<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:
    struct CompareLength {
        inline bool operator() (const string& l, const string& r) {
            return l.length() < r.length();
        }
    };
    vector<string> findAllConcatenatedWordsInADict(vector<string>& words) {
        int n = words.size();
        sort(words.begin(), words.end(), CompareLength());
        unordered_set<string> exists;
        vector<string> ans;
        vector<vector<bool>> dp(n, vector<bool>(30, false));
        for (int l=0;l<n;l++) {
            // cout << w << "\n";
            const string w = words[l];
            int m = w.length();
            for (int i=0;i<m;i++) {
                for (int j=i;j>=0;j--) {
                    if (exists.find(w.substr(j, i-j+1)) != exists.end()) {
                        if (j == 0) dp[l][i] = true;
                        else dp[l][i] = dp[l][i] || dp[l][j-1];
                    }
                }
            }
            if (dp[l][m-1]) ans.push_back(w);
            exists.insert(w);
        }

        return ans;
    }
};
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