<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>

#include <vector>
#include <unordered_map>
#include <string>

using namespace std;

class Solution {
public:
    bool isConcatenated(string str, unordered_map<string, bool>& wordMap, unordered_map<string, bool>& memo) {
        if (memo.count(str)) return memo[str];
        if (str.empty()) return false;

        bool result = false;
        for (int i = 1; i < str.length(); ++i) {
            string prefix = str.substr(0, i);
            string suffix = str.substr(i);

            if (wordMap.count(prefix)) {
                if (wordMap.count(suffix) || isConcatenated(suffix, wordMap, memo)) {
                    result = true;
                    break;
                }
            }
        }

        memo[str] = result;
        return result;
    }

    vector<string> findAllConcatenatedWordsInADict(vector<string>& words) {
        unordered_map<string, bool> wordMap;
        for (const string& word : words) {
            wordMap[word] = true;
        }

        vector<string> result;
        unordered_map<string, bool> memo;

        for (const string& word : words) {
            wordMap.erase(word);
            if (isConcatenated(word, wordMap, memo)) {
                result.push_back(word);
            }
            wordMap[word] = true;
        }

        return result;
    }
};

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