(!temp->contains(word[i])){
                temp->put(word[i],new node());
            }
            temp=temp->get(word[i]);
        }
        temp->setflag();
    }

    bool func(int ind,int cnt,string word,map<pair<int,int>,int>& dp){
        if(ind>=word.size()) return cnt>1;
        if(dp.find({ind,cnt})!=dp.end()) return dp[{ind,cnt}];
        node* temp=root;
        for(int i=ind;i<word.size();i++){
            if(!temp->contains(word[i])) return dp[{ind,cnt}]=false;
            temp=temp->get(word[i]);
            if(temp->retflag()){
                if(func(i+1,cnt+1,word,dp)) return dp[{ind,cnt}]=true;
            }
        }
        return dp[{ind,cnt}]=false;
    }

};

class Solution {
public:
    vector<string> findAllConcatenatedWordsInADict(vector<string>& words) {
        Trie trie;
        for(auto value: words){
            trie.insert(value);
        }
        vector<string> ans;
       
        for(auto value: words){
            map<pair<int,int>,int> dp;
            if(trie.func(0,0,value,dp)) ans.push_back(value);
        }
        return ans;
    }
};
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