<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:
    int dp[31][3];
    bool fn (string& s, map<string, int>& ht, int i, int cnt) {
        if (i == s.size()) {
            if (cnt == 2) return dp[i][cnt] = true;
            return dp[i][cnt] = false;
        }
        if (dp[i][cnt] != -1) return dp[i][cnt];

        string x;
        for (int j=i ; j<s.size() ; j++) {
            x += s[j];
            if (ht[x] > 0) {
                if (cnt >= 1) {
                    if (fn (s, ht, j+1, 2)) return dp[i][cnt] = true;
                }
                else {
                    if (fn (s, ht, j+1, cnt+1)) return dp[i][cnt] = true;
                }
            }
        }

        return dp[i][cnt] = false;
    }
    vector<string> findAllConcatenatedWordsInADict(vector<string>& words) {
        map<string, int> ht;
        for (auto &it:words) {
            ht[it]++;
        }

        vector<string> ans;
        for (int i=0 ; i<words.size() ; i++) {
            memset(dp, -1, sizeof(dp));
            if (fn (words[i], ht, 0, 0)) ans.push_back(words[i]);
        }

        return ans;
    }
};
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