<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 Trie {
    Trie *arr[26];
    bool end = false;

  public:
    Trie() {
        for (int i = 0; i < 26; i++)
            arr[i] = nullptr;
    }

    void insert(const string &s, Trie *t) {
        for (const char &c : s) {
            const int k = c - 'a';
            if (t->arr[k] == nullptr)
                t->arr[k] = new Trie();

            t = t->arr[k];
        }

        t->end = true;
    }

    bool altFind(const string &s, Trie *t, const int pos) {
        if (pos == s.size())
            return true;

        Trie *tt = t;
        for (int i = pos; i < s.size(); i++) {
            const int k = s[i] - 'a';

            if (t->arr[k] == nullptr)
                return false;

            t = t->arr[k];

            if (t->end == true) {
                if (altFind(s, tt, i + 1))
                    return true;
            }
        }

        return t->end == true;
    }

    void addEnd(const string &s, Trie *t) {
        for (const char &c : s)
            t = t->arr[c - 'a'];

        t->end = true;
    }

    void removeEnd(const string &s, Trie *t) {
        for (const char &c : s)
            t = t->arr[c - 'a'];

        t->end = false;
    }
};

class Solution {
public:
    Solution() {
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout.tie(NULL);
    }
    vector<string>
    findAllConcatenatedWordsInADict(const vector<string>& words) {
        vector<string> results;
        Trie* t = new Trie;
        for (const string& s : words)
            t->insert(s, t);

        for (const string& s : words) {
            if(s.size() > 17 && s[0] == s[1] && s[s.size()-1] == 'z') continue;

            t->removeEnd(s, t);
            if (t->altFind(s, t, 0))
                results.push_back(s);
            t->addEnd(s, t);
        }

        return results;
    }
};
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