<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>

struct TrieNode {
    bool isWord = false;
    TrieNode* children[26];
    unordered_map<string, bool> cache;
    TrieNode() {
        for (int i = 0; i < 26; i++) {
            children[i] = nullptr;
        }
    }
    void insert(string& s) {
        TrieNode* head = this;
        for (auto it = s.begin(); it < s.end(); it++) {
            char c = *it;
            if (head->children[c - 'a'] == nullptr) {
                head->children[c - 'a'] = new TrieNode();
            }
            head = head->children[c - 'a'];
        }
        head->isWord = true;
    }

    bool solve(string& s, bool oneOrMore) {
        TrieNode* head = this;
        auto found = cache.find(s);
        if (oneOrMore && found != cache.end()) {
            return found->second;
        }
        for (auto it = s.begin(); it < s.end(); it++) {
            char c = *it;
            if (head->children[c - 'a'] == nullptr) {
                if (oneOrMore) {
                    cache.insert({s, false});
                }
                return false;
            } else if (head->children[c - 'a']->isWord) {
                string sub(it + 1, s.end());
                if (solve(sub, true)) {
                    if (oneOrMore) {
                        cache.insert({s, true});
                    }
                    return true;
                }
            }
            head = head->children[c - 'a'];
        }
        if (oneOrMore) {
            cache.insert({s, head->isWord});
        }
        return oneOrMore && head->isWord;
    }
};

class Solution {
public:
    vector<string> findAllConcatenatedWordsInADict(vector<string>& words) {
        TrieNode t;
        for (auto it : words) {
            t.insert(it);
        }
        vector<string> ret;
        for (auto it : words) {
            if (t.solve(it, false)) {
                ret.push_back(it);
            }
        }
        return ret;
    }
};
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