<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 {

    bool is_end;

    unordered_map<char, node*> mp;

    node(): is_end(false) {}
};

class Solution {
public:
    vector<string> findAllConcatenatedWordsInADict(vector<string>& arr) {
        
        vector<string> res;
        
        node* root = new node();

        sort( arr.begin(), arr.end(), []( const string & ls, const string & rs)->bool {
            return ls.length() < rs.length();
        });

        function<void( node*, int, string &)> insert;

        function<void( node*, int, string &, vector<bool> &)> match;

        insert = [&]( node* nodeptr, int pos, string & s)->void {

            bool & is_end = nodeptr->is_end;
            unordered_map<char,node*> & mp = nodeptr->mp;

            if(pos>=s.length()) {
                is_end = true;
                return;
            } else {
                if(mp.find(s[pos])==mp.end()) {
                    mp[s[pos]] = new node();
                }
                insert( mp[s[pos]], pos+1, s);
            }
        };

        match = [&]( node* nodeptr, int pos, string & s, vector<bool> & v)->void {
            if(pos>=s.length()) {
                return;
            } else {
                unordered_map<char,node*> & mp = nodeptr->mp;
                if(mp.find(s[pos])==mp.end()) {
                    return;
                }
                nodeptr = mp[s[pos]];
                bool & is_end = nodeptr->is_end;
                if(is_end) {
                    v[pos] = true;
                }
                match( nodeptr, pos+1, s, v);
            }
        };

        for( auto & s: arr) {
            int m = s.length();
            vector<bool> v( m, false);
            for( int i=0; i<m; i++) {
                if((i==0) || (v[i-1])) {
                    match( root, i, s, v);
                }
            }
            insert( root, 0, s);
            if(v.back()) {
                res.push_back(s);
            }
        }

        return res;
    }
};
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