"""
A valid encoding of an array of words is any reference string s and array of indices indices such that:

words.length == indices.length
The reference string s ends with the '#' character.
For each index indices[i], the substring of s starting from indices[i] and up to (but not including) the next '#' character is equal to words[i].
Given an array of words, return the length of the shortest reference string s possible of any valid encoding of words.

Example 1:
Input: words = ["time", "me", "bell"]
Output: 10
Explanation: A valid encoding would be s = "time#bell#" and indices = [0, 2, 5].
words[0] = "time", the substring of s starting from indices[0] = 0 to the next '#' is underlined in "time#bell#"
words[1] = "me", the substring of s starting from indices[1] = 2 to the next '#' is underlined in "time#bell#"
words[2] = "bell", the substring of s starting from indices[2] = 5 to the next '#' is underlined in "time#bell#"

Example 2:
Input: words = ["t"]
Output: 2
Explanation: A valid encoding would be s = "t#" and indices = [0].

Constraints:
1 <= words.length <= 2000
1 <= words[i].length <= 7
words[i] consists of only lowercase letters.
"""
import collections
from typing import List

class TrieNode:
    def __init__(self):
        self.children = collections.defaultdict(TrieNode)

class ShortEncodingOfWords:
    def minimumLengthEncoding(self, words: List[str]) -> int:
        leaves = []
        root = TrieNode()
        for word in set(words):
            cur = root
            for c in word[::-1]:
                cur = cur.children[c]
            leaves.append((cur, len(word) + 1))
        return sum(depth for node, depth in leaves if len(node.children) == 0)