<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 {
    #define pb push_back
    int dp[35][35][4];
    bool func(int index,int last, int cnt , string temp, string& s1, map<string,int>& mp){
        if(index == s1.size()){
            if(temp.size()==0 && cnt==2) return true;
            else return false;
        }
        if( dp[index][last+2][cnt] != -1) return dp[index][last+2][cnt];
        
        bool ans1=false,ans2=false;  
        temp.pb(s1[index]); string temp2;
        ans1=func(index+1,last,cnt,temp,s1,mp);
        if( mp[temp]==1){
            int d=0;
            if( cnt<2) cnt++,d++;
            ans2=func(index+1,index,cnt,temp2,s1,mp);
            if( d != 0) cnt--;
        } 
        return dp[index][last+2][cnt]= ans1|ans2;
    }
public:
    vector<string> findAllConcatenatedWordsInADict(vector<string>& v1) {
        map<string,int> mp; vector<string> res;
        for(int i=0; i<v1.size(); i++) mp[v1[i]]=1;
        for(int i=0; i<v1.size(); i++){
            string s1=v1[i]; string temp;
            memset(dp,-1,sizeof(dp));
            if( func(0,0,0,temp,s1,mp)) res.push_back(s1);      
        }
        return res;
    }
};
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