"""
You are given an array of strings products and a string searchWord.

Design a system that suggests at most three product names from products after each character of searchWord is typed. Suggested products should have common prefix with searchWord. If there are more than three products with a common prefix return the three lexicographically minimums products.

Return a list of lists of the suggested products after each character of searchWord is typed.

Example 1:
Input: products = ["mobile","mouse","moneypot","monitor","mousepad"], searchWord = "mouse"
Output: [
["mobile","moneypot","monitor"],
["mobile","moneypot","monitor"],
["mouse","mousepad"],
["mouse","mousepad"],
["mouse","mousepad"]
]
Explanation: products sorted lexicographically = ["mobile","moneypot","monitor","mouse","mousepad"]
After typing m and mo all products match and we show user ["mobile","moneypot","monitor"]
After typing mou, mous and mouse the system suggests ["mouse","mousepad"]

Example 2:
Input: products = ["havana"], searchWord = "havana"
Output: [["havana"],["havana"],["havana"],["havana"],["havana"],["havana"]]

Example 3:
Input: products = ["bags","baggage","banner","box","cloths"], searchWord = "bags"
Output: [["baggage","bags","banner"],["baggage","bags","banner"],["baggage","bags"],["bags"]]

Constraints:
1 <= products.length <= 1000
1 <= products[i].length <= 3000
1 <= sum(products[i].length) <= 2 * 104
All the strings of products are unique.
products[i] consists of lowercase English letters.
1 <= searchWord.length <= 1000
searchWord consists of lowercase English letters.

hint:
1 Brute force is a good choice because length of the string is ≤ 1000.
2 Binary search the answer.
3 Use Trie data structure to store the best three matching. Traverse the Trie.
"""
import collections
from typing import List


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


class SearchSuggestionsSystem:
    def suggestedProducts(self, products: List[str], searchWord: str) -> List[List[str]]:
        self.root = TrieNode()
        for p in products:
            self.insert(p)
        return self.search(searchWord)

    def insert(self, word):
        cur = self.root
        for c in word:
            cur = cur.children[c]
            cur.suggestions.append(word)
            cur.suggestions.sort()
            if len(cur.suggestions) > 3:
                cur.suggestions.pop()

    def search(self, word):
        res = []
        cur = self.root
        for c in word:
            cur = cur.children[c]
            if cur.suggestions:
                res.append(cur.suggestions.copy())
            else:
                res.append([])
        return res
