<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:
    class Tire {
        struct TireNode {
            bool has = false;
            unique_ptr<TireNode> child[26] = {};
        };

        unique_ptr<TireNode> root;

      public:
        Tire() : root(std::make_unique<TireNode>()) {}

        unordered_map<string, bool> memo;

        bool IsCat(string_view word) {
            if (word.empty()) {
                return true;
            }

            if (memo.contains(string(word))) {
                return memo[string(word)];
            }

            auto* curr = root.get();
            bool ans = false;
            for (int i = 0; i < word.size(); ++i) {
                if (ans) {
                    break;
                }

                auto c = word[i];

                if (auto& next = curr->child[c - 'a']; next == nullptr) {
                    return ans;
                }

                curr = curr->child[c - 'a'].get();

                if (curr->has) {
                    ans |= IsCat(word.substr(i + 1));
                }
            }

            return memo[std::string(word)] = ans;
        }

        void InsertWord(string_view word) {
            if (word.empty()) {
                return;
            }

            auto* curr = root.get();

            for (int i = 0; i < word.size(); ++i) {
                auto c = word[i];

                if (auto& next = curr->child[c - 'a']; next == nullptr) {
                    next = std::make_unique<TireNode>();
                }

                curr = curr->child[c - 'a'].get();
            }

            curr->has = true;
        }
    };

    vector<string> findAllConcatenatedWordsInADict(vector<string>& words) {
        ranges::sort(words, [](auto& a, auto& b) { return a.size() < b.size(); });

        vector<string> ans;
        Tire t;
        for (auto& w : words) {
            if (t.IsCat(w)) {
                ans.push_back(w);
            } else {
                t.InsertWord(w);
            }
        }
        return ans;
    }
};

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