<p>A <strong>valid encoding</strong> of an array of <code>words</code> is any reference string <code>s</code> and array of indices <code>indices</code> such that:</p>

<ul>
	<li><code>words.length == indices.length</code></li>
	<li>The reference string <code>s</code> ends with the <code>&#39;#&#39;</code> character.</li>
	<li>For each index <code>indices[i]</code>, the <strong>substring</strong> of <code>s</code> starting from <code>indices[i]</code> and up to (but not including) the next <code>&#39;#&#39;</code> character is equal to <code>words[i]</code>.</li>
</ul>

<p>Given an array of <code>words</code>, return <em>the <strong>length of the shortest reference string</strong> </em><code>s</code><em> possible of any <strong>valid encoding</strong> of </em><code>words</code><em>.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> words = [&quot;time&quot;, &quot;me&quot;, &quot;bell&quot;]
<strong>Output:</strong> 10
<strong>Explanation:</strong> A valid encoding would be s = <code>&quot;time#bell#&quot; and indices = [0, 2, 5</code>].
words[0] = &quot;time&quot;, the substring of s starting from indices[0] = 0 to the next &#39;#&#39; is underlined in &quot;<u>time</u>#bell#&quot;
words[1] = &quot;me&quot;, the substring of s starting from indices[1] = 2 to the next &#39;#&#39; is underlined in &quot;ti<u>me</u>#bell#&quot;
words[2] = &quot;bell&quot;, the substring of s starting from indices[2] = 5 to the next &#39;#&#39; is underlined in &quot;time#<u>bell</u>#&quot;
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> words = [&quot;t&quot;]
<strong>Output:</strong> 2
<strong>Explanation:</strong> A valid encoding would be s = &quot;t#&quot; and indices = [0].
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= words.length &lt;= 2000</code></li>
	<li><code>1 &lt;= words[i].length &lt;= 7</code></li>
	<li><code>words[i]</code> consists of only lowercase letters.</li>
</ul>

class Solution {
public:
    class Trie {
    public:
        unordered_map<char, std::shared_ptr<Trie>> children = unordered_map<char, std::shared_ptr<Trie>>(26);
        string word;
    };

    int minimumLengthEncoding(vector<string>& words) {
        for (string& word : words) {
            reverse(word.begin(), word.end());
            insert(word);
        }
        return collect(root);
    }

private:
    std::shared_ptr<Trie> root = std::make_shared<Trie>();

    void insert(const string& word) {
        auto current = root;

        for (const char c : word) {
            if (!current->children.contains(c)) {
                current->children[c] = std::make_shared<Trie>();
            }
            current = current->children[c];
        }
        current->word = word;
    }

    int collect(std::shared_ptr<Trie> current) {
        int count = 0;
        if (current == nullptr) {
            return 0;
        }

        if (current->children.size() == 0) {
            //std::cout << current->word << std::endl;
            return current->word.size() + 1;
        } 

        for (auto& [key, child] : current->children) {
            count += collect(child);
        }
        return count;
    }
};
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