<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 Node:
    def __init__(self):
        self.children = [None] * 26
        self.is_word = False
        self.word = None


class Trie:
    def __init__(self):
        self.root = Node()
    
    def insert(self, word):
        node = self.root
        n = len(word)
        for i in range(n - 1, -1, -1):
            c = word[i]
            idx = ord(c) - ord("a")
            if not node.children[idx]:
                node.children[idx] = Node()
            node = node.children[idx]
        node.is_word = True
        node.word = word

class Solution:
    def minimumLengthEncoding(self, words: List[str]) -> int:
        trie = Trie()
        for word in words:
            trie.insert(word)
        results = []
        self.dfs(trie.root, results)
        n = 0
        for word in results:
            n += len(word)
        n += len(results)
        return n
        
    def dfs(self, node, results):
        if not node:
            return
        if node.is_word and self.has_no_children(node):
            results.append(node.word)
            return
        
        for i in range(26):
            if node.children[i] is None:
                continue
            self.dfs(node.children[i], results)
        
    
    def has_no_children(self, node):
        for i in range(26):
            if node.children[i] is not None:
                return False
        return True
        
19900