<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 {
public:
   
    bool checkConcatenation(int currIndex, int lastIndex, int sz, string &s, set<string> &st, vector<vector<int>> &dp){
        if(currIndex==sz-1){
            if(lastIndex==0) return 0;
            string str=s.substr(lastIndex,currIndex-lastIndex+1);
            if(st.count(str)) return 1;
            return 0;
        }
        if(dp[currIndex][lastIndex]!=-1) return dp[currIndex][lastIndex];
        string str=s.substr(lastIndex,currIndex-lastIndex+1);
        bool check=checkConcatenation(currIndex+1,lastIndex,sz,s,st,dp);
        if(st.count(str)){
            check|=checkConcatenation(currIndex+1,currIndex+1,sz,s,st,dp);
        }
        return dp[currIndex][lastIndex]=check;
        
    }
    vector<string> findAllConcatenatedWordsInADict(vector<string>& words) {
        int n=words.size();
        set<string> st;
        for(auto &i:words){
            st.insert(i);
        }
        vector<string> concatenatedWords;
        for(int i=0;i<n;++i){
            string s=words[i];
            vector<vector<int>> dp(s.size()+1,vector<int>(s.size()+1,-1));
            if(checkConcatenation(0,0,s.size(),s,st,dp)){
                concatenatedWords.push_back(s);
            }
        }
       return concatenatedWords;
    }
};
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