<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 func(int i, string& s, string dum, map<string, int>& m, int flag, map<pair<int, string>, int>& dp) {
        if (i == s.length()) {
            return dum.empty() && flag >= 2;
        }

        if (dp.find({i, dum}) != dp.end()) return dp[{i, dum}];
        
        dum += s[i];
        bool take = false, no = false;

        if (m[dum]) {
            take = func(i + 1, s, "", m, flag + 1, dp);
        }
        no = func(i + 1, s, dum, m, flag, dp);

        return dp[{i, dum}] = take || no;
    }

    vector<string> findAllConcatenatedWordsInADict(vector<string>& words) {
        map<string, int> m;
        int n = words.size();
        
        for (int i = 0; i < n; i++) {
            m[words[i]]++;
        }

        vector<string> ans;

        for (int i = 0; i < n; i++) {
            map<pair<int, string>, int> dp;
            if (func(0, words[i], "", m, 0, dp)) {
                ans.push_back(words[i]);
            }
        }

        return ans;
    }
};

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